diff --git a/prism-examples/pta/csma/abst/csma1-digital.nm b/prism-examples/pta/csma/abst/csma1-digital.nm deleted file mode 100644 index ae903b38..00000000 --- a/prism-examples/pta/csma/abst/csma1-digital.nm +++ /dev/null @@ -1,100 +0,0 @@ -// CSMA/CD protocol - probabilistic version of kronos model adapted to model a single station -// gxn/dxp 04/12/01 - -nondeterministic - -// note made changes since cannot have strict inequalities -// in digital clocks approach and suppose a station only sends one message - -//---------------------------------------------------------------------------------------------------------------------------- -// actual parameters -const int K=1; // exponential backoff limit -const int slot=2*sigma; // length of slot -const int M=floor(pow(2, K)); // max number of slots to wait -const int sigma=26; -const int lambda=808; - -//---------------------------------------------------------------------------------------------------------------------------- -// the bus -module bus - - b : [0..2]; - // b=0 - idle - // b=1 - active - // b=2 - collision - - // clock of bus - y : [0..sigma+1]; - - // station starts sending - [send1] (b=0) -> (b'=1) & (y'=0); // no message being sent - [send2] (b=0) -> (b'=1) & (y'=0); // no message being sent - [send1] (b=1) & (y<=sigma) -> (b'=2) & (y'=0); // message being sent (move to collision) - [send2] (b=1) & (y<=sigma) -> (b'=2) & (y'=0); // message being sent (move to collision) - - // message being sent - [busy1] (b=1) & (y>=sigma) -> (b'=1); - [busy2] (b=1) & (y>=sigma) -> (b'=1); - - // station finishes - [end1] (b=1) -> (b'=0) & (y'=0); - [end2] (b=1) -> (b'=0) & (y'=0); - - // collision detected - [cd] (b=2) & (y<=sigma) -> (b'=0) & (y'=0); - - // time transitions - [time] (b=0) -> (y'=min(y+1,sigma+1)); // value of y does not matter in state 0 - [time] (b=1) -> (y'=min(y+1,sigma+1)); // no invariant in state 1 - [time] (b=2) & (y (y'=min(y+1,sigma+1)); // invariant in state 2 - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// model of first sender -module station1 - - // LOCAL STATE - s1 : [0..4]; - // s1=0 - initial state - // s1=1 - transmit - // s1=2 - collision (set backoff) - // s1=3 - wait (bus busy) - // s1=4 -done (since sending only one message) - // LOCAL CLOCK - x1 : [0..max(lambda,M*slot)+1]; - // COLLISION COUNTER - cd1 : [0..K]; - - // start sending - [send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending - [busy1] (s1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // detects channel is busy so go into backoff - - // transmitting - [time] (s1=1) & (x1 (x1'=min(x1+1,lambda)); // let time pass - [end1] (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished - [cd] (s1=1) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // collision detected - - // set backoff (no time can pass in this state) - // first retransmission - [] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (x1'=0*slot) - + 1/2 : (s1'=3) & (x1'=1*slot); - - // wait until backoff counter reaches 0 then send again - [time] (s1=3) & (cd1=1) & (x1<2*slot) -> (x1'=x1+1); // let time pass (in slot) - - // finished backoff - [send1] (s1=3) & cd1=1 & (x1=2*slot) -> (s1'=1) & (x1'=0); // channel free - [busy1] (s1=3) & cd1=1 & (x1=2*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // channel busy - - // finished - [done] (s1=4) -> true; - [time] (s1=4) -> (x1'=min(x1+1,max(lambda,M*slot)+1)); - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- - -// construct further stations through renaming -module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule - diff --git a/prism-examples/pta/csma/abst/csma1-test.nm b/prism-examples/pta/csma/abst/csma1-test.nm deleted file mode 100644 index daf6cc5d..00000000 --- a/prism-examples/pta/csma/abst/csma1-test.nm +++ /dev/null @@ -1,106 +0,0 @@ -// CSMA/CD protocol - probabilistic version of kronos model adapted to model a single station -// gxn/dxp 04/12/01 - -pta - -// note made changes since cannot have strict inequalities -// in digital clocks approach and suppose a station only sends one message - -//---------------------------------------------------------------------------------------------------------------------------- -// actual parameters -const int K=1; // exponential backoff limit -const int slot=2*sigma; // length of slot -const int sigma=26; -const int lambda=808; - -//---------------------------------------------------------------------------------------------------------------------------- -// the bus -module bus - - b : [0..2]; - // b=0 - idle - // b=1 - active - // b=2 - collision - - // clock of bus - y : clock; - - invariant - (b=0 => true) & - (b=1 => true) & - (b=2 => y<=sigma) - endinvariant - - // station starts sending - [send1] (b=0) -> (b'=1) & (y'=0); // no message being sent - [send2] (b=0) -> (b'=1) & (y'=0); // no message being sent - [send1] (b=1) & (y<=sigma) -> (b'=2) & (y'=0); // message being sent (move to collision) - [send2] (b=1) & (y<=sigma) -> (b'=2) & (y'=0); // message being sent (move to collision) - - // message being sent - [busy1] (b=1) & (y>=sigma) -> (b'=1); - [busy2] (b=1) & (y>=sigma) -> (b'=1); - - // station finishes - [end1] (b=1) -> (b'=0) & (y'=0); - [end2] (b=1) -> (b'=0) & (y'=0); - - // collision detected - [cd] (b=2) & (y<=sigma) -> (b'=0) & (y'=0); - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// model of first sender -module station1 - - // LOCAL STATE - s1 : [0..4]; - // s1=0 - initial state - // s1=1 - transmit - // s1=2 - collision (set backoff) - // s1=3 - wait (bus busy) - // s1=4 -done (since sending only one message) - - // LOCAL CLOCK - x1 : clock; - - invariant - (s1=0 => x1=0) & - (s1=1 => x1<=lambda) & - (s1=2 => x1<=0) & - (s1=3 => x1<=104) & - (s1=4 => true) - endinvariant - - // start sending - [send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending - [busy1] (s1=0) -> (s1'=2) & (x1'=0); // detects channel is busy so go into backoff - - // transmitting - [end1] (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished - [cd] (s1=1) -> (s1'=2) & (x1'=0); // collision detected - - // set backoff (no time can pass in this state) - // first retransmission - [] s1=2 -> 1/2 : (s1'=3) & (x1'=0) - + 1/2 : (s1'=3) & (x1'=52); - - // finished backoff - [send1] s1=3 & x1>=104 -> (s1'=1) & (x1'=0); // channel free - [busy1] s1=3 & x1>=104 -> (s1'=2) & (x1'=0); // channel busy - - // once finished nothing matters - [done] s1=4 -> true; - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- - -// construct further stations through renaming -module station2=station1[s1=s2,x1=x2,send1=send2,busy1=busy2,end1=end2] endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// LABELS - -label "done" = s1=4 & s2=4; diff --git a/prism-examples/pta/csma/abst/csma2-digital.nm b/prism-examples/pta/csma/abst/csma2-digital.nm deleted file mode 100644 index b3ed53b9..00000000 --- a/prism-examples/pta/csma/abst/csma2-digital.nm +++ /dev/null @@ -1,109 +0,0 @@ -// CSMA/CD protocol - probabilistic version of kronos model adapted to model a single station -// gxn/dxp 04/12/01 - -nondeterministic - -// note made changes since cannot have strict inequalities -// in digital clocks approach and suppose a station only sends one message - -//---------------------------------------------------------------------------------------------------------------------------- -// actual parameters -const int K=2; // exponential backoff limit -const int slot=2*sigma; // length of slot -const int M=floor(pow(2, K)); // max number of slots to wait -const int sigma=26; -const int lambda=808; - -//---------------------------------------------------------------------------------------------------------------------------- -// the bus -module bus - - b : [0..2]; - // b=0 - idle - // b=1 - active - // b=2 - collision - - // clock of bus - y : [0..sigma+1]; - - // station starts sending - [send1] (b=0) -> (b'=1) & (y'=0); // no message being sent - [send2] (b=0) -> (b'=1) & (y'=0); // no message being sent - [send1] (b=1) & (y<=sigma) -> (b'=2) & (y'=0); // message being sent (move to collision) - [send2] (b=1) & (y<=sigma) -> (b'=2) & (y'=0); // message being sent (move to collision) - - // message being sent - [busy1] (b=1) & (y>=sigma) -> (b'=1); - [busy2] (b=1) & (y>=sigma) -> (b'=1); - - // station finishes - [end1] (b=1) -> (b'=0) & (y'=0); - [end2] (b=1) -> (b'=0) & (y'=0); - - // collision detected - [cd] (b=2) & (y<=sigma) -> (b'=0) & (y'=0); - - // time transitions - [time] (b=0) -> (y'=min(y+1,sigma+1)); // value of y does not matter in state 0 - [time] (b=1) -> (y'=min(y+1,sigma+1)); // no invariant in state 1 - [time] (b=2) & (y (y'=min(y+1,sigma+1)); // invariant in state 2 - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// model of first sender -module station1 - - // LOCAL STATE - s1 : [0..4]; - // s1=0 - initial state - // s1=1 - transmit - // s1=2 - collision (set backoff) - // s1=3 - wait (bus busy) - // s1=4 -done (since sending only one message) - // LOCAL CLOCK - x1 : [0..max(lambda,M*slot)+1]; - // COLLISION COUNTER - cd1 : [0..K]; - - // start sending - [send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending - [busy1] (s1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // detects channel is busy so go into backoff - - // transmitting - [time] (s1=1) & (x1 (x1'=min(x1+1,lambda)); // let time pass - [end1] (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished - [cd] (s1=1) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // collision detected - - // set backoff (no time can pass in this state) - // first retransmission - [] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (x1'=0*slot) - + 1/2 : (s1'=3) & (x1'=1*slot); - // second retransmission - [] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (x1'=0*slot) - + 1/4 : (s1'=3) & (x1'=1*slot) - + 1/4 : (s1'=3) & (x1'=2*slot) - + 1/4 : (s1'=3) & (x1'=3*slot); - - // wait until backoff counter reaches 0 then send again - [time] (s1=3) & (cd1=1) & (x1<2*slot) -> (x1'=x1+1); // let time pass (in slot) - [time] (s1=3) & (cd1=2) & (x1<4*slot) -> (x1'=x1+1); // let time pass (in slot) - - // finished backoff - [send1] (s1=3) & cd1=1 & (x1=2*slot) -> (s1'=1) & (x1'=0); // channel free - [busy1] (s1=3) & cd1=1 & (x1=2*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // channel busy - - [send1] (s1=3) & cd1=2 & (x1=4*slot) -> (s1'=1) & (x1'=0); // channel free - [busy1] (s1=3) & cd1=2 & (x1=4*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // channel busy - - // finished - [done] (s1=4) -> true; - [time] (s1=4) -> (x1'=min(x1+1,max(lambda,M*slot)+1)); - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- - -// construct further stations through renaming -module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule - diff --git a/prism-examples/pta/csma/abst/csma3-digital.nm b/prism-examples/pta/csma/abst/csma3-digital.nm deleted file mode 100644 index 239c9e42..00000000 --- a/prism-examples/pta/csma/abst/csma3-digital.nm +++ /dev/null @@ -1,122 +0,0 @@ -// CSMA/CD protocol - probabilistic version of kronos model adapted to model a single station -// gxn/dxp 04/12/01 - -nondeterministic - -// note made changes since cannot have strict inequalities -// in digital clocks approach and suppose a station only sends one message - -//---------------------------------------------------------------------------------------------------------------------------- -// actual parameters -const int K=3; // exponential backoff limit -const int slot=2*sigma; // length of slot -const int M=floor(pow(2, K)); // max number of slots to wait -const int sigma=26; -const int lambda=808; - -//---------------------------------------------------------------------------------------------------------------------------- -// the bus -module bus - - b : [0..2]; - // b=0 - idle - // b=1 - active - // b=2 - collision - - // clock of bus - y : [0..sigma+1]; - - // station starts sending - [send1] (b=0) -> (b'=1) & (y'=0); // no message being sent - [send2] (b=0) -> (b'=1) & (y'=0); // no message being sent - [send1] (b=1) & (y (b'=2) & (y'=0); // message being sent (move to collision) - [send2] (b=1) & (y (b'=2) & (y'=0); // message being sent (move to collision) - - // message being sent - [busy1] (b=1) & (y>=sigma) -> (b'=1); - [busy2] (b=1) & (y>=sigma) -> (b'=1); - - // station finishes - [end1] (b=1) -> (b'=0) & (y'=0); - [end2] (b=1) -> (b'=0) & (y'=0); - - // collision detected - [cd] (b=2) & (y<=sigma) -> (b'=0) & (y'=0); - - // time transitions - [time] (b=0) -> (y'=min(y+1,sigma+1)); // value of y does not matter in state 0 - [time] (b=1) -> (y'=min(y+1,sigma+1)); // no invariant in state 1 - [time] (b=2) & (y (y'=min(y+1,sigma+1)); // invariant in state 2 - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// model of first sender -module station1 - - // LOCAL STATE - s1 : [0..4]; - // s1=0 - initial state - // s1=1 - transmit - // s1=2 - collision (set backoff) - // s1=3 - wait (bus busy) - // s1=4 -done (since sending only one message) - // LOCAL CLOCK - x1 : [0..max(lambda,M*slot)+1]; - // COLLISION COUNTER - cd1 : [0..K]; - - // start sending - [send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending - [busy1] (s1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // detects channel is busy so go into backoff - - // transmitting - [time] (s1=1) & (x1 (x1'=min(x1+1,lambda)); // let time pass - [end1] (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished - [cd] (s1=1) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // collision detected - - // set backoff (no time can pass in this state) - // first retransmission - [] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (x1'=0*slot) - + 1/2 : (s1'=3) & (x1'=1*slot); - // second retransmission - [] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (x1'=0*slot) - + 1/4 : (s1'=3) & (x1'=1*slot) - + 1/4 : (s1'=3) & (x1'=2*slot) - + 1/4 : (s1'=3) & (x1'=3*slot); - // thrid retransmission - [] s1=2 & cd1=3 -> 1/8 : (s1'=3) & (x1'=0*slot) - + 1/8 : (s1'=3) & (x1'=1*slot) - + 1/8 : (s1'=3) & (x1'=2*slot) - + 1/8 : (s1'=3) & (x1'=3*slot) - + 1/8 : (s1'=3) & (x1'=4*slot) - + 1/8 : (s1'=3) & (x1'=5*slot) - + 1/8 : (s1'=3) & (x1'=6*slot) - + 1/8 : (s1'=3) & (x1'=7*slot); - - // wait until backoff counter reaches 0 then send again - [time] (s1=3) & (cd1=1) & (x1<2*slot) -> (x1'=x1+1); // let time pass (in slot) - [time] (s1=3) & (cd1=2) & (x1<4*slot) -> (x1'=x1+1); // let time pass (in slot) - [time] (s1=3) & (cd1=3) & (x1<8*slot) -> (x1'=x1+1); // let time