diff --git a/prism-examples/consensus/.autopp b/prism-examples/consensus/.autopp new file mode 100755 index 00000000..3bdfc864 --- /dev/null +++ b/prism-examples/consensus/.autopp @@ -0,0 +1,8 @@ +#!/bin/csh + +foreach N ( 2 4 6 8 10 ) + echo "Generating for N=$N" + prismpp .coinN.nm.pp $N >! coin"$N".nm + unix2dos coin"$N".nm +end + diff --git a/prism-examples/consensus/.coinN.nm.pp b/prism-examples/consensus/.coinN.nm.pp new file mode 100644 index 00000000..f6e9f252 --- /dev/null +++ b/prism-examples/consensus/.coinN.nm.pp @@ -0,0 +1,63 @@ +#const N# +// COIN FLIPPING PROTOCOL FOR POLYNOMIAL RANDOMIZED CONSENSUS [AH90] +// gxn/dxp 20/11/00 + +mdp + +// constants +const int N=#N#; +const int K; +const int range = 2*(K+1)*N; +const int counter_init = (K+1)*N; +const int left = N; +const int right = 2*(K+1)*N - N; + +// shared coin +global counter : [0..range] init counter_init; + +module process1 + + // program counter + pc1 : [0..3]; + // 0 - flip + // 1 - write + // 2 - check + // 3 - finished + + // local coin + coin1 : [0..1]; + + // flip coin + [] (pc1=0) -> 0.5 : (coin1'=0) & (pc1'=1) + 0.5 : (coin1'=1) & (pc1'=1); + // write tails -1 (reset coin to add regularity) + [] (pc1=1) & (coin1=0) & (counter>0) -> (counter'=counter-1) & (pc1'=2) & (coin1'=0); + // write heads +1 (reset coin to add regularity) + [] (pc1=1) & (coin1=1) & (counter (counter'=counter+1) & (pc1'=2) & (coin1'=0); + // check + // decide tails + [] (pc1=2) & (counter<=left