pass (in slot) - - // finished backoff - [send1] (s1=3) & cd1=1 & (x1=2*slot) -> (s1'=1) & (x1'=0); // channel free - [busy1] (s1=3) & cd1=1 & (x1=2*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // channel busy - - [send1] (s1=3) & cd1=2 & (x1=4*slot) -> (s1'=1) & (x1'=0); // channel free - [busy1] (s1=3) & cd1=2 & (x1=4*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // channel busy - - [send1] (s1=3) & cd1=3 & (x1=8*slot) -> (s1'=1) & (x1'=0); // channel free - [busy1] (s1=3) & cd1=3 & (x1=8*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // channel busy - - // finished - [done] (s1=4) -> true; - [time] (s1=4) -> (x1'=min(x1+1,max(lambda,M*slot)+1)); - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- - -// construct further stations through renaming -module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule - diff --git a/prism-examples/pta/csma/abst/csma4-digital.nm b/prism-examples/pta/csma/abst/csma4-digital.nm deleted file mode 100644 index 76d67489..00000000 --- a/prism-examples/pta/csma/abst/csma4-digital.nm +++ /dev/null @@ -1,139 +0,0 @@ -// CSMA/CD protocol - probabilistic version of kronos model adapted to model a single station -// gxn/dxp 04/12/01 - -nondeterministic - -// note made changes since cannot have strict inequalities -// in digital clocks approach and suppose a station only sends one message - -// actual parameters -const int K=4; // exponential backoff limit -const int slot=2*sigma; // length of slot -const int M=floor(pow(2, K)); // max number of slots to wait -const int sigma=26; -const int lambda=808; - -//---------------------------------------------------------------------------------------------------------------------------- -// the bus -module bus - - b : [0..2]; - // b=0 - idle - // b=1 - active - // b=2 - collision - - // clock of bus - y : [0..sigma+1]; - - // station starts sending - [send1] (b=0) -> (b'=1) & (y'=0); // no message being sent - [send2] (b=0) -> (b'=1) & (y'=0); // no message being sent - [send1] (b=1) & (y (b'=2) & (y'=0); // message being sent (move to collision) - [send2] (b=1) & (y (b'=2) & (y'=0); // message being sent (move to collision) - - // message being sent - [busy1] (b=1) & (y>=sigma) -> (b'=1); - [busy2] (b=1) & (y>=sigma) -> (b'=1); - - // station finishes - [end1] (b=1) -> (b'=0) & (y'=0); - [end2] (b=1) -> (b'=0) & (y'=0); - - // collision detected - [cd] (b=2) & (y<=sigma) -> (b'=0) & (y'=0); - - // time transitions - [time] (b=0) -> (y'=min(y+1,sigma+1)); // value of y does not matter in state 0 - [time] (b=1) -> (y'=min(y+1,sigma+1)); // no invariant in state 1 - [time] (b=2) & (y (y'=min(y+1,sigma+1)); // invariant in state 2 - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// model of first sender -module station1 - - // LOCAL STATE - s1 : [0..4]; - // s1=0 - initial state - // s1=1 - transmit - // s1=2 - collision (set backoff) - // s1=3 - wait (bus busy) - // s1=4 -done (since sending only one message) - // LOCAL CLOCK - x1 : [0..max(lambda,M*slot)+1]; - // COLLISION COUNTER - cd1 : [0..K]; - - // start sending - [send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending - [busy1] (s1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // detects channel is busy so go into backoff - - // transmitting - [time] (s1=1) & (x1 (x1'=min(x1+1,lambda)); // let time pass - [end1] (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished - [cd] (s1=1) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // collision detected - - // set backoff (no time can pass in this state) - // first retransmission - [] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (x1'=0*slot) - + 1/2 : (s1'=3) & (x1'=1*slot); - // second retransmission - [] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (x1'=0*slot) - + 1/4 : (s1'=3) & (x1'=1*slot) - + 1/4 : (s1'=3) & (x1'=2*slot) - + 1/4 : (s1'=3) & (x1'=3*slot); - // thrid retransmission - [] s1=2 & cd1=3 -> 1/8 : (s1'=3) & (x1'=0*slot) - + 1/8 : (s1'=3) & (x1'=1*slot) - + 1/8 : (s1'=3) & (x1'=2*slot) - + 1/8 : (s1'=3) & (x1'=3*slot) - + 1/8 : (s1'=3) & (x1'=4*slot) - + 1/8 : (s1'=3) & (x1'=5*slot) - + 1/8 : (s1'=3) & (x1'=6*slot) - + 1/8 : (s1'=3) & (x1'=7*slot); - // fourth retransmission - [] s1=2 & cd1=4 -> 1/16 : (s1'=3) & (x1'=0*slot) - + 1/16 : (s1'=3) & (x1'=1*slot) - + 1/16 : (s1'=3) & (x1'=2*slot) - + 1/16 : (s1'=3) & (x1'=3*slot) - + 1/16 : (s1'=3) & (x1'=4*slot) - + 1/16 : (s1'=3) & (x1'=5*slot) - + 1/16 : (s1'=3) & (x1'=6*slot) - + 1/16 : (s1'=3) & (x1'=7*slot) - + 1/16 : (s1'=3) & (x1'=8*slot) - + 1/16 : (s1'=3) & (x1'=9*slot) - + 1/16 : (s1'=3) & (x1'=10*slot) - + 1/16 : (s1'=3) & (x1'=11*slot) - + 1/16 : (s1'=3) & (x1'=12*slot) - + 1/16 : (s1'=3) & (x1'=13*slot) - + 1/16 : (s1'=3) & (x1'=14*slot) - + 1/16 : (s1'=3) & (x1'=15*slot); - - // wait until backoff counter reaches 0 then send again - [time] (s1=3) & (cd1=1) & (x1<2*slot) -> (x1'=x1+1); // let time pass (in slot) - [time] (s1=3) & (cd1=2) & (x1<4*slot) -> (x1'=x1+1); // let time pass (in slot) - [time] (s1=3) & (cd1=3) & (x1<8*slot) -> (x1'=x1+1); // let time pass (in slot) - [time] (s1=3) & (cd1=4) & (x1<16*slot) -> (x1'=x1+1); // let time pass (in slot) - - // finished backoff - [send1] (s1=3) & cd1=1 & (x1=2*slot) -> (s1'=1) & (x1'=0); // channel free - [busy1] (s1=3) & cd1=1 & (x1=2*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // channel busy - [send1] (s1=3) & cd1=2 & (x1=4*slot) -> (s1'=1) & (x1'=0); // channel free - [busy1] (s1=3) & cd1=2 & (x1=4*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // channel busy - [send1] (s1=3) & cd1=3 & (x1=8*slot) -> (s1'=1) & (x1'=0); // channel free - [busy1] (s1=3) & cd1=3 & (x1=8*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // channel busy - [send1] (s1=3) & cd1=4 & (x1=16*slot) -> (s1'=1) & (x1'=0); // channel free - [busy1] (s1=3) & cd1=4 & (x1=16*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // channel busy - - // finished - [done] (s1=4) -> true; - [time] (s1=4) -> (x1'=min(x1+1,max(lambda,M*slot)+1)); - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- - -// construct further stations through renaming -module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule - diff --git a/prism-examples/pta/csma/full/auto b/prism-examples/pta/csma/full/auto index 6940d1b2..61845146 100755 --- a/prism-examples/pta/csma/full/auto +++ b/prism-examples/pta/csma/full/auto @@ -5,7 +5,7 @@ prism csma.nm collisions.pctl -const bmax=2,K=8 -aroptions refine=all,nopre,opt prism csma.nm collisions.pctl -const bmax=4,K=4 -aroptions refine=all,nopre,opt prism csma.nm collisions.pctl -const bmax=4,K=8 -aroptions refine=all,nopre,opt -prism csma.nm time.pctl -const bmax=1,K=0 -aroptions refine=all,nopre,opt -prism csma.nm time.pctl -const bmax=2,K=0 -aroptions refine=all,nopre,opt -prism csma.nm time.pctl -const bmax=3,K=0 -aroptions refine=all,nopre,opt -prism csma.nm time.pctl -const bmax=4,K=0 -aroptions refine=all,nopre,opt \ No newline at end of file +#prism csma.nm time.pctl -const bmax=1,K=0 -aroptions refine=all,nopre,opt +#prism csma.nm time.pctl -const bmax=2,K=0 -aroptions refine=all,nopre,opt +#prism csma.nm time.pctl -const bmax=3,K=0 -aroptions refine=all,nopre,opt +#prism csma.nm time.pctl -const bmax=4,K=0 -aroptions refine=all,nopre,opt \ No newline at end of file diff --git a/prism-examples/pta/csma/full/csma-digital.nm b/prism-examples/pta/csma/full/csma-digital.nm deleted file mode 100644 index ff5b7a7b..00000000 --- a/prism-examples/pta/csma/full/csma-digital.nm +++ /dev/null @@ -1,2203 +0,0 @@ -// CSMA/CD protocol - two stations (PTA model using digital clocks) -// gxn/mxd 31/05/05 - -// based on kronos (non-probabilistic) TA model and that which appears in: -// M. Duflot, L. Fribourg, T. Hérault, R. Lassaigne, F. Magniette, S. Messika, S. Peyronnet and C. Picaronny -// Probabilistic model checking of the CSMA/CD protocol using PRISM and APMC -// In Proc. AVoCS'04, 2004 - -// uses explicit probabilistic choices for backoff 0..1023 - -nondeterministic - -// PARAMETERS - -const int K; // collision counter limit - -// actual parameters -const int bmax; // exponential backoff limit (vary to get graphs) -const int slot=2*sigma; // length of slot -const int M=pow(2,bmax)-1; // max number of slots to wait - -// simplified parameters scaled (by 12) -const int sigma=26; // time for messages to propagate along the bus -const int delay=sigma; -const int lambda=808; // time to send a message - -//---------------------------------------------------------------------------------------------------------------------------- -// collision counter -module collisions - - c : [0..K]; - - [csend1] c=0 -> c'=min(K,c+1)); - [csend2] c=0 -> c'=min(K,c+1)); - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// the bus -module bus - - b : [0..4]; - // b=0 - idle - // b=1 - active - // b=2 - collision - // b=3 - collision1 - // b=4 - collision2 - - y1 : [0..sigma+1]; // clock of bus - y2 : [0..sigma+1]; // clock of bus - - // stations starts sending - [send1] b=0 -> (b'=1) & (y1'=0); // no message being sent - [send2] b=0 -> (b'=1) & (y2'=0); // no message being sent - - // collision occurs - [send1] b=1 & y2<=delay -> (b'=2) & (y1'=y2) & (y2'=0); // message being sent (move to collision) - [send2] b=1 & y1<=delay -> (b'=2) & (y2'=y1) & (y1'=0); // message being sent (move to collision) - - // message being sent - [busy1] b=1 & y2>delay -> (b'=1); - [busy2] b=1 & y1>delay -> (b'=1); - - // station finishes - [end1] b=1 -> (b'=0) & (y1'=0); - [end2] b=1 -> (b'=0) & (y2'=0); - - // collision detected - [cd1] b=2 & y1=delay -> (b'=4); // station one detects collision before station two - [cd2] b=2 & y2=delay -> (b'=3); // station two detects collision before station one - - [cd1] b=3 & y1=delay -> (b'=0) & (y1'=0) & (y2'=0); // station one detects collision after station two - [cd2] b=4 & y2=delay -> (b'=0) & (y1'=0) & (y2'=0); // station two detects collision after station one - - // time transitions - [time] b=0 -> true; // value of clocks does not matter in state 0 - [time] b=1 & s1=1 -> (y1'=min(y1+1,sigma+1)); // station 1 sending - [time] b=1 & s2=1 -> (y2'=min(y2+1,sigma+1)); // station 2 sending - [time] b=2 & max(y1,y2) (y1'=min(y1+1,delay)) & (y2'=min(y2+1,delay)); // both sending - [time] b=3 & y1 (y1'=min(y1+1,delay)); // station 1 sending and station 2 stopped - [time] b=4 & y2 (y2'=min(y2+1,delay)); // station 2 sending and station 1 stopped - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// STATION 1 -module station1 - - // LOCAL STATE - s1 : [0..4]; - // s1=0 - initial state - // s1=1 - transmit - // s1=2 - collision (set backoff) - // s1=3 - wait (bus busy) - // s1=4 - done (since sending only one message) - - x1 : [0..lambda]; // local clock - bc1 : [0..M]; // backoff counter (number of slots to wait) - cd1 : [0..bmax]; // collision counter - - // start sending (make sure there is a collision, i.e. start before x1 equals delay) - [time] s1=0 & x1<=delay-1 -> (x1'=x1+1); - [send1] s1=0 -> (s1'=1) & (x1'=0); // start sending - [csend1] s1=0 -> (s1'=1) & (x1'=0); // start sending - [busy1] s1=0 -> (s1'=2) & (x1'=0) & (cd1'=min(bmax,cd1+1)); // detects channel is busy so go into backoff - - // transmitting - [time] s1=1 & x1 (x1'=min(x1+1,lambda)); // let time pass - [end1] s1=1 & x1=lambda -> (s1'=4) & (x1'=0); // finished - [cd1] s1=1 -> (s1'=2) & (x1'=0) & (cd1'=min(bmax,cd1+1)); // collision detected - - // set backoff (no time can pass in this state) - // first retransmission - [] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (bc1'=0) - + 1/2 : (s1'=3) & (bc1'=1); - // second retransmission - [] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (bc1'=0) - + 1/4 : (s1'=3) & (bc1'=1) - + 1/4 : (s1'=3) & (bc1'=2) - + 1/4 : (s1'=3) & (bc1'=3); - // third retransmission - [] s1=2 & cd1=3 -> 1/8 : (s1'=3) & (bc1'=0) - + 1/8 : (s1'=3) & (bc1'=1) - + 1/8 : (s1'=3) & (bc1'=2) - + 1/8 : (s1'=3) & (bc1'=3) - + 1/8 : (s1'=3) & (bc1'=4) - + 1/8 : (s1'=3) & (bc1'=5) - + 1/8 : (s1'=3) & (bc1'=6) - + 1/8 : (s1'=3) & (bc1'=7); - // fourth retransmission - [] s1=2 & cd1=4 -> 1/16 : (s1'=3) & (bc1'=0) - + 1/16 : (s1'=3) & (bc1'=1) - + 1/16 : (s1'=3) & (bc1'=2) - + 1/16 : (s1'=3) & (bc1'=3) - + 1/16 : (s1'=3) & (bc1'=4) - + 1/16 : (s1'=3) & (bc1'=5) - + 1/16 : (s1'=3) & (bc1'=6) - + 1/16 : (s1'=3) & (bc1'=7) - + 1/16 : (s1'=3) & (bc1'=8) - + 1/16 : (s1'=3) & (bc1'=9) - + 1/16 : (s1'=3) & (bc1'=10) - + 1/16 : (s1'=3) & (bc1'=11) - + 1/16 : (s1'=3) & (bc1'=12) - + 1/16 : (s1'=3) & (bc1'=13) - + 1/16 : (s1'=3) & (bc1'=14) - + 1/16 : (s1'=3) & (bc1'=15); - // fifth retransmission - [] s1=2 & cd1=5 -> 1/32 : (s1'=3) & (bc1'=0) - + 1/32 : (s1'=3) & (bc1'=1) - + 1/32 : (s1'=3) & (bc1'=2) - + 1/32 : (s1'=3) & (bc1'=3) - + 1/32 : (s1'=3) & (bc1'=4) - + 1/32 : (s1'=3) & (bc1'=5) - + 1/32 : (s1'=3) & (bc1'=6) - + 1/32 : (s1'=3) & (bc1'=7) - + 1/32 : (s1'=3) & (bc1'=8) - + 1/32 : (s1'=3) & (bc1'=9) - + 1/32 : (s1'=3) & (bc1'=10) - + 1/32 : (s1'=3) & (bc1'=11) - + 1/32 : (s1'=3) & (bc1'=12) - + 1/32 : (s1'=3) & (bc1'=13) - + 1/32 : (s1'=3) & (bc1'=14) - + 1/32 : (s1'=3) & (bc1'=15) - + 1/32 : (s1'=3) & (bc1'=16) - + 1/32 : (s1'=3) & (bc1'=17) - + 1/32 : (s1'=3) & (bc1'=18) - + 1/32 : (s1'=3) & (bc1'=19) - + 1/32 : (s1'=3) & (bc1'=20) - + 1/32 : (s1'=3) & (bc1'=21) - + 1/32 : (s1'=3) & (bc1'=22) - + 1/32 : (s1'=3) & (bc1'=23) - + 1/32 : (s1'=3) & (bc1'=24) - + 1/32 : (s1'=3) & (bc1'=25) - + 1/32 : (s1'=3) & (bc1'=26) - + 1/32 : (s1'=3) & (bc1'=27) - + 1/32 : (s1'=3) & (bc1'=28) - + 1/32 : (s1'=3) & (bc1'=29) - + 1/32 : (s1'=3) & (bc1'=30) - + 1/32 : (s1'=3) & (bc1'=31); - // sixth retransmission - [] s1=2 & cd1=6 -> 1/64 : (s1'=3) & (bc1'=0) - + 1/64 : (s1'=3) & (bc1'=1) - + 1/64 : (s1'=3) & (bc1'=2) - + 1/64 : (s1'=3) & (bc1'=3) - + 1/64 : (s1'=3) & (bc1'=4) - + 1/64 : (s1'=3) & (bc1'=5) - + 1/64 : (s1'=3) & (bc1'=6) - + 1/64 : (s1'=3) & (bc1'=7) - + 1/64 : (s1'=3) & (bc1'=8) - + 1/64 : (s1'=3) & (bc1'=9) - + 1/64 : (s1'=3) & (bc1'=10) - + 1/64 : (s1'=3) & (bc1'=11) - + 1/64 : (s1'=3) & (bc1'=12) - + 1/64 : (s1'=3) & (bc1'=13) - + 1/64 : (s1'=3) & (bc1'=14) - + 1/64 : (s1'=3) & (bc1'=15) - + 1/64 : (s1'=3) & (bc1'=16) - + 1/64 : (s1'=3) & (bc1'=17) - + 1/64 : (s1'=3) & (bc1'=18) - + 1/64 : (s1'=3) & (bc1'=19) - + 1/64 : (s1'=3) & (bc1'=20) - + 1/64 : (s1'=3) & (bc1'=21) - + 1/64 : (s1'=3) & (bc1'=22) - + 1/64 : (s1'=3) & (bc1'=23) - + 1/64 : (s1'=3) & (bc1'=24) - + 1/64 : (s1'=3) & (bc1'=25) - + 1/64 : (s1'=3) & (bc1'=26) - + 1/64 : (s1'=3) & (bc1'=27) - + 1/64 : (s1'=3) & (bc1'=28) - + 1/64 : (s1'=3) & (bc1'=29) - + 1/64 : (s1'=3) & (bc1'=30) - + 1/64 : (s1'=3) & (bc1'=31) - + 1/64 : (s1'=3) & (bc1'=32) - + 1/64 : (s1'=3) & (bc1'=33) - + 1/64 : (s1'=3) & (bc1'=34) - + 1/64 : (s1'=3) & (bc1'=35) - + 1/64 : (s1'=3) & (bc1'=36) - + 1/64 : (s1'=3) & (bc1'=37) - + 1/64 : (s1'=3) & (bc1'=38) - + 1/64 : (s1'=3) & (bc1'=39) - + 1/64 : (s1'=3) & (bc1'=40) - + 1/64 : (s1'=3) & (bc1'=41) - + 1/64 : (s1'=3) & (bc1'=42) - + 1/64 : (s1'=3) & (bc1'=43) - + 1/64 : (s1'=3) & (bc1'=44) - + 1/64 : (s1'=3) & (bc1'=45) - + 1/64 : (s1'=3) & (bc1'=46) - + 1/64 : (s1'=3) & (bc1'=47) - + 1/64 : (s1'=3) & (bc1'=48) - + 1/64 : (s1'=3) & (bc1'=49) - + 1/64 : (s1'=3) & (bc1'=50) - + 1/64 : (s1'=3) & (bc1'=51) - + 1/64 : (s1'=3) & (bc1'=52) - + 1/64 : (s1'=3) & (bc1'=53) - + 1/64 : (s1'=3) & (bc1'=54) - + 1/64 : (s1'=3) & (bc1'=55) - + 1/64 : (s1'=3) & (bc1'=56) - + 1/64 : (s1'=3) & (bc1'=57) - + 1/64 : (s1'=3) & (bc1'=58) - + 1/64 : (s1'=3) & (bc1'=59) - + 1/64 : (s1'=3) & (bc1'=60) - + 1/64 : (s1'=3) & (bc1'=61) - + 1/64 : (s1'=3) & (bc1'=62) - + 1/64 : (s1'=3) & (bc1'=63); - // seventh retransmission - [] s1=2 & cd1=7 -> 1/128 : (s1'=3) & (bc1'=0) - + 1/128 : (s1'=3) & (bc1'=1) - + 1/128 : (s1'=3) & (bc1'=2) - + 1/128 : (s1'=3) & (bc1'=3) - + 1/128 : (s1'=3) & (bc1'=4) - + 1/128 : (s1'=3) & (bc1'=5) - + 1/128 : (s1'=3) & (bc1'=6) - + 1/128 : (s1'=3) & (bc1'=7) - + 1/128 : (s1'=3) & (bc1'=8) - + 1/128 : (s1'=3) & (bc1'=9) - + 1/128 : (s1'=3) & (bc1'=10) - + 1/128 : (s1'=3) & (bc1'=11) - + 1/128 : (s1'=3) & (bc1'=12) - + 1/128 : (s1'=3) & (bc1'=13) - + 1/128 : (s1'=3) & (bc1'=14) - + 1/128 : (s1'=3) & (bc1'=15) - + 1/128 : (s1'=3) & (bc1'=16) - + 1/128 : (s1'=3) & (bc1'=17) - + 1/128 : (s1'=3) & (bc1'=18) - + 1/128 : (s1'=3) & (bc1'=19) - + 1/128 : (s1'=3) & (bc1'=20) - + 1/128 : (s1'=3) & (bc1'=21) - + 1/128 : (s1'=3) & (bc1'=22) - + 1/128 : (s1'=3) & (bc1'=23) - + 1/128 : (s1'=3) & (bc1'=24) - + 1/128 : (s1'=3) & (bc1'=25) - + 1/128 : (s1'=3) & (bc1'=26) - + 1/128 : (s1'=3) & (bc1'=27) - + 1/128 : (s1'=3) & (bc1'=28) - + 1/128 : (s1'=3) & (bc1'=29) - + 1/128 : (s1'=3) & (bc1'=30) - + 1/128 : (s1'=3) & (bc1'=31) - + 1/128 : (s1'=3) & (bc1'=32) - + 1/128 : (s1'=3) & (bc1'=33) - + 1/128 : (s1'=3) & (bc1'=34) - + 1/128 : (s1'=3) & (bc1'=35) - + 1/128 : (s1'=3) & (bc1'=36) - + 1/128 : (s1'=3) & (bc1'=37) - + 1/128 : (s1'=3) & (bc1'=38) - + 1/128 : (s1'=3) & (bc1'=39) - + 1/128 : (s1'=3) & (bc1'=40) - + 1/128 : (s1'=3) & (bc1'=41) - + 1/128 : (s1'=3) & (bc1'=42) - + 1/128 : (s1'=3) & (bc1'=43) - + 1/128 : (s1'=3) & (bc1'=44) - + 1/128 : (s1'=3) & (bc1'=45) - + 1/128 : (s1'=3) & (bc1'=46) - + 1/128 : (s1'=3) & (bc1'=47) - + 1/128 : (s1'=3) & (bc1'=48) - + 1/128 : (s1'=3) & (bc1'=49) - + 1/128 : (s1'=3) & (bc1'=50) - + 1/128 : (s1'=3) & (bc1'=51) - + 1/128 : (s1'=3) & (bc1'=52) - + 1/128 : (s1'=3) & (bc1'=53) - + 1/128 : (s1'=3) & (bc1'=54) - + 1/128 : (s1'=3) & (bc1'=55) - + 1/128 : (s1'=3) & (bc1'=56) - + 1/128 : (s1'=3) & (bc1'=57) - + 1/128 : (s1'=3) & (bc1'=58) - + 1/128 : (s1'=3) & (bc1'=59) - + 1/128 : (s1'=3) & (bc1'=60) - + 1/128 : (s1'=3) & (bc1'=61) - + 1/128 : (s1'=3) & (bc1'=62) - + 1/128 : (s1'=3) & (bc1'=63) - + 1/128 : (s1'=3) & (bc1'=64) - + 1/128 : (s1'=3) & (bc1'=65) - + 1/128 : (s1'=3) & (bc1'=66) - + 1/128 : (s1'=3) & (bc1'=67) - + 1/128 : (s1'=3) & (bc1'=68) - + 1/128 : (s1'=3) & (bc1'=69) - + 1/128 : (s1'=3) & (bc1'=70) - + 1/128 : (s1'=3) & (bc1'=71) - + 1/128 : (s1'=3) & (bc1'=72) - + 1/128 : (s1'=3) & (bc1'=73) - + 1/128 : (s1'=3) & (bc1'=74) - + 1/128 : (s1'=3) & (bc1'=75) - + 1/128 : (s1'=3) & (bc1'=76) - + 1/128 : (s1'=3) & (bc1'=77) - + 1/128 : (s1'=3) & (bc1'=78) - + 1/128 : (s1'=3) & (bc1'=79) - + 1/128 : (s1'=3) & (bc1'=80) - + 1/128 : (s1'=3) & (bc1'=81) - + 1/128 : (s1'=3) & (bc1'=82) - + 1/128 : (s1'=3) & (bc1'=83) - + 1/128 : (s1'=3) & (bc1'=84) - + 1/128 : (s1'=3) & (bc1'=85) - + 1/128 : (s1'=3) & (bc1'=86) - + 1/128 : (s1'=3) & (bc1'=87) - + 1/128 : (s1'=3) & (bc1'=88) - + 1/128 : (s1'=3) & (bc1'=89) - + 1/128 : (s1'=3) & (bc1'=90) - + 1/128 : (s1'=3) & (bc1'=91) - + 1/128 : (s1'=3) & (bc1'=92) - + 1/128 : (s1'=3) & (bc1'=93) - + 1/128 : (s1'=3) & (bc1'=94) - + 1/128 : (s1'=3) & (bc1'=95) - + 1/128 : (s1'=3) & (bc1'=96) - + 1/128 : (s1'=3) & (bc1'=97) - + 1/128 : (s1'=3) & (bc1'=98) - + 1/128 : (s1'=3) & (bc1'=99) - + 1/128 : (s1'=3) & (bc1'=100) - + 1/128 : (s1'=3) & (bc1'=101) - + 1/128 : (s1'=3) & (bc1'=102) - + 1/128 : (s1'=3) & (bc1'=103) - + 1/128 : (s1'=3) & (bc1'=104) - + 1/128 : (s1'=3) & (bc1'=105) - + 1/128 : (s1'=3) & (bc1'=106) - + 1/128 : (s1'=3) & (bc1'=107) - + 1/128 : (s1'=3) & (bc1'=108) - + 1/128 : (s1'=3) & (bc1'=109) - + 1/128 : (s1'=3) & (bc1'=110) - + 1/128 : (s1'=3) & (bc1'=111) - + 1/128 : (s1'=3) & (bc1'=112) - + 1/128 : (s1'=3) & (bc1'=113) - + 1/128 : (s1'=3) & (bc1'=114) - + 1/128 : (s1'=3) & (bc1'=115) - + 1/128 : (s1'=3) & (bc1'=116) - + 1/128 : (s1'=3) & (bc1'=117) - + 1/128 : (s1'=3) & (bc1'=118) - + 1/128 : (s1'=3) & (bc1'=119) - + 1/128 : (s1'=3) & (bc1'=120) - + 1/128 : (s1'=3) & (bc1'=121) - + 1/128 : (s1'=3) & (bc1'=122) - + 1/128 : (s1'=3) & (bc1'=123) - + 1/128 : (s1'=3) & (bc1'=124) - + 1/128 : (s1'=3) & (bc1'=125) - + 1/128 : (s1'=3) & (bc1'=126) - + 1/128 : (s1'=3) & (bc1'=127); - // eigth retransmission - [] s1=2 & cd1=8 -> 1/256 : (s1'=3) & (bc1'=0) - + 1/256 : (s1'=3) & (bc1'=1) - + 1/256 : (s1'=3) & (bc1'=2) - + 1/256 : (s1'=3) & (bc1'=3) - + 1/256 : (s1'=3) & (bc1'=4) - + 1/256 : (s1'=3) & (bc1'=5) - + 1/256 : (s1'=3) & (bc1'=6) - + 1/256 : (s1'=3) & (bc1'=7) - + 1/256 : (s1'=3) & (bc1'=8) - + 1/256 : (s1'=3) & (bc1'=9) - + 1/256 : (s1'=3) & (bc1'=10) - + 1/256 : (s1'=3) & (bc1'=11) - + 1/256 : (s1'=3) & (bc1'=12) - + 1/256 : (s1'=3) & (bc1'=13) - + 1/256 : (s1'=3) & (bc1'=14) - + 1/256 : (s1'=3) & (bc1'=15) - + 1/256 : (s1'=3) & (bc1'=16) - + 1/256 : (s1'=3) & (bc1'=17) - + 1/256 : (s1'=3) & (bc1'=18) - + 1/256 : (s1'=3) & (bc1'=19) - + 1/256 : (s1'=3) & (bc1'=20) - + 1/256 : (s1'=3) & (bc1'=21) - + 1/256 : (s1'=3) & (bc1'=22) - + 1/256 : (s1'=3) & (bc1'=23) - + 1/256 : (s1'=3) & (bc1'=24) - + 1/256 : (s1'=3) & (bc1'=25) - + 1/256 : (s1'=3) & (bc1'=26) - + 1/256 : (s1'=3) & (bc1'=27) - + 1/256 : (s1'=3) & (bc1'=28) - + 1/256 : (s1'=3) & (bc1'=29) - + 1/256 : (s1'=3) & (bc1'=30) - + 1/256 : (s1'=3) & (bc1'=31) - + 1/256 : (s1'=3) & (bc1'=32) - + 1/256 : (s1'=3) & (bc1'=33) - + 1/256 : (s1'=3) & (bc1'=34) - + 1/256 : (s1'=3) & (bc1'=35) - + 1/256 : (s1'=3) & (bc1'=36) - + 1/256 : (s1'=3) & (bc1'=37) - + 1/256 : (s1'=3) & (bc1'=38) - + 1/256 : (s1'=3) & (bc1'=39) - + 1/256 : (s1'=3) & (bc1'=40) - + 1/256 : (s1'=3) & (bc1'=41) - + 1/256 : (s1'=3) & (bc1'=42) - + 1/256 : (s1'=3) & (bc1'=43) - + 1/256 : (s1'=3) & (bc1'=44) - + 1/256 : (s1'=3) & (bc1'=45) - + 1/256 : (s1'=3) & (bc1'=46) - + 1/256 : (s1'=3) & (bc1'=47) - + 1/256 : (s1'=3) & (bc1'=48) - + 1/256 : (s1'=3) & (bc1'=49) - + 1/256 : (s1'=3) & (bc1'=50) - + 1/256 : (s1'=3) & (bc1'=51) - + 1/256 : (s1'=3) & (bc1'=52) - + 1/256 : (s1'=3) & (bc1'=53) - + 1/256 : (s1'=3) & (bc1'=54) - + 1/256 : (s1'=3) & (bc1'=55) - + 1/256 : (s1'=3) & (bc1'=56) - + 1/256 : (s1'=3) & (bc1'=57) - + 1/256 : (s1'=3) & (bc1'=58) - + 1/256 : (s1'=3) & (bc1'=59) - + 1/256 : (s1'=3) & (bc1'=60) - + 1/256 : (s1'=3) & (bc1'=61) - + 1/256 : (s1'=3) & (bc1'=62) - + 1/256 : (s1'=3) & (bc1'=63) - + 1/256 : (s1'=3) & (bc1'=64) - + 1/256 : (s1'=3) & (bc1'=65) - + 1/256 : (s1'=3) & (bc1'=66) - + 1/256 : (s1'=3) & (bc1'=67) - + 1/256 : (s1'=3) & (bc1'=68) - + 1/256 : (s1'=3) & (bc1'=69) - + 1/256 : (s1'=3) & (bc1'=70) - + 1/256 : (s1'=3) & (bc1'=71) - + 1/256 : (s1'=3) & (bc1'=72) - + 1/256 : (s1'=3) & (bc1'=73) - + 1/256 : (s1'=3) & (bc1'=74) - + 1/256 : (s1'=3) & (bc1'=75) - + 1/256 : (s1'=3) & (bc1'=76) - + 1/256 : (s1'=3) & (bc1'=77) - + 1/256 : (s1'=3) & (bc1'=78) - + 1/256 : (s1'=3) & (bc1'=79) - + 1/256 : (s1'=3) & (bc1'=80) - + 1/256 : (s1'=3) & (bc1'=81) - + 1/256 : (s1'=3) & (bc1'=82) - + 1/256 : (s1'=3) & (bc1'=83) - + 1/256 : (s1'=3) & (bc1'=84) - + 1/256 : (s1'=3) & (bc1'=85) - + 1/256 : (s1'=3) & (bc1'=86) - + 1/256 : (s1'=3) & (bc1'=87) - + 1/256 : (s1'=3) & (bc1'=88) - + 1/256 : (s1'=3) & (bc1'=89) - + 1/256 : (s1'=3) & (bc1'=90) - + 1/256 : (s1'=3) & (bc1'=91) - + 1/256 : (s1'=3) & (bc1'=92) - + 1/256 : (s1'=3) & (bc1'=93) - + 1/256 : (s1'=3) & (bc1'=94) - + 1/256 : (s1'=3) & (bc1'=95) - + 1/256 : (s1'=3) & (bc1'=96) - + 1/256 : (s1'=3) & (bc1'=97) - + 1/256 : (s1'=3) & (bc1'=98) - + 1/256 : (s1'=3) & (bc1'=99) - + 1/256 : (s1'=3) & (bc1'=100) - + 1/256 : (s1'=3) & (bc1'=101) - + 1/256 : (s1'=3) & (bc1'=102) - + 1/256 : (s1'=3) & (bc1'=103) - + 1/256 : (s1'=3) & (bc1'=104) - + 1/256 : (s1'=3) & (bc1'=105) - + 1/256 : (s1'=3) & (bc1'=106) - + 1/256 : (s1'=3) & (bc1'=107) - + 1/256 : (s1'=3) & (bc1'=108) - + 1/256 : (s1'=3) & (bc1'=109) - + 1/256 : (s1'=3) & (bc1'=110) - + 1/256 : (s1'=3) & (bc1'=111) - + 1/256 : (s1'=3) & (bc1'=112) - + 1/256 : (s1'=3) & (bc1'=113) - + 1/256 : (s1'=3) & (bc1'=114) - + 1/256 : (s1'=3) & (bc1'=115) - + 1/256 : (s1'=3) & (bc1'=116) - + 1/256 : (s1'=3) & (bc1'=117) - + 1/256 : (s1'=3) & (bc1'=118) - + 1/256 : (s1'=3) & (bc1'=119) - + 1/256 : (s1'=3) & (bc1'=120) - + 1/256 : (s1'=3) & (bc1'=121) - + 1/256 : (s1'=3) & (bc1'=122) - + 1/256 : (s1'=3) & (bc1'=123) - + 1/256 : (s1'=3) & (bc1'=124) - + 1/256 : (s1'=3) & (bc1'=125) - + 1/256 : (s1'=3) & (bc1'=126) - + 1/256 : (s1'=3) & (bc1'=127) - + 1/256 : (s1'=3) & (bc1'=128) - + 1/256 : (s1'=3) & (bc1'=129) - + 1/256 : (s1'=3) & (bc1'=130) - + 1/256 : (s1'=3) & (bc1'=131) - + 1/256 : (s1'=3) & (bc1'=132) - + 1/256 : (s1'=3) & (bc1'=133) - + 1/256 : (s1'=3) & (bc1'=134) - + 1/256 : (s1'=3) & (bc1'=135) - + 1/256 : (s1'=3) & (bc1'=136) - + 1/256 : (s1'=3) & (bc1'=137) - + 1/256 : (s1'=3) & (bc1'=138) - + 1/256 : (s1'=3) & (bc1'=139) - + 1/256 : (s1'=3) & (bc1'=140) - + 1/256 : (s1'=3) & (bc1'=141) - + 1/256 : (s1'=3) & (bc1'=142) - + 1/256 : (s1'=3) & (bc1'=143) - + 1/256 : (s1'=3) & (bc1'=144) - + 1/256 : (s1'=3) & (bc1'=145) - + 1/256 : (s1'=3) & (bc1'=146) - + 1/256 : (s1'=3) & (bc1'=147) - + 1/256 : (s1'=3) & (bc1'=148) - + 1/256 : (s1'=3) & (bc1'=149) - + 1/256 : (s1'=3) & (bc1'=150) - + 1/256 : (s1'=3) & (bc1'=151) - + 1/256 : (s1'=3) & (bc1'=152) - + 1/256 : (s1'=3) & (bc1'=153) - + 1/256 : (s1'=3) & (bc1'=154) - + 1/256 : (s1'=3) & (bc1'=155) - + 1/256 : (s1'=3) & (bc1'=156) - + 1/256 : (s1'=3) & (bc1'=157) - + 1/256 : (s1'=3) & (bc1'=158) - + 1/256 : (s1'=3) & (bc1'=159) - + 1/256 : (s1'=3) & (bc1'=160) - + 1/256 : (s1'=3) & (bc1'=161) - + 1/256 : (s1'=3) & (bc1'=162) - + 1/256 : (s1'=3) & (bc1'=163) - + 1/256 : (s1'=3) & (bc1'=164) - + 1/256 : (s1'=3) & (bc1'=165) - + 1/256 : (s1'=3) & (bc1'=166) - + 1/256 : (s1'=3) & (bc1'=167) - + 1/256 : (s1'=3) & (bc1'=168) - + 1/256 : (s1'=3) & (bc1'=169) - + 1/256 : (s1'=3) & (bc1'=170) - + 1/256 : (s1'=3) & (bc1'=171) - + 1/256 : (s1'=3) & (bc1'=172) - + 1/256 : (s1'=3) & (bc1'=173) - + 1/256 : (s1'=3) & (bc1'=174) - + 1/256 : (s1'=3) & (bc1'=175) - + 1/256 : (s1'=3) & (bc1'=176) - + 1/256 : (s1'=3) & (bc1'=177) - + 1/256 : (s1'=3) & (bc1'=178) - + 1/256 : (s1'=3) & (bc1'=179) - + 1/256 : (s1'=3) & (bc1'=180) - + 1/256 : (s1'=3) & (bc1'=181) - + 1/256 : (s1'=3) & (bc1'=182) - + 1/256 : (s1'=3) & (bc1'=183) - + 1/256 : (s1'=3) & (bc1'=184) - + 1/256 : (s1'=3) & (bc1'=185) - + 1/256 : (s1'=3) & (bc1'=186) - + 1/256 : (s1'=3) & (bc1'=187) - + 1/256 : (s1'=3) & (bc1'=188) - + 1/256 : (s1'=3) & (bc1'=189) - + 1/256 : (s1'=3) & (bc1'=190) - + 1/256 : (s1'=3) & (bc1'=191) - + 1/256 : (s1'=3) & (bc1'=192) - + 1/256 : (s1'=3) & (bc1'=193) - + 1/256 : (s1'=3) & (bc1'=194) - + 1/256 : (s1'=3) & (bc1'=195) - + 1/256 : (s1'=3) & (bc1'=196) - + 1/256 : (s1'=3) & (bc1'=197) - + 1/256 : (s1'=3) & (bc1'=198) - + 1/256 : (s1'=3) & (bc1'=199) - + 1/256 : (s1'=3) & (bc1'=200) - + 1/256 : (s1'=3) & (bc1'=201) - + 1/256 : (s1'=3) & (bc1'=202) - + 1/256 : (s1'=3) & (bc1'=203) - + 1/256 : (s1'=3) & (bc1'=204) - + 1/256 : (s1'=3) & (bc1'=205) - + 1/256 : (s1'=3) & (bc1'=206) - + 1/256 : (s1'=3) & (bc1'=207) - + 1/256 : (s1'=3) & (bc1'=208) - + 1/256 : (s1'=3) & (bc1'=209) - + 1/256 : (s1'=3) & (bc1'=210) - + 1/256 : (s1'=3) & (bc1'=211) - + 1/256 : (s1'=3) & (bc1'=212) - + 1/256 : (s1'=3) & (bc1'=213) - + 1/256 : (s1'=3) & (bc1'=214) - + 1/256 : (s1'=3) & (bc1'=215) - + 1/256 : (s1'=3) & (bc1'=216) - + 1/256 : (s1'=3) & (bc1'=217) - + 1/256 : (s1'=3) & (bc1'=218) - + 1/256 : (s1'=3) & (bc1'=219) - + 1/256 : (s1'=3) & (bc1'=220) - + 1/256 : (s1'=3) & (bc1'=221) - + 1/256 : (s1'=3) & (bc1'=222) - + 1/256 : (s1'=3) & (bc1'=223) - + 1/256 : (s1'=3) & (bc1'=224) - + 1/256 : (s1'=3) & (bc1'=225) - + 1/256 : (s1'=3) & (bc1'=226) - + 1/256 : (s1'=3) & (bc1'=227) - + 1/256 : (s1'=3) & (bc1'=228) - + 1/256 : (s1'=3) & (bc1'=229) - + 1/256 : (s1'=3) & (bc1'=230) - + 1/256 : (s1'=3) & (bc1'=231) - + 1/256 : (s1'=3) & (bc1'=232) - + 1/256 : (s1'=3) & (bc1'=233) - + 1/256 : (s1'=3) & (bc1'=234) - + 1/256 : (s1'=3) & (bc1'=235) - + 1/256 : (s1'=3) & (bc1'=236) - + 1/256 : (s1'=3) & (bc1'=237) - + 1/256 : (s1'=3) & (bc1'=238) - + 1/256 : (s1'=3) & (bc1'=239) - + 1/256 : (s1'=3) & (bc1'=240) - + 1/256 : (s1'=3) & (bc1'=241) - + 1/256 : (s1'=3) & (bc1'=242) - + 1/256 : (s1'=3) & (bc1'=243) - + 1/256 : (s1'=3) & (bc1'=244) - + 1/256 : (s1'=3) & (bc1'=245) - + 1/256 : (s1'=3) & (bc1'=246) - + 1/256 : (s1'=3) & (bc1'=247) - + 1/256 : (s1'=3) & (bc1'=248) - + 1/256 : (s1'=3) & (bc1'=249) - + 1/256 : (s1'=3) & (bc1'=250) - + 1/256 : (s1'=3) & (bc1'=251) - + 1/256 : (s1'=3) & (bc1'=252) - + 1/256 : (s1'=3) & (bc1'=253) - + 1/256 : (s1'=3) & (bc1'=254) - + 1/256 : (s1'=3) & (bc1'=255); - // ninth retransmission - [] s1=2 & cd1=9 -> 1/512 : (s1'=3) & (bc1'=0) - + 1/512 : (s1'=3) & (bc1'=1) - + 1/512 : (s1'=3) & (bc1'=2) - + 1/512 : (s1'=3) & (bc1'=3) - + 1/512 : (s1'=3) & (bc1'=4) - + 1/512 : (s1'=3) & (bc1'=5) - + 1/512 : (s1'=3) & (bc1'=6) - + 1/512 : (s1'=3) & (bc1'=7) - + 1/512 : (s1'=3) & (bc1'=8) - + 1/512 : (s1'=3) & (bc1'=9) - + 1/512 : (s1'=3) & (bc1'=10) - + 1/512 : (s1'=3) & (bc1'=11) - + 1/512 : (s1'=3) & (bc1'=12) - + 1/512 : (s1'=3) & (bc1'=13) - + 1/512 : (s1'=3) & (bc1'=14) - + 1/512 : (s1'=3) & (bc1'=15) - + 1/512 : (s1'=3) & (bc1'=16) - + 1/512 : (s1'=3) & (bc1'=17) - + 1/512 : (s1'=3) & (bc1'=18) - + 1/512 : (s1'=3) & (bc1'=19) - + 1/512 : (s1'=3) & (bc1'=20) - + 1/512 : (s1'=3) & (bc1'=21) - + 1/512 : (s1'=3) & (bc1'=22) - + 1/512 : (s1'=3) & (bc1'=23) - + 1/512 : (s1'=3) & (bc1'=24) - + 1/512 : (s1'=3) & (bc1'=25) - + 1/512 : (s1'=3) & (bc1'=26) - + 1/512 : (s1'=3) & (bc1'=27) - + 1/512 : (s1'=3) & (bc1'=28) - + 1/512 : (s1'=3) & (bc1'=29) - + 1/512 : (s1'=3) & (bc1'=30) - + 1/512 : (s1'=3) & (bc1'=31) - + 1/512 : (s1'=3) & (bc1'=32) - + 1/512 : (s1'=3) & (bc1'=33) - + 1/512 : (s1'=3) & (bc1'=34) - + 1/512 : (s1'=3) & (bc1'=35) - + 1/512 : (s1'=3) & (bc1'=36) - + 1/512 : (s1'=3) & (bc1'=37) - + 1/512 : (s1'=3) & (bc1'=38) - + 1/512 : (s1'=3) & (bc1'=39) - + 1/512 : (s1'=3) & (bc1'=40) - + 1/512 : (s1'=3) & (bc1'=41) - + 1/512 : (s1'=3) & (bc1'=42) - + 1/512 : (s1'=3) & (bc1'=43) - + 1/512 : (s1'=3) & (bc1'=44) - + 1/512 : (s1'=3) & (bc1'=45) - + 1/512 : (s1'=3) & (bc1'=46) - + 1/512 : (s1'=3) & (bc1'=47) - + 1/512 : (s1'=3) & (bc1'=48) - + 1/512 : (s1'=3) & (bc1'=49) - + 1/512 : (s1'=3) & (bc1'=50) - + 1/512 : (s1'=3) & (bc1'=51) - + 1/512 : (s1'=3) & (bc1'=52) - + 1/512 : (s1'=3) & (bc1'=53) - + 1/512 : (s1'=3) & (bc1'=54) - + 1/512 : (s1'=3) & (bc1'=55) - + 1/512 : (s1'=3) & (bc1'=56) - + 1/512 : (s1'=3) & (bc1'=57) - + 1/512 : (s1'=3) & (bc1'=58) - + 1/512 : (s1'=3) & (bc1'=59) - + 1/512 : (s1'=3) & (bc1'=60) - + 1/512 : (s1'=3) & (bc1'=61) - + 1/512 : (s1'=3) & (bc1'=62) - + 1/512 : (s1'=3) & (bc1'=63) - + 1/512 : (s1'=3) & (bc1'=64) - 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+ 1/1024 : (s1'=3) & (bc1'=920) - + 1/1024 : (s1'=3) & (bc1'=921) - + 1/1024 : (s1'=3) & (bc1'=922) - + 1/1024 : (s1'=3) & (bc1'=923) - + 1/1024 : (s1'=3) & (bc1'=924) - + 1/1024 : (s1'=3) & (bc1'=925) - + 1/1024 : (s1'=3) & (bc1'=926) - + 1/1024 : (s1'=3) & (bc1'=927) - + 1/1024 : (s1'=3) & (bc1'=928) - + 1/1024 : (s1'=3) & (bc1'=929) - + 1/1024 : (s1'=3) & (bc1'=930) - + 1/1024 : (s1'=3) & (bc1'=931) - + 1/1024 : (s1'=3) & (bc1'=932) - + 1/1024 : (s1'=3) & (bc1'=933) - + 1/1024 : (s1'=3) & (bc1'=934) - + 1/1024 : (s1'=3) & (bc1'=935) - + 1/1024 : (s1'=3) & (bc1'=936) - + 1/1024 : (s1'=3) & (bc1'=937) - + 1/1024 : (s1'=3) & (bc1'=938) - + 1/1024 : (s1'=3) & (bc1'=939) - + 1/1024 : (s1'=3) & (bc1'=940) - + 1/1024 : (s1'=3) & (bc1'=941) - + 1/1024 : (s1'=3) & (bc1'=942) - + 1/1024 : (s1'=3) & (bc1'=943) - + 1/1024 : (s1'=3) & (bc1'=944) - + 1/1024 : (s1'=3) & (bc1'=945) - + 1/1024 : (s1'=3) & (bc1'=946) - + 1/1024 : (s1'=3) & (bc1'=947) - + 1/1024 : (s1'=3) & (bc1'=948) - + 1/1024 : (s1'=3) & (bc1'=949) - + 1/1024 : (s1'=3) & (bc1'=950) - + 1/1024 : (s1'=3) & (bc1'=951) - + 1/1024 : (s1'=3) & (bc1'=952) - + 1/1024 : (s1'=3) & (bc1'=953) - + 1/1024 : (s1'=3) & (bc1'=954) - + 1/1024 : (s1'=3) & (bc1'=955) - + 1/1024 : (s1'=3) & (bc1'=956) - + 1/1024 : (s1'=3) & (bc1'=957) - + 1/1024 : (s1'=3) & (bc1'=958) - + 1/1024 : (s1'=3) & (bc1'=959) - + 1/1024 : (s1'=3) & (bc1'=960) - + 1/1024 : (s1'=3) & (bc1'=961) - + 1/1024 : (s1'=3) & (bc1'=962) - + 1/1024 : (s1'=3) & (bc1'=963) - + 1/1024 : (s1'=3) & (bc1'=964) - + 1/1024 : (s1'=3) & (bc1'=965) - + 1/1024 : (s1'=3) & (bc1'=966) - + 1/1024 : (s1'=3) & (bc1'=967) - + 1/1024 : (s1'=3) & (bc1'=968) - + 1/1024 : (s1'=3) & (bc1'=969) - + 1/1024 : (s1'=3) & (bc1'=970) - + 1/1024 : (s1'=3) & (bc1'=971) - + 1/1024 : (s1'=3) & (bc1'=972) - + 1/1024 : (s1'=3) & (bc1'=973) - + 1/1024 : (s1'=3) & (bc1'=974) - + 1/1024 : (s1'=3) & (bc1'=975) - + 1/1024 : (s1'=3) & (bc1'=976) - + 1/1024 : (s1'=3) & (bc1'=977) - + 1/1024 : (s1'=3) & (bc1'=978) - + 1/1024 : (s1'=3) & (bc1'=979) - + 1/1024 : (s1'=3) & (bc1'=980) - + 1/1024 : (s1'=3) & (bc1'=981) - + 1/1024 : (s1'=3) & (bc1'=982) - + 1/1024 : (s1'=3) & (bc1'=983) - + 1/1024 : (s1'=3) & (bc1'=984) - + 1/1024 : (s1'=3) & (bc1'=985) - + 1/1024 : (s1'=3) & (bc1'=986) - + 1/1024 : (s1'=3) & (bc1'=987) - + 1/1024 : (s1'=3) & (bc1'=988) - + 1/1024 : (s1'=3) & (bc1'=989) - + 1/1024 : (s1'=3) & (bc1'=990) - + 1/1024 : (s1'=3) & (bc1'=991) - + 1/1024 : (s1'=3) & (bc1'=992) - + 1/1024 : (s1'=3) & (bc1'=993) - + 1/1024 : (s1'=3) & (bc1'=994) - + 1/1024 : (s1'=3) & (bc1'=995) - + 1/1024 : (s1'=3) & (bc1'=996) - + 1/1024 : (s1'=3) & (bc1'=997) - + 1/1024 : (s1'=3) & (bc1'=998) - + 1/1024 : (s1'=3) & (bc1'=999) - + 1/1024 : (s1'=3) & (bc1'=1000) - + 1/1024 : (s1'=3) & (bc1'=1001) - + 1/1024 : (s1'=3) & (bc1'=1002) - + 1/1024 : (s1'=3) & (bc1'=1003) - + 1/1024 : (s1'=3) & (bc1'=1004) - + 1/1024 : (s1'=3) & (bc1'=1005) - + 1/1024 : (s1'=3) & (bc1'=1006) - + 1/1024 : (s1'=3) & (bc1'=1007) - + 1/1024 : (s1'=3) & (bc1'=1008) - + 1/1024 : (s1'=3) & (bc1'=1009) - + 1/1024 : (s1'=3) & (bc1'=1010) - + 1/1024 : (s1'=3) & (bc1'=1011) - + 1/1024 : (s1'=3) & (bc1'=1012) - + 1/1024 : (s1'=3) & (bc1'=1013) - + 1/1024 : (s1'=3) & (bc1'=1014) - + 1/1024 : (s1'=3) & (bc1'=1015) - + 1/1024 : (s1'=3) & (bc1'=1016) - + 1/1024 : (s1'=3) & (bc1'=1017) - + 1/1024 : (s1'=3) & (bc1'=1018) - + 1/1024 : (s1'=3) & (bc1'=1019) - + 1/1024 : (s1'=3) & (bc1'=1020) - + 1/1024 : (s1'=3) & (bc1'=1021) - + 1/1024 : (s1'=3) & (bc1'=1022) - + 1/1024 : (s1'=3) & (bc1'=1023); - - // wait until backoff counter reaches 0 then send again - [time] s1=3 & x1 (x1'=x1+1); // let time pass (in slot) - [time] s1=3 & x1=slot & bc1>0 -> (x1'=1) & (bc1'=bc1-1); // let time pass (move slots) - [send1] s1=3 & x1=slot & bc1=0 -> (s1'=1) & (x1'=0); // finished backoff (bus appears free) - [csend1] s1=3 & x1=slot & bc1=0 -> (s1'=1) & (x1'=0); // finished backoff (bus appears free) - [busy1] s1=3 & x1=slot & bc1=0 -> (s1'=2) & (x1'=0) & (cd1'=min(bmax,cd1+1)); // finished backoff (bus busy) - - // once finished nothing matters - [time] s1=4 -> true; - -endmodule - -// construct station 2 through renaming -module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,csend1=csend2,busy1=busy2,end1=end2] endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// REWARD STRUCTURES -// time -rewards "time" - [time] true : 12; -endrewards -// number of collisions -rewards "collisions" - [send1] b=1 : 1; - [send2] b=1 : 1; -endrewards - -//---------------------------------------------------------------------------------------------------------------------------- -// LABELS - -label "s1_done" = s1=4; -label "s2_done" = s2=4; -label "done" = s1=4 & s2=4; -label "cmax" = c=4; diff --git a/prism-examples/pta/csma/full/csma-slots.nm b/prism-examples/pta/csma/full/csma-slots.nm deleted file mode 100644 index 4b617acb..00000000 --- a/prism-examples/pta/csma/full/csma-slots.nm +++ /dev/null @@ -1,2208 +0,0 @@ -// CSMA/CD protocol - two stations (PTA model using digital clocks) -// gxn/mxd 31/05/05 - -// based on kronos (non-probabilistic) TA model and that which appears in: -// M. Duflot, L. Fribourg, T. Hérault, R. Lassaigne, F. Magniette, S. Messika, S. Peyronnet and C. Picaronny -// Probabilistic model checking of the CSMA/CD protocol using PRISM and APMC -// In Proc. AVoCS'04, 2004 - -pta - -const K; - -// PARAMETERS - -// parameters -const int sigma=26; // time for messages to propagate along the bus -const int lambda=808; // time to send a message -const int delay=26; // wire delay -const int slot=2*sigma; // size of back off slot - -const int bmax; // exponential backoff limit -const int M=pow(2,bmax)-1; // max number of slots to wait - -//---------------------------------------------------------------------------------------------------------------------------- -// collision counter -module collisions - - c : [0..K]; - - [csend1] true -> (c'=min(K,c+1)); - [csend2] true -> (c'=min(K,c+1)); - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// the bus -module bus - - b : [0..4]; - // b=0 - idle - // b=1 - active - // b=2 - collision - // b=3 - collision1 - // b=4 - collision2 - - y1 : clock; // clock of bus - y2 : clock; // clock of bus - - invariant - (b=0 => true) & - (b=1 => true) & - (b=2 => y1<=delay & y2<=delay) & - (b=3 => y1<=delay) & - (b=4 => y2<=delay) - endinvariant - - // stations starts sending - [send1] b=0 -> (b'=1) & (y1'=0); // no message being sent - [send2] b=0 -> (b'=1) & (y2'=0); // no message being sent - - // collision occurs - [csend1] b=1 & y2<=delay -> (b'=2) & (y1'=0); // message being sent (move to collision) - [csend2] b=1 & y1<=delay -> (b'=2) & (y2'=0); // message being sent (move to collision) - - // message being sent - [busy1] b=1 & y2>delay -> (b'=1); - [busy2] b=1 & y1>delay -> (b'=1); - - // station finishes - [end1] b=1 -> (b'=0) & (y1'=0); - [end2] b=1 -> (b'=0) & (y2'=0); - - // collision detected - [cd1] b=2 & y1>=delay -> (b'=4); // station one detects collision before station two - [cd2] b=2 & y2>=delay -> (b'=3); // station two detects collision before station one - - [cd1] b=3 & y1>=delay -> (b'=0) & (y1'=0) & (y2'=0); // station one detects collision after station two - [cd2] b=4 & y2>=delay -> (b'=0) & (y1'=0) & (y2'=0); // station two detects collision after station one - -endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// STATION 1 -module station1 - - // LOCAL STATE - s1 : [0..4]; - // s1=0 - initial state - // s1=1 - transmit - // s1=2 - collision (set backoff) - // s1=3 - wait (bus busy) - // s1=4 - done (since sending only one message) - - x1 : clock; // local clock - - bc1 : [0..pow(2,bmax)-1]; // backoff counter - cd1 : [0..bmax]; // collision counter - - invariant - (s1=0 => x1<=delay) & - (s1=1 => x1<=lambda) & - (s1=2 => x1<=0) & - (s1=3 => x1<=slot) & - (s1=4 => true) - endinvariant - - // start sending (make sure there is a collision, i.e. start before x1 equals delay) - [send1] s1=0 -> (s1'=1) & (x1'=0); // start sending - [csend1] s1=0 -> (s1'=1) & (x1'=0); // start sending - [busy1] s1=0 -> (s1'=2) & (x1'=0) & (cd1'=min(bmax,cd1+1)); // detects channel is busy so go into backoff - - // transmitting - [end1] s1=1 & x1=lambda -> (s1'=4) & (x1'=0); // finished - [cd1] s1=1 -> (s1'=2) & (x1'=0) & (cd1'=min(bmax,cd1+1)); // collision detected - - // set backoff (no time can pass in this state) - // first retransmission - [] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (bc1'=0) - + 1/2 : (s1'=3) & (bc1'=1); - // second retransmission - [] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (bc1'=0) - + 1/4 : (s1'=3) & (bc1'=1) - + 1/4 : (s1'=3) & (bc1'=2) - + 1/4 : (s1'=3) & (bc1'=3); - // third retransmission - [] s1=2 & cd1=3 -> 1/8 : (s1'=3) & (bc1'=0) - + 1/8 : (s1'=3) & (bc1'=1) - + 1/8 : (s1'=3) & (bc1'=2) - + 1/8 : (s1'=3) & (bc1'=3) - + 1/8 : (s1'=3) & (bc1'=4) - + 1/8 : (s1'=3) & (bc1'=5) - + 1/8 : (s1'=3) & (bc1'=6) - + 1/8 : (s1'=3) & (bc1'=7); - // fourth retransmission - [] s1=2 & cd1=4 -> 1/16 : (s1'=3) & (bc1'=0) - + 1/16 : (s1'=3) & (bc1'=1) - + 1/16 : (s1'=3) & (bc1'=2) - + 1/16 : (s1'=3) & (bc1'=3) - + 1/16 : (s1'=3) & (bc1'=4) - + 1/16 : (s1'=3) & (bc1'=5) - + 1/16 : (s1'=3) & (bc1'=6) - + 1/16 : (s1'=3) & (bc1'=7) - + 1/16 : (s1'=3) & (bc1'=8) - + 1/16 : (s1'=3) & (bc1'=9) - + 1/16 : (s1'=3) & (bc1'=10) - + 1/16 : (s1'=3) & (bc1'=11) - + 1/16 : (s1'=3) & (bc1'=12) - + 1/16 : (s1'=3) & (bc1'=13) - + 1/16 : (s1'=3) & (bc1'=14) - + 1/16 : (s1'=3) & (bc1'=15); - // fifth retransmission - [] s1=2 & cd1=5 -> 1/32 : (s1'=3) & (bc1'=0) - + 1/32 : (s1'=3) & (bc1'=1) - + 1/32 : (s1'=3) & (bc1'=2) - + 1/32 : (s1'=3) & (bc1'=3) - + 1/32 : (s1'=3) & (bc1'=4) - + 1/32 : (s1'=3) & (bc1'=5) - + 1/32 : (s1'=3) & (bc1'=6) - + 1/32 : (s1'=3) & (bc1'=7) - + 1/32 : (s1'=3) & (bc1'=8) - + 1/32 : (s1'=3) & (bc1'=9) - + 1/32 : (s1'=3) & (bc1'=10) - + 1/32 : (s1'=3) & (bc1'=11) - + 1/32 : (s1'=3) & (bc1'=12) - + 1/32 : (s1'=3) & (bc1'=13) - + 1/32 : (s1'=3) & (bc1'=14) - + 1/32 : (s1'=3) & (bc1'=15) - + 1/32 : (s1'=3) & (bc1'=16) - + 1/32 : (s1'=3) & (bc1'=17) - + 1/32 : (s1'=3) & (bc1'=18) - + 1/32 : (s1'=3) & (bc1'=19) - + 1/32 : (s1'=3) & (bc1'=20) - + 1/32 : (s1'=3) & (bc1'=21) - + 1/32 : (s1'=3) & (bc1'=22) - + 1/32 : (s1'=3) & (bc1'=23) - + 1/32 : (s1'=3) & (bc1'=24) - + 1/32 : (s1'=3) & (bc1'=25) - + 1/32 : (s1'=3) & (bc1'=26) - + 1/32 : (s1'=3) & (bc1'=27) - + 1/32 : (s1'=3) & (bc1'=28) - + 1/32 : (s1'=3) & (bc1'=29) - + 1/32 : (s1'=3) & (bc1'=30) - + 1/32 : (s1'=3) & (bc1'=31); - // sixth retransmission - [] s1=2 & cd1=6 -> 1/64 : (s1'=3) & (bc1'=0) - + 1/64 : (s1'=3) & (bc1'=1) - + 1/64 : (s1'=3) & (bc1'=2) - + 1/64 : (s1'=3) & (bc1'=3) - + 1/64 : (s1'=3) & (bc1'=4) - + 1/64 : (s1'=3) & (bc1'=5) - + 1/64 : (s1'=3) & (bc1'=6) - + 1/64 : (s1'=3) & (bc1'=7) - + 1/64 : (s1'=3) & (bc1'=8) - + 1/64 : (s1'=3) & (bc1'=9) - + 1/64 : (s1'=3) & (bc1'=10) - + 1/64 : (s1'=3) & (bc1'=11) - + 1/64 : (s1'=3) & (bc1'=12) - + 1/64 : (s1'=3) & (bc1'=13) - + 1/64 : (s1'=3) & (bc1'=14) - + 1/64 : (s1'=3) & (bc1'=15) - + 1/64 : (s1'=3) & (bc1'=16) - + 1/64 : (s1'=3) & (bc1'=17) - + 1/64 : (s1'=3) & (bc1'=18) - + 1/64 : (s1'=3) & (bc1'=19) - + 1/64 : (s1'=3) & (bc1'=20) - + 1/64 : (s1'=3) & (bc1'=21) - + 1/64 : (s1'=3) & (bc1'=22) - + 1/64 : (s1'=3) & (bc1'=23) - + 1/64 : (s1'=3) & (bc1'=24) - + 1/64 : (s1'=3) & (bc1'=25) - + 1/64 : (s1'=3) & (bc1'=26) - + 1/64 : (s1'=3) & (bc1'=27) - + 1/64 : (s1'=3) & (bc1'=28) - + 1/64 : (s1'=3) & (bc1'=29) - + 1/64 : (s1'=3) & (bc1'=30) - + 1/64 : (s1'=3) & (bc1'=31) - + 1/64 : (s1'=3) & (bc1'=32) - + 1/64 : (s1'=3) & (bc1'=33) - + 1/64 : (s1'=3) & (bc1'=34) - + 1/64 : (s1'=3) & (bc1'=35) - + 1/64 : (s1'=3) & (bc1'=36) - + 1/64 : (s1'=3) & (bc1'=37) - + 1/64 : (s1'=3) & (bc1'=38) - + 1/64 : (s1'=3) & (bc1'=39) - + 1/64 : (s1'=3) & (bc1'=40) - + 1/64 : (s1'=3) & (bc1'=41) - + 1/64 : (s1'=3) & (bc1'=42) - + 1/64 : (s1'=3) & (bc1'=43) - + 1/64 : (s1'=3) & (bc1'=44) - + 1/64 : (s1'=3) & (bc1'=45) - + 1/64 : (s1'=3) & (bc1'=46) - + 1/64 : (s1'=3) & (bc1'=47) - + 1/64 : (s1'=3) & (bc1'=48) - + 1/64 : (s1'=3) & (bc1'=49) - + 1/64 : (s1'=3) & (bc1'=50) - + 1/64 : (s1'=3) & (bc1'=51) - + 1/64 : (s1'=3) & (bc1'=52) - + 1/64 : (s1'=3) & (bc1'=53) - + 1/64 : (s1'=3) & (bc1'=54) - + 1/64 : (s1'=3) & (bc1'=55) - + 1/64 : (s1'=3) & (bc1'=56) - + 1/64 : (s1'=3) & (bc1'=57) - + 1/64 : (s1'=3) & (bc1'=58) - + 1/64 : (s1'=3) & (bc1'=59) - + 1/64 : (s1'=3) & (bc1'=60) - + 1/64 : (s1'=3) & (bc1'=61) - + 1/64 : (s1'=3) & (bc1'=62) - + 1/64 : (s1'=3) & (bc1'=63); - // seventh retransmission - [] s1=2 & cd1=7 -> 1/128 : (s1'=3) & (bc1'=0) - + 1/128 : (s1'=3) & (bc1'=1) - + 1/128 : (s1'=3) & (bc1'=2) - + 1/128 : (s1'=3) & (bc1'=3) - + 1/128 : (s1'=3) & (bc1'=4) - + 1/128 : (s1'=3) & (bc1'=5) - + 1/128 : (s1'=3) & (bc1'=6) - + 1/128 : (s1'=3) & (bc1'=7) - + 1/128 : (s1'=3) & (bc1'=8) - + 1/128 : (s1'=3) & (bc1'=9) - + 1/128 : (s1'=3) & (bc1'=10) - + 1/128 : (s1'=3) & (bc1'=11) - + 1/128 : (s1'=3) & (bc1'=12) - + 1/128 : (s1'=3) & (bc1'=13) - + 1/128 : (s1'=3) & (bc1'=14) - + 1/128 : (s1'=3) & (bc1'=15) - + 1/128 : (s1'=3) & (bc1'=16) - + 1/128 : (s1'=3) & (bc1'=17) - + 1/128 : (s1'=3) & (bc1'=18) - + 1/128 : (s1'=3) & (bc1'=19) - + 1/128 : (s1'=3) & (bc1'=20) - + 1/128 : (s1'=3) & (bc1'=21) - + 1/128 : (s1'=3) & (bc1'=22) - + 1/128 : (s1'=3) & (bc1'=23) - + 1/128 : (s1'=3) & (bc1'=24) - + 1/128 : (s1'=3) & (bc1'=25) - + 1/128 : (s1'=3) & (bc1'=26) - + 1/128 : (s1'=3) & (bc1'=27) - + 1/128 : (s1'=3) & (bc1'=28) - + 1/128 : (s1'=3) & (bc1'=29) - + 1/128 : (s1'=3) & (bc1'=30) - + 1/128 : (s1'=3) & (bc1'=31) - + 1/128 : (s1'=3) & (bc1'=32) - + 1/128 : (s1'=3) & (bc1'=33) - + 1/128 : (s1'=3) & (bc1'=34) - + 1/128 : (s1'=3) & (bc1'=35) - + 1/128 : (s1'=3) & (bc1'=36) - + 1/128 : (s1'=3) & (bc1'=37) - + 1/128 : (s1'=3) & (bc1'=38) - + 1/128 : (s1'=3) & (bc1'=39) - + 1/128 : (s1'=3) & (bc1'=40) - + 1/128 : (s1'=3) & (bc1'=41) - + 1/128 : (s1'=3) & (bc1'=42) - + 1/128 : (s1'=3) & (bc1'=43) - + 1/128 : (s1'=3) & (bc1'=44) - + 1/128 : (s1'=3) & (bc1'=45) - + 1/128 : (s1'=3) & (bc1'=46) - + 1/128 : (s1'=3) & (bc1'=47) - + 1/128 : (s1'=3) & (bc1'=48) - + 1/128 : (s1'=3) & (bc1'=49) - + 1/128 : (s1'=3) & (bc1'=50) - + 1/128 : (s1'=3) & (bc1'=51) - + 1/128 : (s1'=3) & (bc1'=52) - + 1/128 : (s1'=3) & (bc1'=53) - + 1/128 : (s1'=3) & (bc1'=54) - + 1/128 : (s1'=3) & (bc1'=55) - + 1/128 : (s1'=3) & (bc1'=56) - + 1/128 : (s1'=3) & (bc1'=57) - + 1/128 : (s1'=3) & (bc1'=58) - + 1/128 : (s1'=3) & (bc1'=59) - + 1/128 : (s1'=3) & (bc1'=60) - + 1/128 : (s1'=3) & (bc1'=61) - + 1/128 : (s1'=3) & (bc1'=62) - + 1/128 : (s1'=3) & (bc1'=63) - + 1/128 : (s1'=3) & (bc1'=64) - + 1/128 : (s1'=3) & (bc1'=65) - + 1/128 : (s1'=3) & (bc1'=66) - + 1/128 : (s1'=3) & (bc1'=67) - + 1/128 : (s1'=3) & (bc1'=68) - + 1/128 : (s1'=3) & (bc1'=69) - + 1/128 : (s1'=3) & (bc1'=70) - + 1/128 : (s1'=3) & (bc1'=71) - + 1/128 : (s1'=3) & (bc1'=72) - + 1/128 : (s1'=3) & (bc1'=73) - + 1/128 : (s1'=3) & (bc1'=74) - + 1/128 : (s1'=3) & (bc1'=75) - + 1/128 : (s1'=3) & (bc1'=76) - + 1/128 : (s1'=3) & (bc1'=77) - + 1/128 : (s1'=3) & (bc1'=78) - + 1/128 : (s1'=3) & (bc1'=79) - + 1/128 : (s1'=3) & (bc1'=80) - + 1/128 : (s1'=3) & (bc1'=81) - + 1/128 : (s1'=3) & (bc1'=82) - + 1/128 : (s1'=3) & (bc1'=83) - + 1/128 : (s1'=3) & (bc1'=84) - + 1/128 : (s1'=3) & (bc1'=85) - + 1/128 : (s1'=3) & (bc1'=86) - + 1/128 : (s1'=3) & (bc1'=87) - + 1/128 : (s1'=3) & (bc1'=88) - + 1/128 : (s1'=3) & (bc1'=89) - + 1/128 : (s1'=3) & (bc1'=90) - + 1/128 : (s1'=3) & (bc1'=91) - + 1/128 : (s1'=3) & (bc1'=92) - + 1/128 : (s1'=3) & (bc1'=93) - + 1/128 : (s1'=3) & (bc1'=94) - + 1/128 : (s1'=3) & (bc1'=95) - + 1/128 : (s1'=3) & (bc1'=96) - + 1/128 : (s1'=3) & (bc1'=97) - + 1/128 : (s1'=3) & (bc1'=98) - + 1/128 : (s1'=3) & (bc1'=99) - + 1/128 : (s1'=3) & (bc1'=100) - + 1/128 : (s1'=3) & (bc1'=101) - + 1/128 : (s1'=3) & (bc1'=102) - + 1/128 : (s1'=3) & (bc1'=103) - + 1/128 : (s1'=3) & (bc1'=104) - + 1/128 : (s1'=3) & (bc1'=105) - + 1/128 : (s1'=3) & (bc1'=106) - + 1/128 : (s1'=3) & (bc1'=107) - + 1/128 : (s1'=3) & (bc1'=108) - + 1/128 : (s1'=3) & (bc1'=109) - + 1/128 : (s1'=3) & (bc1'=110) - + 1/128 : (s1'=3) & (bc1'=111) - + 1/128 : (s1'=3) & (bc1'=112) - + 1/128 : (s1'=3) & (bc1'=113) - + 1/128 : (s1'=3) & (bc1'=114) - + 1/128 : (s1'=3) & (bc1'=115) - + 1/128 : (s1'=3) & (bc1'=116) - + 1/128 : (s1'=3) & (bc1'=117) - + 1/128 : (s1'=3) & (bc1'=118) - + 1/128 : (s1'=3) & (bc1'=119) - + 1/128 : (s1'=3) & (bc1'=120) - + 1/128 : (s1'=3) & (bc1'=121) - + 1/128 : (s1'=3) & (bc1'=122) - + 1/128 : (s1'=3) & (bc1'=123) - + 1/128 : (s1'=3) & (bc1'=124) - + 1/128 : (s1'=3) & (bc1'=125) - + 1/128 : (s1'=3) & (bc1'=126) - + 1/128 : (s1'=3) & (bc1'=127); - // eigth retransmission - [] s1=2 & cd1=8 -> 1/256 : (s1'=3) & (bc1'=0) - + 1/256 : (s1'=3) & (bc1'=1) - + 1/256 : (s1'=3) & (bc1'=2) - + 1/256 : (s1'=3) & (bc1'=3) - + 1/256 : (s1'=3) & (bc1'=4) - + 1/256 : (s1'=3) & (bc1'=5) - + 1/256 : (s1'=3) & (bc1'=6) - + 1/256 : (s1'=3) & (bc1'=7) - + 1/256 : (s1'=3) & (bc1'=8) - + 1/256 : (s1'=3) & (bc1'=9) - + 1/256 : (s1'=3) & (bc1'=10) - + 1/256 : (s1'=3) & (bc1'=11) - + 1/256 : (s1'=3) & (bc1'=12) - + 1/256 : (s1'=3) & (bc1'=13) - + 1/256 : (s1'=3) & (bc1'=14) - + 1/256 : (s1'=3) & (bc1'=15) - + 1/256 : (s1'=3) & (bc1'=16) - + 1/256 : (s1'=3) & (bc1'=17) - + 1/256 : (s1'=3) & (bc1'=18) - + 1/256 : (s1'=3) & (bc1'=19) - + 1/256 : (s1'=3) & (bc1'=20) - + 1/256 : (s1'=3) & (bc1'=21) - + 1/256 : (s1'=3) & (bc1'=22) - + 1/256 : (s1'=3) & (bc1'=23) - + 1/256 : (s1'=3) & (bc1'=24) - + 1/256 : (s1'=3) & (bc1'=25) - + 1/256 : (s1'=3) & (bc1'=26) - + 1/256 : (s1'=3) & (bc1'=27) - + 1/256 : (s1'=3) & (bc1'=28) - + 1/256 : (s1'=3) & (bc1'=29) - + 1/256 : (s1'=3) & (bc1'=30) - + 1/256 : (s1'=3) & (bc1'=31) - + 1/256 : (s1'=3) & (bc1'=32) - + 1/256 : (s1'=3) & (bc1'=33) - + 1/256 : (s1'=3) & (bc1'=34) - + 1/256 : (s1'=3) & (bc1'=35) - + 1/256 : (s1'=3) & (bc1'=36) - + 1/256 : (s1'=3) & (bc1'=37) - + 1/256 : (s1'=3) & (bc1'=38) - + 1/256 : (s1'=3) & (bc1'=39) - + 1/256 : (s1'=3) & (bc1'=40) - + 1/256 : (s1'=3) & (bc1'=41) - + 1/256 : (s1'=3) & (bc1'=42) - + 1/256 : (s1'=3) & (bc1'=43) - + 1/256 : (s1'=3) & (bc1'=44) - + 1/256 : (s1'=3) & (bc1'=45) - + 1/256 : (s1'=3) & (bc1'=46) - + 1/256 : (s1'=3) & (bc1'=47) - + 1/256 : (s1'=3) & (bc1'=48) - + 1/256 : (s1'=3) & (bc1'=49) - + 1/256 : (s1'=3) & (bc1'=50) - + 1/256 : (s1'=3) & (bc1'=51) - + 1/256 : (s1'=3) & (bc1'=52) - + 1/256 : (s1'=3) & (bc1'=53) - + 1/256 : (s1'=3) & (bc1'=54) - + 1/256 : (s1'=3) & (bc1'=55) - + 1/256 : (s1'=3) & (bc1'=56) - + 1/256 : (s1'=3) & (bc1'=57) - + 1/256 : (s1'=3) & (bc1'=58) - + 1/256 : (s1'=3) & (bc1'=59) - + 1/256 : (s1'=3) & (bc1'=60) - + 1/256 : (s1'=3) & (bc1'=61) - + 1/256 : (s1'=3) & (bc1'=62) - + 1/256 : (s1'=3) & (bc1'=63) - + 1/256 : (s1'=3) & (bc1'=64) - + 1/256 : (s1'=3) & (bc1'=65) - + 1/256 : (s1'=3) & (bc1'=66) - + 1/256 : (s1'=3) & (bc1'=67) - + 1/256 : (s1'=3) & (bc1'=68) - + 1/256 : (s1'=3) & (bc1'=69) - + 1/256 : (s1'=3) & (bc1'=70) - + 1/256 : (s1'=3) & (bc1'=71) - + 1/256 : (s1'=3) & (bc1'=72) - + 1/256 : (s1'=3) & (bc1'=73) - + 1/256 : (s1'=3) & (bc1'=74) - + 1/256 : (s1'=3) & (bc1'=75) - + 1/256 : (s1'=3) & (bc1'=76) - + 1/256 : (s1'=3) & (bc1'=77) - + 1/256 : (s1'=3) & (bc1'=78) - + 1/256 : (s1'=3) & (bc1'=79) - + 1/256 : (s1'=3) & (bc1'=80) - + 1/256 : (s1'=3) & (bc1'=81) - + 1/256 : (s1'=3) & (bc1'=82) - + 1/256 : (s1'=3) & (bc1'=83) - + 1/256 : (s1'=3) & (bc1'=84) - + 1/256 : (s1'=3) & (bc1'=85) - + 1/256 : (s1'=3) & (bc1'=86) - + 1/256 : (s1'=3) & (bc1'=87) - + 1/256 : (s1'=3) & (bc1'=88) - + 1/256 : (s1'=3) & (bc1'=89) - + 1/256 : (s1'=3) & (bc1'=90) - + 1/256 : (s1'=3) & (bc1'=91) - + 1/256 : (s1'=3) & (bc1'=92) - + 1/256 : (s1'=3) & (bc1'=93) - + 1/256 : (s1'=3) & (bc1'=94) - + 1/256 : (s1'=3) & (bc1'=95) - + 1/256 : (s1'=3) & (bc1'=96) - + 1/256 : (s1'=3) & (bc1'=97) - + 1/256 : (s1'=3) & (bc1'=98) - + 1/256 : (s1'=3) & (bc1'=99) - + 1/256 : (s1'=3) & (bc1'=100) - + 1/256 : (s1'=3) & (bc1'=101) - + 1/256 : (s1'=3) & (bc1'=102) - + 1/256 : (s1'=3) & (bc1'=103) - + 1/256 : (s1'=3) & (bc1'=104) - + 1/256 : (s1'=3) & (bc1'=105) - + 1/256 : (s1'=3) & (bc1'=106) - + 1/256 : (s1'=3) & (bc1'=107) - + 1/256 : (s1'=3) & (bc1'=108) - + 1/256 : (s1'=3) & (bc1'=109) - + 1/256 : (s1'=3) & (bc1'=110) - + 1/256 : (s1'=3) & (bc1'=111) - + 1/256 : (s1'=3) & (bc1'=112) - + 1/256 : (s1'=3) & (bc1'=113) - + 1/256 : (s1'=3) & (bc1'=114) - + 1/256 : (s1'=3) & (bc1'=115) - + 1/256 : (s1'=3) & (bc1'=116) - + 1/256 : (s1'=3) & (bc1'=117) - + 1/256 : (s1'=3) & (bc1'=118) - + 1/256 : (s1'=3) & (bc1'=119) - + 1/256 : (s1'=3) & (bc1'=120) - + 1/256 : (s1'=3) & (bc1'=121) - + 1/256 : (s1'=3) & (bc1'=122) - + 1/256 : (s1'=3) & (bc1'=123) - + 1/256 : (s1'=3) & (bc1'=124) - + 1/256 : (s1'=3) & (bc1'=125) - + 1/256 : (s1'=3) & (bc1'=126) - + 1/256 : (s1'=3) & (bc1'=127) - + 1/256 : (s1'=3) & (bc1'=128) - + 1/256 : (s1'=3) & (bc1'=129) - + 1/256 : (s1'=3) & (bc1'=130) - + 1/256 : (s1'=3) & (bc1'=131) - + 1/256 : (s1'=3) & (bc1'=132) - + 1/256 : (s1'=3) & (bc1'=133) - + 1/256 : (s1'=3) & (bc1'=134) - + 1/256 : (s1'=3) & (bc1'=135) - + 1/256 : (s1'=3) & (bc1'=136) - + 1/256 : (s1'=3) & (bc1'=137) - + 1/256 : (s1'=3) & (bc1'=138) - + 1/256 : (s1'=3) & (bc1'=139) - + 1/256 : (s1'=3) & (bc1'=140) - + 1/256 : (s1'=3) & (bc1'=141) - + 1/256 : (s1'=3) & (bc1'=142) - + 1/256 : (s1'=3) & (bc1'=143) - + 1/256 : (s1'=3) & (bc1'=144) - + 1/256 : (s1'=3) & (bc1'=145) - + 1/256 : (s1'=3) & (bc1'=146) - + 1/256 : (s1'=3) & (bc1'=147) - + 1/256 : (s1'=3) & (bc1'=148) - + 1/256 : (s1'=3) & (bc1'=149) - + 1/256 : (s1'=3) & (bc1'=150) - + 1/256 : (s1'=3) & (bc1'=151) - + 1/256 : (s1'=3) & (bc1'=152) - + 1/256 : (s1'=3) & (bc1'=153) - + 1/256 : (s1'=3) & (bc1'=154) - + 1/256 : (s1'=3) & (bc1'=155) - + 1/256 : (s1'=3) & (bc1'=156) - + 1/256 : (s1'=3) & (bc1'=157) - + 1/256 : (s1'=3) & (bc1'=158) - + 1/256 : (s1'=3) & (bc1'=159) - + 1/256 : (s1'=3) & (bc1'=160) - + 1/256 : (s1'=3) & (bc1'=161) - + 1/256 : (s1'=3) & (bc1'=162) - + 1/256 : (s1'=3) & (bc1'=163) - + 1/256 : (s1'=3) & (bc1'=164) - + 1/256 : (s1'=3) & (bc1'=165) - + 1/256 : (s1'=3) & (bc1'=166) - + 1/256 : (s1'=3) & (bc1'=167) - + 1/256 : (s1'=3) & (bc1'=168) - + 1/256 : (s1'=3) & (bc1'=169) - + 1/256 : (s1'=3) & (bc1'=170) - + 1/256 : (s1'=3) & (bc1'=171) - + 1/256 : (s1'=3) & (bc1'=172) - + 1/256 : (s1'=3) & (bc1'=173) - + 1/256 : (s1'=3) & (bc1'=174) - + 1/256 : (s1'=3) & (bc1'=175) - + 1/256 : (s1'=3) & (bc1'=176) - + 1/256 : (s1'=3) & (bc1'=177) - + 1/256 : (s1'=3) & (bc1'=178) - + 1/256 : (s1'=3) & (bc1'=179) - + 1/256 : (s1'=3) & (bc1'=180) - + 1/256 : (s1'=3) & (bc1'=181) - + 1/256 : (s1'=3) & (bc1'=182) - + 1/256 : (s1'=3) & (bc1'=183) - + 1/256 : (s1'=3) & (bc1'=184) - + 1/256 : (s1'=3) & (bc1'=185) - + 1/256 : (s1'=3) & (bc1'=186) - + 1/256 : (s1'=3) & (bc1'=187) - + 1/256 : (s1'=3) & (bc1'=188) - + 1/256 : (s1'=3) & (bc1'=189) - + 1/256 : (s1'=3) & (bc1'=190) - + 1/256 : (s1'=3) & (bc1'=191) - + 1/256 : (s1'=3) & (bc1'=192) - + 1/256 : (s1'=3) & (bc1'=193) - + 1/256 : (s1'=3) & (bc1'=194) - + 1/256 : (s1'=3) & (bc1'=195) - + 1/256 : (s1'=3) & (bc1'=196) - + 1/256 : (s1'=3) & (bc1'=197) - + 1/256 : (s1'=3) & (bc1'=198) - + 1/256 : (s1'=3) & (bc1'=199) - + 1/256 : (s1'=3) & (bc1'=200) - + 1/256 : (s1'=3) & (bc1'=201) - + 1/256 : (s1'=3) & (bc1'=202) - + 1/256 : (s1'=3) & (bc1'=203) - + 1/256 : (s1'=3) & (bc1'=204) - + 1/256 : (s1'=3) & (bc1'=205) - + 1/256 : (s1'=3) & (bc1'=206) - + 1/256 : (s1'=3) & (bc1'=207) - + 1/256 : (s1'=3) & (bc1'=208) - + 1/256 : (s1'=3) & (bc1'=209) - + 1/256 : (s1'=3) & (bc1'=210) - + 1/256 : (s1'=3) & (bc1'=211) - + 1/256 : (s1'=3) & (bc1'=212) - + 1/256 : (s1'=3) & (bc1'=213) - + 1/256 : (s1'=3) & (bc1'=214) - + 1/256 : (s1'=3) & (bc1'=215) - + 1/256 : (s1'=3) & (bc1'=216) - + 1/256 : (s1'=3) & (bc1'=217) - + 1/256 : (s1'=3) & (bc1'=218) - + 1/256 : (s1'=3) & (bc1'=219) - + 1/256 : (s1'=3) & (bc1'=220) - + 1/256 : (s1'=3) & (bc1'=221) - + 1/256 : (s1'=3) & (bc1'=222) - + 1/256 : (s1'=3) & (bc1'=223) - + 1/256 : (s1'=3) & (bc1'=224) - + 1/256 : (s1'=3) & (bc1'=225) - + 1/256 : (s1'=3) & (bc1'=226) - + 1/256 : (s1'=3) & (bc1'=227) - + 1/256 : (s1'=3) & (bc1'=228) - + 1/256 : (s1'=3) & (bc1'=229) - + 1/256 : (s1'=3) & (bc1'=230) - + 1/256 : (s1'=3) & (bc1'=231) - + 1/256 : (s1'=3) & (bc1'=232) - + 1/256 : (s1'=3) & (bc1'=233) - + 1/256 : (s1'=3) & (bc1'=234) - + 1/256 : (s1'=3) & (bc1'=235) - + 1/256 : (s1'=3) & (bc1'=236) - + 1/256 : (s1'=3) & (bc1'=237) - + 1/256 : (s1'=3) & (bc1'=238) - + 1/256 : (s1'=3) & (bc1'=239) - + 1/256 : (s1'=3) & (bc1'=240) - + 1/256 : (s1'=3) & (bc1'=241) - + 1/256 : (s1'=3) & (bc1'=242) - + 1/256 : (s1'=3) & (bc1'=243) - + 1/256 : (s1'=3) & (bc1'=244) - + 1/256 : (s1'=3) & (bc1'=245) - + 1/256 : (s1'=3) & (bc1'=246) - + 1/256 : (s1'=3) & (bc1'=247) - + 1/256 : (s1'=3) & (bc1'=248) - + 1/256 : (s1'=3) & (bc1'=249) - + 1/256 : (s1'=3) & (bc1'=250) - + 1/256 : (s1'=3) & (bc1'=251) - + 1/256 : (s1'=3) & (bc1'=252) - + 1/256 : (s1'=3) & (bc1'=253) - + 1/256 : (s1'=3) & (bc1'=254) - + 1/256 : (s1'=3) & (bc1'=255); - // ninth retransmission - [] s1=2 & cd1=9 -> 1/512 : (s1'=3) & (bc1'=0) - + 1/512 : (s1'=3) & (bc1'=1) - + 1/512 : (s1'=3) & (bc1'=2) - + 1/512 : (s1'=3) & (bc1'=3) - + 1/512 : (s1'=3) & (bc1'=4) - + 1/512 : (s1'=3) & (bc1'=5) - + 1/512 : (s1'=3) & (bc1'=6) - + 1/512 : (s1'=3) & (bc1'=7) - + 1/512 : (s1'=3) & (bc1'=8) - + 1/512 : (s1'=3) & (bc1'=9) - + 1/512 : (s1'=3) & (bc1'=10) - + 1/512 : (s1'=3) & (bc1'=11) - + 1/512 : (s1'=3) & (bc1'=12) - + 1/512 : (s1'=3) & (bc1'=13) - + 1/512 : (s1'=3) & (bc1'=14) - + 1/512 : (s1'=3) & (bc1'=15) - + 1/512 : (s1'=3) & (bc1'=16) - + 1/512 : (s1'=3) & (bc1'=17) - + 1/512 : (s1'=3) & (bc1'=18) - + 1/512 : (s1'=3) & (bc1'=19) - + 1/512 : (s1'=3) & (bc1'=20) - + 1/512 : (s1'=3) & (bc1'=21) - + 1/512 : (s1'=3) & (bc1'=22) - + 1/512 : (s1'=3) & (bc1'=23) - + 1/512 : (s1'=3) & (bc1'=24) - + 1/512 : (s1'=3) & (bc1'=25) - + 1/512 : (s1'=3) & (bc1'=26) - + 1/512 : (s1'=3) & (bc1'=27) - + 1/512 : (s1'=3) & (bc1'=28) - + 1/512 : (s1'=3) & (bc1'=29) - + 1/512 : (s1'=3) & (bc1'=30) - + 1/512 : (s1'=3) & (bc1'=31) - + 1/512 : (s1'=3) & (bc1'=32) - + 1/512 : (s1'=3) & (bc1'=33) - + 1/512 : (s1'=3) & (bc1'=34) - + 1/512 : (s1'=3) & (bc1'=35) - + 1/512 : (s1'=3) & (bc1'=36) - + 1/512 : (s1'=3) & (bc1'=37) - + 1/512 : (s1'=3) & (bc1'=38) - + 1/512 : (s1'=3) & (bc1'=39) - + 1/512 : (s1'=3) & (bc1'=40) - + 1/512 : (s1'=3) & (bc1'=41) - + 1/512 : (s1'=3) & (bc1'=42) - + 1/512 : (s1'=3) & (bc1'=43) - + 1/512 : (s1'=3) & (bc1'=44) - + 1/512 : (s1'=3) & (bc1'=45) - + 1/512 : (s1'=3) & (bc1'=46) - + 1/512 : (s1'=3) & (bc1'=47) - 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+ 1/1024 : (s1'=3) & (bc1'=904) - + 1/1024 : (s1'=3) & (bc1'=905) - + 1/1024 : (s1'=3) & (bc1'=906) - + 1/1024 : (s1'=3) & (bc1'=907) - + 1/1024 : (s1'=3) & (bc1'=908) - + 1/1024 : (s1'=3) & (bc1'=909) - + 1/1024 : (s1'=3) & (bc1'=910) - + 1/1024 : (s1'=3) & (bc1'=911) - + 1/1024 : (s1'=3) & (bc1'=912) - + 1/1024 : (s1'=3) & (bc1'=913) - + 1/1024 : (s1'=3) & (bc1'=914) - + 1/1024 : (s1'=3) & (bc1'=915) - + 1/1024 : (s1'=3) & (bc1'=916) - + 1/1024 : (s1'=3) & (bc1'=917) - + 1/1024 : (s1'=3) & (bc1'=918) - + 1/1024 : (s1'=3) & (bc1'=919) - + 1/1024 : (s1'=3) & (bc1'=920) - + 1/1024 : (s1'=3) & (bc1'=921) - + 1/1024 : (s1'=3) & (bc1'=922) - + 1/1024 : (s1'=3) & (bc1'=923) - + 1/1024 : (s1'=3) & (bc1'=924) - + 1/1024 : (s1'=3) & (bc1'=925) - + 1/1024 : (s1'=3) & (bc1'=926) - + 1/1024 : (s1'=3) & (bc1'=927) - + 1/1024 : (s1'=3) & (bc1'=928) - + 1/1024 : (s1'=3) & (bc1'=929) - + 1/1024 : (s1'=3) & (bc1'=930) - + 1/1024 : (s1'=3) & (bc1'=931) - + 1/1024 : (s1'=3) & (bc1'=932) - + 1/1024 : (s1'=3) & (bc1'=933) - + 1/1024 : (s1'=3) & (bc1'=934) - + 1/1024 : (s1'=3) & (bc1'=935) - + 1/1024 : (s1'=3) & (bc1'=936) - + 1/1024 : (s1'=3) & (bc1'=937) - + 1/1024 : (s1'=3) & (bc1'=938) - + 1/1024 : (s1'=3) & (bc1'=939) - + 1/1024 : (s1'=3) & (bc1'=940) - + 1/1024 : (s1'=3) & (bc1'=941) - + 1/1024 : (s1'=3) & (bc1'=942) - + 1/1024 : (s1'=3) & (bc1'=943) - + 1/1024 : (s1'=3) & (bc1'=944) - + 1/1024 : (s1'=3) & (bc1'=945) - + 1/1024 : (s1'=3) & (bc1'=946) - + 1/1024 : (s1'=3) & (bc1'=947) - + 1/1024 : (s1'=3) & (bc1'=948) - + 1/1024 : (s1'=3) & (bc1'=949) - + 1/1024 : (s1'=3) & (bc1'=950) - + 1/1024 : (s1'=3) & (bc1'=951) - + 1/1024 : (s1'=3) & (bc1'=952) - + 1/1024 : (s1'=3) & (bc1'=953) - + 1/1024 : (s1'=3) & (bc1'=954) - + 1/1024 : (s1'=3) & (bc1'=955) - + 1/1024 : (s1'=3) & (bc1'=956) - + 1/1024 : (s1'=3) & (bc1'=957) - + 1/1024 : (s1'=3) & (bc1'=958) - + 1/1024 : (s1'=3) & (bc1'=959) - + 1/1024 : (s1'=3) & (bc1'=960) - + 1/1024 : (s1'=3) & (bc1'=961) - + 1/1024 : (s1'=3) & (bc1'=962) - + 1/1024 : (s1'=3) & (bc1'=963) - + 1/1024 : (s1'=3) & (bc1'=964) - + 1/1024 : (s1'=3) & (bc1'=965) - + 1/1024 : (s1'=3) & (bc1'=966) - + 1/1024 : (s1'=3) & (bc1'=967) - + 1/1024 : (s1'=3) & (bc1'=968) - + 1/1024 : (s1'=3) & (bc1'=969) - + 1/1024 : (s1'=3) & (bc1'=970) - + 1/1024 : (s1'=3) & (bc1'=971) - + 1/1024 : (s1'=3) & (bc1'=972) - + 1/1024 : (s1'=3) & (bc1'=973) - + 1/1024 : (s1'=3) & (bc1'=974) - + 1/1024 : (s1'=3) & (bc1'=975) - + 1/1024 : (s1'=3) & (bc1'=976) - + 1/1024 : (s1'=3) & (bc1'=977) - + 1/1024 : (s1'=3) & (bc1'=978) - + 1/1024 : (s1'=3) & (bc1'=979) - + 1/1024 : (s1'=3) & (bc1'=980) - + 1/1024 : (s1'=3) & (bc1'=981) - + 1/1024 : (s1'=3) & (bc1'=982) - + 1/1024 : (s1'=3) & (bc1'=983) - + 1/1024 : (s1'=3) & (bc1'=984) - + 1/1024 : (s1'=3) & (bc1'=985) - + 1/1024 : (s1'=3) & (bc1'=986) - + 1/1024 : (s1'=3) & (bc1'=987) - + 1/1024 : (s1'=3) & (bc1'=988) - + 1/1024 : (s1'=3) & (bc1'=989) - + 1/1024 : (s1'=3) & (bc1'=990) - + 1/1024 : (s1'=3) & (bc1'=991) - + 1/1024 : (s1'=3) & (bc1'=992) - + 1/1024 : (s1'=3) & (bc1'=993) - + 1/1024 : (s1'=3) & (bc1'=994) - + 1/1024 : (s1'=3) & (bc1'=995) - + 1/1024 : (s1'=3) & (bc1'=996) - + 1/1024 : (s1'=3) & (bc1'=997) - + 1/1024 : (s1'=3) & (bc1'=998) - + 1/1024 : (s1'=3) & (bc1'=999) - + 1/1024 : (s1'=3) & (bc1'=1000) - + 1/1024 : (s1'=3) & (bc1'=1001) - + 1/1024 : (s1'=3) & (bc1'=1002) - + 1/1024 : (s1'=3) & (bc1'=1003) - + 1/1024 : (s1'=3) & (bc1'=1004) - + 1/1024 : (s1'=3) & (bc1'=1005) - + 1/1024 : (s1'=3) & (bc1'=1006) - + 1/1024 : (s1'=3) & (bc1'=1007) - + 1/1024 : (s1'=3) & (bc1'=1008) - + 1/1024 : (s1'=3) & (bc1'=1009) - + 1/1024 : (s1'=3) & (bc1'=1010) - + 1/1024 : (s1'=3) & (bc1'=1011) - + 1/1024 : (s1'=3) & (bc1'=1012) - + 1/1024 : (s1'=3) & (bc1'=1013) - + 1/1024 : (s1'=3) & (bc1'=1014) - + 1/1024 : (s1'=3) & (bc1'=1015) - + 1/1024 : (s1'=3) & (bc1'=1016) - + 1/1024 : (s1'=3) & (bc1'=1017) - + 1/1024 : (s1'=3) & (bc1'=1018) - + 1/1024 : (s1'=3) & (bc1'=1019) - + 1/1024 : (s1'=3) & (bc1'=1020) - + 1/1024 : (s1'=3) & (bc1'=1021) - + 1/1024 : (s1'=3) & (bc1'=1022) - + 1/1024 : (s1'=3) & (bc1'=1023); - - // wait until backoff counter reaches 0 then send again - [] s1=3 & x1=slot & bc1>0 -> (x1'=0) & (bc1'=bc1-1); // move slots - [send1] s1=3 & x1=slot & bc1=0 -> (s1'=1) & (x1'=0); // finished backoff (bus appears free) - [csend1] s1=3 & x1=slot & bc1=0 -> (s1'=1) & (x1'=0); // finished backoff (bus appears free) - [busy1] s1=3 & x1=slot & bc1=0 -> (s1'=2) & (x1'=0) & (cd1'=min(bmax,cd1+1)); // finished backoff (bus busy) - - // once finished loop (wait for other station to finish) - [done] s1=4 -> (s1'=4); - -endmodule - -// construct station 2 through renaming -module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,csend1=csend2,busy1=busy2,end1=end2] endmodule - -//---------------------------------------------------------------------------------------------------------------------------- -// REWARD STRUCTURES - -// time -rewards "time" - [time] true : 1; -endrewards - -// number of collisions -rewards "collisions" - [csend1] true : 1; - [csend2] true : 1; -endrewards - -//---------------------------------------------------------------------------------------------------------------------------- -// LABELS - -label "s1_done" = s1=4; -label "s2_done" = s2=4; -label "done" = s1=4 & s2=4; -label "cmax" = c; diff --git a/prism-examples/pta/firewire/abst/firewire-digital.nm b/prism-examples/pta/firewire/abst/firewire-digital.nm deleted file mode 100644 index de55bbe9..00000000 --- a/prism-examples/pta/firewire/abst/firewire-digital.nm +++ /dev/null @@ -1,74 +0,0 @@ -// discrete version of abstract firewire protocol -// gxn 23/05/2001 - -nondeterministic - -// wire delay -const int delay; - -// probability of choosing fast and slow -const double fast; -const double slow = 1-fast; - -// maximal constant -const int kx = 167; - -module abstract_firewire - - // clock - x : [0..kx+1]; - - // local state - s : [0..9]; - // 0 -start_start - // 1 -fast_start - // 2 -start_fast - // 3 -start_slow - // 4 -slow_start - // 5 -fast_fast - // 6 -fast_slow - // 7 -slow_fast - // 8 -slow_slow - // 9 -done - - // initial state - [time] s=0 & x (x'=min(x+1,kx+1)); - [round] s=0 -> fast : (s'=1) + slow : (s'=4); - [round] s=0 -> fast : (s'=2) + slow : (s'=3); - // fast_start - [time] s=1 & x (x'=min(x+1,kx+1)); - [] s=1 -> fast : (s'=5) & (x'=0) + slow : (s'=6) & (x'=0); - // start_fast - [time] s=2 & x (x'=min(x+1,kx+1)); - [] s=2 -> fast : (s'=5) & (x'=0) + slow : (s'=7) & (x'=0); - // start_slow - [time] s=3 & x (x'=min(x+1,kx+1)); - [] s=3 -> fast : (s'=6) & (x'=0) + slow : (s'=8) & (x'=0); - // slow_start - [time] s=4 & x (x'=min(x+1,kx+1)); - [] s=4 -> fast : (s'=7) & (x'=0) + slow : (s'=8) & (x'=0); - // fast_fast - [time] s=5 & (x<85) -> (x'=min(x+1,kx+1)); - [] s=5 & (x>=76) -> (s'=0) & (x'=0); - [] s=5 & (x>=76-delay) -> (s'=9) & (x'=0); - // fast_slow - [time] s=6 & x<167 -> (x'=min(x+1,kx+1)); - [] s=6 & x>=159-delay -> (s'=9) & (x'=0); - // slow_fast - [time] s=7 & x<167 -> (x'=min(x+1,kx+1)); - [] s=7 & x>=159-delay -> (s'=9) & (x'=0); - // slow_slow - [time] s=8 & x<167 -> (x'=min(x+1,kx+1)); - [] s=8 & x>=159 -> (s'=0) & (x'=0); - [] s=8 & x>=159-delay -> (s'=9) & (x'=0); - // done - [] s=9 -> (s'=s); - -endmodule - -// labels -label "done" = (s=9); - -rewards - [time] true : 1; -endrewards diff --git a/prism-examples/pta/firewire/abst/firewire-max.nm b/prism-examples/pta/firewire/abst/firewire-max.nm deleted file mode 100644 index 70d8a1fc..00000000 --- a/prism-examples/pta/firewire/abst/firewire-max.nm +++ /dev/null @@ -1,82 +0,0 @@ -// Abstract model of Firewire protocol (PTA model) -// dxp/gxn 08/07/09 - -pta - -// maximum and minimum delays -// fast -const int rc_fast_max = 850; -const int rc_fast_min = 760; -// slow -const int rc_slow_max = 1670; -const int rc_slow_min = 1590; -// delay caused by the wire length -const int delay; -// probability of choosing fast and slow -const double fast = 0.5; -const double slow = 1-fast; -const int T; - -module abstract_firewire - - // clock - x : clock; - z : clock; - // local state - s : [0..9]; - // 0 - start_start - // 1 - fast_start - // 2 - start_fast - // 3 - start_slow - // 4 - slow_start - // 5 - fast_fast - // 6 - fast_slow - // 7 - slow_fast - // 8 - slow_slow - // 9 - done - - // clock invariant - invariant - (s=0 => x<=delay) & - (s=1 => x<=delay) & - (s=2 => x<=delay) & - (s=3 => x<=delay) & - (s=4 => x<=delay) & - (s=5 => x<=rc_fast_max) & - (s=6 => x<=rc_slow_max) & - (s=7 => x<=rc_slow_max) & - (s=8 => x<=rc_slow_max) & - (s=9 => x<=0) - endinvariant - - // start_start (initial state) - [] s=0 -> fast : (s'=1) + slow : (s'=4); - [] s=0 -> fast : (s'=2) + slow : (s'=3); - // fast_start - [] s=1 -> fast : (s'=5) & (x'=0) + slow : (s'=6) & (x'=0); - // start_fast - [] s=2 -> fast : (s'=5) & (x'=0) + slow : (s'=7) & (x'=0); - // start_slow - [] s=3 -> fast : (s'=6) & (x'=0) + slow : (s'=8) & (x'=0); - // slow_start - [] s=4 -> fast : (s'=7) & (x'=0) + slow : (s'=8) & (x'=0); - // fast_fast - [] s=5 & (x>=rc_fast_min) -> (s'=0) & (x'=0); - [] s=5 & (x>=rc_fast_min-delay) -> (s'=9) & (x'=0); - // fast_slow - [] s=6 & x>=rc_slow_min-delay -> (s'=9) & (x'=0); - // slow_fast - [] s=7 & x>=rc_slow_min-delay -> (s'=9) & (x'=0); - // slow_slow - [] s=8 & x>=rc_slow_min -> (s'=0) & (x'=0); - [] s=8 & x>=rc_slow_min-delay -> (s'=9) & (x'=0); - // done - [] s=9 & z>=T -> (s'=10); - [] s=9 & z (s'=11); - [] s>9 -> true; - -endmodule - -// labels -label "done_after" = (s=10); - diff --git a/prism-examples/pta/firewire/impl/firewire-digital.nm b/prism-examples/pta/firewire/impl/firewire-digital.nm deleted file mode 100644 index b50daf02..00000000 --- a/prism-examples/pta/firewire/impl/firewire-digital.nm +++ /dev/null @@ -1,167 +0,0 @@ -// firewire protocol with integer semantics -// dxp/gxn 14/06/01 - -// CLOCKS -// x1 (x2) clock for node1 (node2) -// y1 and y2 (z1 and z2) clocks for wire12 (wire21) - -// maximum and minimum delays -// fast -const int rc_fast_max = 85; -const int rc_fast_min = 76; -// slow -const int rc_slow_max = 167; -const int rc_slow_min = 159; -// delay caused by the wire length -const int delay; -// probability of choosing fast -const double fast = 0.5; -const double slow = 1-fast; - -module wire12 - - // local state - w12 : [0..9]; - // 0 - empty - // 1 - rec_req - // 2 - rec_req_ack - // 3 - rec_ack - // 4 - rec_ack_idle - // 5 - rec_idle - // 6 - rec_idle_req - // 7 - rec_ack_req - // 8 - rec_req_idle - // 9 - rec_idle_ack - - // clock for wire12 - y1 : [0..delay+1]; - y2 : [0..delay+1]; - - // empty - // do not need y1 and y2 to increase as always reset when this state is left - // similarly can reset y1 and y2 when we re-enter this state - [snd_req12] w12=0 -> (w12'=1) & (y1'=0) & (y2'=0); - [snd_ack12] w12=0 -> (w12'=3) & (y1'=0) & (y2'=0); - [snd_idle12] w12=0 -> (w12'=5) & (y1'=0) & (y2'=0); - [time] w12=0 -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); - // rec_req - [snd_req12] w12=1 -> (w12'=1); - [rec_req12] w12=1 -> (w12'=0) & (y1'=0) & (y2'=0); - [snd_ack12] w12=1 -> (w12'=2) & (y2'=0); - [snd_idle12] w12=1 -> (w12'=8) & (y2'=0); - [time] w12=1 & y2 (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); - // rec_req_ack - [snd_ack12] w12=2 -> (w12'=2); - [rec_req12] w12=2 -> (w12'=3); - [time] w12=2 & y1 (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); - // rec_ack - [snd_ack12] w12=3 -> (w12'=3); - [rec_ack12] w12=3 -> (w12'=0) & (y1'=0) & (y2'=0); - [snd_idle12] w12=3 -> (w12'=4) & (y2'=0); - [snd_req12] w12=3 -> (w12'=7) & (y2'=0); - [time] w12=3 & y2 (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); - // rec_ack_idle - [snd_idle12] w12=4 -> (w12'=4); - [rec_ack12] w12=4 -> (w12'=5); - [time] w12=4 & y1 (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); - // rec_idle - [snd_idle12] w12=5 -> (w12'=5); - [rec_idle12] w12=5 -> (w12'=0) & (y1'=0) & (y2'=0); - [snd_req12] w12=5 -> (w12'=6) & (y2'=0); - [snd_ack12] w12=5 -> (w12'=9) & (y2'=0); - [time] w12=5 & y2 (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); - // rec_idle_req - [snd_req12] w12=6 -> (w12'=6); - [rec_idle12] w12=6 -> (w12'=1); - [time] w12=6 & y1 (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); - // rec_ack_req - [snd_req12] w12=7 -> (w12'=7); - [rec_ack12] w12=7 -> (w12'=1); - [time] w12=7 & y1 (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); - // rec_req_idle - [snd_idle12] w12=8 -> (w12'=8); - [rec_req12] w12=8 -> (w12'=5); - [time] w12=8 & y1 (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); - // rec_idle_ack - [snd_ack12] w12=9 -> (w12'=9); - [rec_idle12] w12=9 -> (w12'=3); - [time] w12=9 & y1 (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); - -endmodule - -module node1 - - // clock for node1 - x1 : [0..168]; - - // local state - s1 : [0..8]; - // 0 - root contention - // 1 - rec_idle - // 2 - rec_req_fast - // 3 - rec_req_slow - // 4 - rec_idle_fast - // 5 - rec_idle_slow - // 6 - snd_req - // 7- almost_root - // 8 - almost_child - - // added resets to x1 when not considered again until after rest - // removed root and child (using almost root and almost child) - - // root contention immediate state) - [snd_idle12] s1=0 & x1=0 -> fast : (s1'=2) + slow : (s1'=3); - [rec_idle21] s1=0 & x1=0 -> (s1'=1); - // rec_idle immediate state) - [snd_idle12] s1=1 & x1=0 -> fast : (s1'=4) + slow : (s1'=5); - [rec_req21] s1=1 & x1=0 -> (s1'=0); - // rec_req_fast - [rec_idle21] s1=2 -> (s1'=4); - [snd_ack12] s1=2 & x1>=rc_fast_min -> (s1'=7) & (x1'=0); - [time] s1=2 & x1 (x1'=min(x1+1,168)); - // rec_req_slow - [rec_idle21] s1=3 -> (s1'=5); - [snd_ack12] s1=3 & x1>=rc_slow_min -> (s1'=7) & (x1'=0); - [time] s1=3 & x1 (x1'=min(x1+1,168)); - // rec_idle_fast - [rec_req21] s1=4 -> (s1'=2); - [snd_req12] s1=4 & x1>=rc_fast_min -> (s1'=6) & (x1'=0); - [time] s1=4 & x1 (x1'=min(x1+1,168)); - // rec_idle_slow - [rec_req21] s1=5 -> (s1'=3); - [snd_req12] s1=5 & x1>=rc_slow_min -> (s1'=6) & (x1'=0); - [time] s1=5 & x1 (x1'=min(x1+1,168)); - // snd_req - // do not use x1 until reset (in state 0 or in state 1) so do not need to increase x1 - // also can set x1 to 0 upon entering this state - [rec_req21] s1=6 -> (s1'=0) & (x1'=0); - [rec_ack21] s1=6 -> (s1'=8) & (x1'=0); - [time] s1=6 -> (x1'=min(x1+1,168)); - // almost root (immediate) - // loop in final states to remove deadlock - [loop] s1=7 & s2=8 -> (s1'=s1); - [loop] s1=8 & s2=7 -> (s1'=s1); - [time] s1=7 -> (x1'=min(x1+1,168)); - [time] s1=8 -> (x1'=min(x1+1,168)); - -endmodule - -// construct remaining automata through renaming -module wire21=wire12[w12=w21, y1=z1, y2=z2, - snd_req12=snd_req21, snd_idle12=snd_idle21, snd_ack12=snd_ack21, - rec_req12=rec_req21, rec_idle12=rec_idle21, rec_ack12=rec_ack21] -endmodule -module node2=node1[s1=s2, s2=s1, x1=x2, - rec_req21=rec_req12, rec_idle21=rec_idle12, rec_ack21=rec_ack12, - snd_req12=snd_req21, snd_idle12=snd_idle21, snd_ack12=snd_ack21,done1=done2,done2=done1] -endmodule - -// reward structures -// time -rewards "time" - [time] true : 1; -endrewards -// time nodes sending -rewards "time_sending" - [time] (w12>0 | w21>0) : 1; -endrewards diff --git a/prism-examples/pta/tests-prism.sh b/prism-examples/pta/tests-prism.sh deleted file mode 100755 index bce849c9..00000000 --- a/prism-examples/pta/tests-prism.sh +++ /dev/null @@ -1,9 +0,0 @@ - -prism-benchmark -exec prism-explicit -logs logs csma -prism-benchmark -exec prism-explicit -logs logs csma/abst -prism-benchmark -exec prism-explicit -logs logs firewire/impl -prism-benchmark -exec prism-explicit -logs logs firewire/abst -prism-benchmark -exec prism-explicit -logs logs zeroconf -prism-benchmark -exec prism-explicit -logs logs repudiation/honest -prism-benchmark -exec prism-explicit -logs logs repudiation/malicious - diff --git a/prism-examples/pta/zeroconf/auto b/prism-examples/pta/zeroconf/auto index 8aaefcbf..179213f6 100755 --- a/prism-examples/pta/zeroconf/auto +++ b/prism-examples/pta/zeroconf/auto @@ -1,20 +1,9 @@ #!/bin/csh -# full (multi-variable) - prism zeroconf.nm incorrect.pctl -aroptions refine=all,nopre,opt prism zeroconf.nm deadline.pctl -const T=100 -aroptions refine=all,nopre,opt prism zeroconf.nm deadline.pctl -const T=150 -aroptions refine=all,nopre,opt prism zeroconf.nm deadline.pctl -const T=200 -aroptions refine=all,nopre,opt -prism zeroconf.nm time.pctl -aroptions refine=all,nopre,opt - -# simple (single variable) - -prism zeroconf-simple.nm incorrect.pctl -aroptions refine=all,nopre,opt - -prism zeroconf-simple.nm deadline.pctl -const T=100 -aroptions refine=all,nopre,opt -prism zeroconf-simple.nm deadline.pctl -const T=150 -aroptions refine=all,nopre,opt -prism zeroconf-simple.nm deadline.pctl -const T=200 -aroptions refine=all,nopre,opt - +#prism zeroconf.nm time.pctl -aroptions refine=all,nopre,opt diff --git a/prism-examples/pta/zeroconf/zeroconf-digital.nm b/prism-examples/pta/zeroconf/zeroconf-digital.nm deleted file mode 100644 index 7292c03d..00000000 --- a/prism-examples/pta/zeroconf/zeroconf-digital.nm +++ /dev/null @@ -1,42 +0,0 @@ -// prism model of pta version of zeroconf -// using digitial clocks - -mdp - -module sender - - s : [0..2]; //local state - probes : [0..4]; // probes sent - ip : [0..2]; // ip address not chosen, fresh or in use - x : [0..21]; // local clock - - // selct probe - // [] s=0 -> 0.99969242125984251969 : (s'=1) & (ip'=0) + 0.00030757874015748031 : (s'=1) & (ip'=1); - - [] s=0 -> 0.5 : (s'=1) & (ip'=1) + 0.5 : (s'=1) & (ip'=2); - // send probes - [time] s=1 & x<20 -> (x'=x+1); - [send_used] s=1 & x=20 & ip=2 & probes<4 -> (probes'=probes+1) & (x'=0); - [send_fresh] s=1 & x=20 & ip=1 & probes<4 -> (probes'=probes+1) & (x'=0); - [] s=1 & x=20 & probes=4 -> (s'=2) & (x'=0); - [recv] s=1 -> (s'=0) & (x'=0) & (ip'=0) & (probes'=0); - - [time] s=2 -> (x'=min(21,x+1)); - -endmodule - -module environment - - e : [0..2]; // ready, send reply - y : [0..6]; - - [time] e=0 -> (y'=min(y+1,6)); - [send_fresh] e=0 -> true; - [send_used] e=0 -> 0.1 : (e'=0) + 0.9 : (e'=1); - - [time] e>0 & y<5 -> (y'=y+1); - [] e=1 & y>=1 -> 0.1 : (e'=0) & (y'=0) + 0.9 : (e'=2) & (y'=0); - [recv] e=2 & y>=1 -> (e'=0) & (y'=0); - -endmodule - diff --git a/prism-examples/pta/zeroconf/zeroconf-full.nm b/prism-examples/pta/zeroconf/zeroconf-full.nm deleted file mode 100644 index 003ce23d..00000000 --- a/prism-examples/pta/zeroconf/zeroconf-full.nm +++ /dev/null @@ -1,299 +0,0 @@ -// IPv4: PTA model with digitial clocks -// one concrete host attempting to choose an ip address -// when a number of (abstract) hosts have already got ip addresses -// gxn/dxp/jzs 02/05/03 - -// reset or noreset model -const bool reset=true; - -//------------------------------------------------------------- - -// we suppose that -// - the abstract hosts have already picked their addresses -// and always defend their addresses -// - the concrete host never picks the same ip address twice -// (this can happen only with a verys small probability) - -// under these assumptions we do not need message types because: -// 1) since messages to the concrete host will never be a probe, -// this host will react to all messages in the same way -// 2) since the abstract hosts always defend their addresses, -// all messages from the host will get an arp reply if the ip matches - -// following from the above assumptions we require only three abstract IP addresses -// (0,1 and 2) which correspond to the following sets of IP addresses: - -// 0 - the IP addresses of the abstract hosts which the concrete host -// previously tried to configure -// 1 - an IP address of an abstract host which the concrete host is -// currently trying to configure -// 2 - a fresh IP address which the concrete host is currently trying to configure - -// if the host picks an address that is being used it may end up picking another ip address -// in which case there may still be messages corresponding to the old ip address -// to be sent both from and to the host which the host should now disregard -// (since it will never pick the same ip address) - -// to deal with this situation: when a host picks a new ip address we reconfigure the -// messages that are still be be sent or are being sent by changing the ip address to 0 -// (an old ip address of the host) - -// all the messages from the abstract hosts for the 'old' address (in fact the -// set of old addresses since it may have started again more than once) -// can arrive in any order since they are equivalent to the host - it ignores then all - -// also the messages for the old and new address will come from different hosts -// (the ones with that ip address) which we model by allowing them to arrive in any order -// i.e. not neccessarily in the order they where sent - -//------------------------------------------------------------- -// model is an pta -pta - -//------------------------------------------------------------- -// VARIABLES -const int N=1000; // number of abstract hosts -const int K=2; // number of probes to send -const double loss = 0.1; // probability of message loss - -// PROBABILITIES -const double old = N/65024; // probability pick an ip address being used -const double new = (1-old); // probability pick a new ip address - -// TIMING CONSTANTS -const int CONSEC = 2; // time interval between sending consecutive probles -const int TRANSTIME = 1; // upper bound on transmission time delay -const int LONGWAIT = 60; // minimum time delay after a high number of address collisions -const int DEFEND = 10; - -const int TIME_MAX_X = 60; // max value of clock x -const int TIME_MAX_Y = 10; // max value of clock y -const int TIME_MAX_Z = 1; // max value of clock z - -// OTHER CONSTANTS -const int MAXCOLL = 10; // maximum number of collisions before long wait -// size of buffers for other hosts -const int B0 = 20; // buffer size for one abstract host -const int B1 = 8; // buffer sizes for all abstract hosts - -//------------------------------------------------------------- -// ENVIRONMENT - models: medium, output buffer of concrete host and all other hosts -module environment - - // buffer of concrete host - b_ip7 : [0..2]; // ip address of message in buffer position 8 - b_ip6 : [0..2]; // ip address of message in buffer position 7 - b_ip5 : [0..2]; // ip address of message in buffer position 6 - b_ip4 : [0..2]; // ip address of message in buffer position 5 - b_ip3 : [0..2]; // ip address of message in buffer position 4 - b_ip2 : [0..2]; // ip address of message in buffer position 3 - b_ip1 : [0..2]; // ip address of message in buffer position 2 - b_ip0 : [0..2]; // ip address of message in buffer position 1 - n : [0..8]; // number of places in the buffer used (from host) - - // messages to be sent from abstract hosts to concrete host - n0 : [0..B0]; // number of messages which do not have the host's current ip address - n1 : [0..B1]; // number of messages which have the host's current ip address - - b : [0..2]; // local state - // 0 - idle - // 1 - sending message from concrete host - // 2 - sending message from abstract host - - z : clock; // clock of environment (needed for the time to send a message) - - ip_mess : [0..2]; // ip in the current message being sent - // 0 - different from concrete host - // 1 - same as the concrete host and in use - // 2 - same as the concrete host and not in use - - invariant - (b=0 & n=0 & n0=0 & n1=0 => true) & // nothing to send - (b=0 & !(n=0 & n0=0 & n1=0) => z<=0) & // something to send - (b>0 => z<=1) // sending - endinvariant - - // RESET/RECONFIG: when host is about to choose new ip address - // suppose that the host cannot choose the same ip address - // (since happens with very small probability). - // Therefore all messages will have a different ip address, - // i.e. all n1 messages become n0 ones. - // Note this include any message currently being sent (ip is set to zero 0) - [reset] true -> (n1'=0) & (n0'=min(B0,n0+n1)) // abstract buffers - & (ip_mess'=0) // message being set - & (n'=(reset)?0:n) // concrete buffer (remove this update to get NO_RESET model) - & (b_ip7'=0) - & (b_ip6'=0) - & (b_ip5'=0) - & (b_ip4'=0) - & (b_ip3'=0) - & (b_ip2'=0) - & (b_ip1'=0) - & (b_ip0'=0); - // note: prevent anything else from happening when reconfiguration needs to take place - - // get messages to be sent (so message has same ip address as host) - [send1] n=0 -> (b_ip0'=1) & (n'=n+1); - [send1] n=1 -> (b_ip1'=1) & (n'=n+1); - [send1] n=2 -> (b_ip2'=1) & (n'=n+1); - [send1] n=3 -> (b_ip3'=1) & (n'=n+1); - [send1] n=4 -> (b_ip4'=1) & (n'=n+1); - [send1] n=5 -> (b_ip5'=1) & (n'=n+1); - [send1] n=6 -> (b_ip6'=1) & (n'=n+1); - [send1] n=7 -> (b_ip7'=1) & (n'=n+1); - [send1] n=8 -> (n'=n); // buffer full so lose message - - [send2] n=0 -> (b_ip0'=2) & (n'=n+1); - [send2] n=1 -> (b_ip1'=2) & (n'=n+1); - [send2] n=2 -> (b_ip2'=2) & (n'=n+1); - [send2] n=3 -> (b_ip3'=2) & (n'=n+1); - [send2] n=4 -> (b_ip4'=2) & (n'=n+1); - [send2] n=5 -> (b_ip5'=2) & (n'=n+1); - [send2] n=6 -> (b_ip6'=2) & (n'=n+1); - [send2] n=7 -> (b_ip7'=2) & (n'=n+1); - [send2] n=8 -> (n'=n); // buffer full so lose message - - // start sending message from host - [a] b=0 & n>0 -> (1-loss) : (b'=1) & (ip_mess'=b_ip0) - & (n'=n-1) - & (b_ip7'=0) - & (b_ip6'=b_ip7) - & (b_ip5'=b_ip6) - & (b_ip4'=b_ip5) - & (b_ip3'=b_ip4) - & (b_ip2'=b_ip3) - & (b_ip1'=b_ip2) - & (b_ip0'=b_ip1) // send message - + loss : (n'=n-1) - & (b_ip7'=0) - & (b_ip6'=b_ip7) - & (b_ip5'=b_ip6) - & (b_ip4'=b_ip5) - & (b_ip3'=b_ip4) - & (b_ip2'=b_ip3) - & (b_ip1'=b_ip2) - & (b_ip0'=b_ip1); // lose message - - // start sending message to host - [a] b=0 & n0>0 -> (1-loss) : (b'=2) & (ip_mess'=0) & (n0'=n0-1) + loss : (n0'=n0-1); // different ip - [a] b=0 & n1>0 -> (1-loss) : (b'=2) & (ip_mess'=1) & (n1'=n1-1) + loss : (n1'=n1-1); // same ip - - // finish sending message from host - [a] b=1 & ip_mess=0 -> (b'=0) & (z'=0) & (n0'=min(n0+1,B0)) & (ip_mess'=0); - [a] b=1 & ip_mess=1 -> (b'=0) & (z'=0) & (n1'=min(n1+1,B1)) & (ip_mess'=0); - [a] b=1 & ip_mess=2 -> (b'=0) & (z'=0) & (ip_mess'=0); - - // finish sending message to host - [rec0] b=2 & ip_mess=0 -> (b'=0) & (z'=0) & (ip_mess'=0); - [rec1] b=2 & ip_mess=1 -> (b'=0) & (z'=0) & (ip_mess'=0); - [rec2] b=2 & ip_mess=2 -> (b'=0) & (z'=0) & (ip_mess'=0); - -endmodule - -//------------------------------------------------------------- -// CONCRETE HOST -module host0 - - x : clock; // first clock of the host - y : clock; // second clock of the host - - coll : [0..MAXCOLL]; // number of address collisions - probes : [0..K]; // counter (number of probes sent) - mess : [0..1]; // need to send a message or not - defend : [0..1]; // defend (if =1, try to defend IP address) - - ip : [1..2]; // ip address (1 - in use & 2 - fresh) - - l : [0..4] init 1; // location - // 0 : RECONFIGURE - // 1 : RANDOM - // 2 : WAITSP - // 3 : WAITSG - // 4 : USE - - invariant - (l=0 => x<=0) & - (l=1 & coll x<=0) & - (l=1 & coll=MAXCOLL => x<=LONGWAIT) & - (l=2 => x<=CONSEC) & - (l=3 => x<=CONSEC) & - (l=4 => true) - endinvariant - - // needed to prevent environment from moving before a reset - [a] l>0 -> true; - - // RECONFIGURE - [reset] l=0 -> (l'=1); - - // RANDOM (choose IP address) - [rec0] (l=1) -> true; // get message (ignore since have no ip address) - [rec1] (l=1) -> true; // get message (ignore since have no ip address) - [rec2] (l=1) -> true; // get message (ignore since have no ip address) - // small number of collisions (choose straight away) - [] l=1 & coll 1/3*old : (l'=2) & (ip'=1) & (x'=0) - + 1/3*old : (l'=2) & (ip'=1) & (x'=1) - + 1/3*old : (l'=2) & (ip'=1) & (x'=2) - + 1/3*new : (l'=2) & (ip'=2) & (x'=0) - + 1/3*new : (l'=2) & (ip'=2) & (x'=1) - + 1/3*new : (l'=2) & (ip'=2) & (x'=2); - // large number of collisions: (wait for LONGWAIT) - [] l=1 & coll=MAXCOLL & x=LONGWAIT -> 1/3*old : (l'=2) & (ip'=1) & (x'=0) - + 1/3*old : (l'=2) & (ip'=1) & (x'=1) - + 1/3*old : (l'=2) & (ip'=1) & (x'=2) - + 1/3*new : (l'=2) & (ip'=2) & (x'=0) - + 1/3*new : (l'=2) & (ip'=2) & (x'=1) - + 1/3*new : (l'=2) & (ip'=2) & (x'=2); - - // WAITSP - // send probe - [send1] l=2 & ip=1 & probes=2 -> (x'=0) & (probes'=probes+1); - [send2] l=2 & ip=2 & probes=2 -> (x'=0) & (probes'=probes+1); - // sent K probes and waited 2 seconds - [] l=2 & probes=K & x>=2 -> (l'=3) & (probes'=0) & (coll'=0) & (x'=0); - // get message and ip does not match: ignore - [rec0] l=2 & 0!=ip -> (l'=l); - [rec1] l=2 & 1!=ip -> (l'=l); - [rec2] l=2 & 2!=ip -> (l'=l); - // get a message with matching ip: reconfigure - [rec0] l=2 & 0=ip -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0); - [rec1] l=2 & 1=ip -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0); - [rec2] l=2 & 2=ip -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0); - - // receive message and same ip: defend - [rec0] l=3 & mess=0 & 0=ip & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0); - [rec1] l=3 & mess=0 & 1=ip & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0); - [rec2] l=3 & mess=0 & 2=ip & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0); - // receive message and same ip: defer - [rec0] l=3 & mess=0 & 0=ip & (defend=0 | y (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0); - [rec1] l=3 & mess=0 & 1=ip & (defend=0 | y (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0); - [rec2] l=3 & mess=0 & 2=ip & (defend=0 | y (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0); - // receive message and different ip - [rec0] l=3 & mess=0 & 0!=ip -> (l'=l); - [rec1] l=3 & mess=0 & 1!=ip -> (l'=l); - [rec2] l=3 & mess=0 & 2!=ip -> (l'=l); - - // send probe reply or message for defence - [send1] l=3 & mess=1 & ip=1 -> (mess'=0); - [send2] l=3 & mess=1 & ip=2 -> (mess'=0); - // send first gratuitous arp message - [send1] l=3 & mess=0 & probes<1 & ip=1 & x>=CONSEC -> (x'=0) & (probes'=probes+1); - [send2] l=3 & mess=0 & probes<1 & ip=2 & x>=CONSEC -> (x'=0) & (probes'=probes+1); - // send second gratuitous arp message (move to use) - [send1] l=3 & mess=0 & probes=1 & ip=1 & x>=CONSEC -> (l'=4) & (x'=0) & (y'=0) & (probes'=0); - [send2] l=3 & mess=0 & probes=1 & ip=2 & x>=CONSEC -> (l'=4) & (x'=0) & (y'=0) & (probes'=0); - - // USE (only interested in reaching this state so do not need to add anything here) - [] l=4 -> true; - -endmodule - -//------------------------------------------------------------- -rewards "time" - true : 1; -endrewards - -label "done" = l=4; -label "done_error" = l=4 & ip=0; -label "done_fresh" = l=4 & ip=1; - diff --git a/prism-examples/pta/zeroconf/zeroconf-full.pctl b/prism-examples/pta/zeroconf/zeroconf-full.pctl deleted file mode 100644 index 632d3c94..00000000 --- a/prism-examples/pta/zeroconf/zeroconf-full.pctl +++ /dev/null @@ -1,3 +0,0 @@ -Pmin=?[F "done"] -Pmin=?[F "done_fresh"] -Pmax=?[F "done_error"] diff --git a/prism-examples/pta/zeroconf/zeroconf-full4.nm b/prism-examples/pta/zeroconf/zeroconf-full4.nm deleted file mode 100644 index d87e1ddc..00000000 --- a/prism-examples/pta/zeroconf/zeroconf-full4.nm +++ /dev/null @@ -1,277 +0,0 @@ -// IPv4: PTA model with digitial clocks -// one concrete host attempting to choose an ip address -// when a number of (abstract) hosts have already got ip addresses -// gxn/dxp/jzs 02/05/03 - -// reset or noreset model -const bool reset=true; - -//------------------------------------------------------------- - -// we suppose that -// - the abstract hosts have already picked their addresses -// and always defend their addresses -// - the concrete host never picks the same ip address twice -// (this can happen only with a verys small probability) - -// under these assumptions we do not need message types because: -// 1) since messages to the concrete host will never be a probe, -// this host will react to all messages in the same way -// 2) since the abstract hosts always defend their addresses, -// all messages from the host will get an arp reply if the ip matches - -// following from the above assumptions we require only three abstract IP addresses -// (0,1 and 2) which correspond to the following sets of IP addresses: - -// 0 - the IP addresses of the abstract hosts which the concrete host -// previously tried to configure -// 1 - an IP address of an abstract host which the concrete host is -// currently trying to configure -// 2 - a fresh IP address which the concrete host is currently trying to configure - -// if the host picks an address that is being used it may end up picking another ip address -// in which case there may still be messages corresponding to the old ip address -// to be sent both from and to the host which the host should now disregard -// (since it will never pick the same ip address) - -// to deal with this situation: when a host picks a new ip address we reconfigure the -// messages that are still be be sent or are being sent by changing the ip address to 0 -// (an old ip address of the host) - -// all the messages from the abstract hosts for the 'old' address (in fact the -// set of old addresses since it may have started again more than once) -// can arrive in any order since they are equivalent to the host - it ignores then all - -// also the messages for the old and new address will come from different hosts -// (the ones with that ip address) which we model by allowing them to arrive in any order -// i.e. not neccessarily in the order they where sent - -//------------------------------------------------------------- -// model is an pta -pta - -//------------------------------------------------------------- -// VARIABLES -const int N=1000; // number of abstract hosts -const int K=2; // number of probes to send -const double loss = 0.1; // probability of message loss - -// PROBABILITIES -const double old = N/65024; // probability pick an ip address being used -const double new = (1-old); // probability pick a new ip address - -// TIMING CONSTANTS -const int CONSEC = 2; // time interval between sending consecutive probles -const int TRANSTIME = 1; // upper bound on transmission time delay -const int LONGWAIT = 60; // minimum time delay after a high number of address collisions -const int DEFEND = 10; - -const int TIME_MAX_X = 60; // max value of clock x -const int TIME_MAX_Y = 10; // max value of clock y -const int TIME_MAX_Z = 1; // max value of clock z - -// OTHER CONSTANTS -const int MAXCOLL = 10; // maximum number of collisions before long wait -// size of buffers for other hosts -//const int B0 = 20; // buffer size for one abstract host -//const int B1 = 8; // buffer sizes for all abstract hosts -const int B0 = 4; // buffer size for one abstract host -const int B1 = 4; // buffer sizes for all abstract hosts - -//------------------------------------------------------------- -// ENVIRONMENT - models: medium, output buffer of concrete host and all other hosts -module environment - - // buffer of concrete host - b_ip3 : [0..2]; // ip address of message in buffer position 4 - b_ip2 : [0..2]; // ip address of message in buffer position 3 - b_ip1 : [0..2]; // ip address of message in buffer position 2 - b_ip0 : [0..2]; // ip address of message in buffer position 1 - n : [0..4]; // number of places in the buffer used (from host) - - // messages to be sent from abstract hosts to concrete host - n0 : [0..B0]; // number of messages which do not have the host's current ip address - n1 : [0..B1]; // number of messages which have the host's current ip address - - b : [0..2]; // local state - // 0 - idle - // 1 - sending message from concrete host - // 2 - sending message from abstract host - - z : clock; // clock of environment (needed for the time to send a message) - - ip_mess : [0..2]; // ip in the current message being sent - // 0 - different from concrete host - // 1 - same as the concrete host and in use - // 2 - same as the concrete host and not in use - - invariant - (b=0 & n=0 & n0=0 & n1=0 => true) & // nothing to send - (b=0 & !(n=0 & n0=0 & n1=0) => z<=0) & // something to send - (b>0 => z<=1) // sending - endinvariant - - // RESET/RECONFIG: when host is about to choose new ip address - // suppose that the host cannot choose the same ip address - // (since happens with very small probability). - // Therefore all messages will have a different ip address, - // i.e. all n1 messages become n0 ones. - // Note this include any message currently being sent (ip is set to zero 0) - [reset] true -> (n1'=0) & (n0'=min(B0,n0+n1)) // abstract buffers - & (ip_mess'=0) // message being set - & (n'=(reset)?0:n) // concrete buffer (remove this update to get NO_RESET model) - & (b_ip3'=0) - & (b_ip2'=0) - & (b_ip1'=0) - & (b_ip0'=0); - // note: prevent anything else from happening when reconfiguration needs to take place - - // get messages to be sent (so message has same ip address as host) - [send1] n=0 -> (b_ip0'=1) & (n'=n+1); - [send1] n=1 -> (b_ip1'=1) & (n'=n+1); - [send1] n=2 -> (b_ip2'=1) & (n'=n+1); - [send1] n=3 -> (b_ip3'=1) & (n'=n+1); - [send1] n=4 -> (n'=n); // buffer full so lose message - - [send2] n=0 -> (b_ip0'=2) & (n'=n+1); - [send2] n=1 -> (b_ip1'=2) & (n'=n+1); - [send2] n=2 -> (b_ip2'=2) & (n'=n+1); - [send2] n=3 -> (b_ip3'=2) & (n'=n+1); - [send2] n=4 -> (n'=n); // buffer full so lose message - - // start sending message from host - [a] b=0 & n>0 -> (1-loss) : (b'=1) & (ip_mess'=b_ip0) - & (n'=n-1) - & (b_ip3'=0) - & (b_ip2'=b_ip3) - & (b_ip1'=b_ip2) - & (b_ip0'=b_ip1) // send message - + loss : (n'=n-1) - & (b_ip3'=0) - & (b_ip2'=b_ip3) - & (b_ip1'=b_ip2) - & (b_ip0'=b_ip1); // lose message - - // start sending message to host - [a] b=0 & n0>0 -> (1-loss) : (b'=2) & (ip_mess'=0) & (n0'=n0-1) + loss : (n0'=n0-1); // different ip - [a] b=0 & n1>0 -> (1-loss) : (b'=2) & (ip_mess'=1) & (n1'=n1-1) + loss : (n1'=n1-1); // same ip - - // finish sending message from host - [a] b=1 & ip_mess=0 -> (b'=0) & (z'=0) & (n0'=min(n0+1,B0)) & (ip_mess'=0); - [a] b=1 & ip_mess=1 -> (b'=0) & (z'=0) & (n1'=min(n1+1,B1)) & (ip_mess'=0); - [a] b=1 & ip_mess=2 -> (b'=0) & (z'=0) & (ip_mess'=0); - - // finish sending message to host - [rec0] b=2 & ip_mess=0 -> (b'=0) & (z'=0) & (ip_mess'=0); - [rec1] b=2 & ip_mess=1 -> (b'=0) & (z'=0) & (ip_mess'=0); - [rec2] b=2 & ip_mess=2 -> (b'=0) & (z'=0) & (ip_mess'=0); - -endmodule - -//------------------------------------------------------------- -// CONCRETE HOST -module host0 - - x : clock; // first clock of the host - y : clock; // second clock of the host - - coll : [0..MAXCOLL]; // number of address collisions - probes : [0..K]; // counter (number of probes sent) - mess : [0..1]; // need to send a message or not - defend : [0..1]; // defend (if =1, try to defend IP address) - - ip : [1..2]; // ip address (1 - in use & 2 - fresh) - - l : [0..4] init 1; // location - // 0 : RECONFIGURE - // 1 : RANDOM - // 2 : WAITSP - // 3 : WAITSG - // 4 : USE - - invariant - (l=0 => x<=0) & - (l=1 & coll x<=0) & - (l=1 & coll=MAXCOLL => x<=LONGWAIT) & - (l=2 => x<=CONSEC) & - (l=3 => x<=CONSEC) & - (l=4 => true) - endinvariant - - // needed to prevent environment from moving before a reset - [a] l>0 -> true; - - // RECONFIGURE - [reset] l=0 -> (l'=1); - - // RANDOM (choose IP address) - [rec0] (l=1) -> true; // get message (ignore since have no ip address) - [rec1] (l=1) -> true; // get message (ignore since have no ip address) - [rec2] (l=1) -> true; // get message (ignore since have no ip address) - // small number of collisions (choose straight away) - [] l=1 & coll 1/3*old : (l'=2) & (ip'=1) & (x'=0) - + 1/3*old : (l'=2) & (ip'=1) & (x'=1) - + 1/3*old : (l'=2) & (ip'=1) & (x'=2) - + 1/3*new : (l'=2) & (ip'=2) & (x'=0) - + 1/3*new : (l'=2) & (ip'=2) & (x'=1) - + 1/3*new : (l'=2) & (ip'=2) & (x'=2); - // large number of collisions: (wait for LONGWAIT) - [] l=1 & coll=MAXCOLL & x=LONGWAIT -> 1/3*old : (l'=2) & (ip'=1) & (x'=0) - + 1/3*old : (l'=2) & (ip'=1) & (x'=1) - + 1/3*old : (l'=2) & (ip'=1) & (x'=2) - + 1/3*new : (l'=2) & (ip'=2) & (x'=0) - + 1/3*new : (l'=2) & (ip'=2) & (x'=1) - + 1/3*new : (l'=2) & (ip'=2) & (x'=2); - - // WAITSP - // send probe - [send1] l=2 & ip=1 & probes=2 -> (x'=0) & (probes'=probes+1); - [send2] l=2 & ip=2 & probes=2 -> (x'=0) & (probes'=probes+1); - // sent K probes and waited 2 seconds - [] l=2 & probes=K & x>=2 -> (l'=3) & (probes'=0) & (coll'=0) & (x'=0); - // get message and ip does not match: ignore - [rec0] l=2 & 0!=ip -> (l'=l); - [rec1] l=2 & 1!=ip -> (l'=l); - [rec2] l=2 & 2!=ip -> (l'=l); - // get a message with matching ip: reconfigure - [rec0] l=2 & 0=ip -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0); - [rec1] l=2 & 1=ip -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0); - [rec2] l=2 & 2=ip -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0); - - // receive message and same ip: defend - [rec0] l=3 & mess=0 & 0=ip & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0); - [rec1] l=3 & mess=0 & 1=ip & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0); - [rec2] l=3 & mess=0 & 2=ip & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0); - // receive message and same ip: defer - [rec0] l=3 & mess=0 & 0=ip & (defend=0 | y (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0); - [rec1] l=3 & mess=0 & 1=ip & (defend=0 | y (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0); - [rec2] l=3 & mess=0 & 2=ip & (defend=0 | y (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0); - // receive message and different ip - [rec0] l=3 & mess=0 & 0!=ip -> (l'=l); - [rec1] l=3 & mess=0 & 1!=ip -> (l'=l); - [rec2] l=3 & mess=0 & 2!=ip -> (l'=l); - - // send probe reply or message for defence - [send1] l=3 & mess=1 & ip=1 -> (mess'=0); - [send2] l=3 & mess=1 & ip=2 -> (mess'=0); - // send first gratuitous arp message - [send1] l=3 & mess=0 & probes<1 & ip=1 & x>=CONSEC -> (x'=0) & (probes'=probes+1); - [send2] l=3 & mess=0 & probes<1 & ip=2 & x>=CONSEC -> (x'=0) & (probes'=probes+1); - // send second gratuitous arp message (move to use) - [send1] l=3 & mess=0 & probes=1 & ip=1 & x>=CONSEC -> (l'=4) & (x'=0) & (y'=0) & (probes'=0); - [send2] l=3 & mess=0 & probes=1 & ip=2 & x>=CONSEC -> (l'=4) & (x'=0) & (y'=0) & (probes'=0); - - // USE (only interested in reaching this state so do not need to add anything here) - [] l=4 -> true; - -endmodule - -//------------------------------------------------------------- -rewards "time" - true : 1; -endrewards - -label "done" = l=4; -label "done_error" = l=4 & ip=0; -label "done_fresh" = l=4 & ip=1; - diff --git a/prism-examples/pta/zeroconf/zeroconf-simple.nm b/prism-examples/pta/zeroconf/zeroconf-simple.nm deleted file mode 100644 index 6ebc30bd..00000000 --- a/prism-examples/pta/zeroconf/zeroconf-simple.nm +++ /dev/null @@ -1,79 +0,0 @@ -pta - -module sender - sender : [0..12] init 0; - // 0 - reconf - // 1 used0 - // 2 used1 - // 3 used2 - // 4 used3 - // 5 used_wait - // 6 used_use - // 7 fresh0 - // 8 fresh1 - // 9 fresh2 - // 10 fresh3 - // 11 fresh_wait - // 12 fresh_use - - x : clock; - - invariant - (sender=0 => x<=0) & - (sender>=1 & sender<=10 => x<=20) & - (sender>10 => true) - endinvariant - - // reconfiguring - [] sender=0 ->0.5 : (sender'=1) + 0.5 : (sender'=7); - [recv] sender=1 -> (sender'=0) & (x'=0); - [recv] sender=2 -> (sender'=0) & (x'=0); - [recv] sender=3 -> (sender'=0) & (x'=0); - [recv] sender=4 -> (sender'=0) & (x'=0); - [recv] sender=5 -> (sender'=0) & (x'=0); - [recv] sender=7 -> (sender'=0) & (x'=0); - [recv] sender=8 -> (sender'=0) & (x'=0); - [recv] sender=9 -> (sender'=0) & (x'=0); - [recv] sender=10 -> (sender'=0) & (x'=0); - [recv] sender=11 -> (sender'=0) & (x'=0); - - // sending fresh - [send_used] sender=1 & x>=20 -> (sender'=2) & (x'=0); - [send_used] sender=2 & x>=20 -> (sender'=3) & (x'=0); - [send_used] sender=3 & x>=20 -> (sender'=4) & (x'=0); - [send_used] sender=4 & x>=20 -> (sender'=5) & (x'=0); - // sending used - [send_fresh] sender=7 & x>=20 -> (sender'=8) & (x'=0); - [send_fresh] sender=8 & x>=20 -> (sender'=9) & (x'=0); - [send_fresh] sender=9 & x>=20 -> (sender'=10) & (x'=0); - [send_fresh] sender=10 & x>=20 -> (sender'=11) & (x'=0); - - // finished - [] sender=5 & x>=20 -> (sender'=6) & (x'=0); - [] sender=11 & x>=20 -> (sender'=12) & (x'=0); - [] sender=6 -> (sender'=6); - [] sender=12 -> (sender'=12); - -endmodule - -module environment - - env : [0..2] init 0; - // 0,1,2 - ready,send,reply - - y : clock; - - invariant - (env=0 => true) & - (env>=1 => y<=5) - endinvariant - - [send_fresh] env=0 -> true; - [send_used] env=0 -> 0.1 : (env'=0) & (y'=0) + 0.9 : (env'=1) & (y'=0); - [] env=1 & y>=1 -> 0.1 : (env'=0) & (y'=0) + 0.9 : (env'=2) & (y'=0); - [recv] env=2 & y>=1 -> (env'=0) & (y'=0); - -endmodule - -label "incorrect" = sender=6; -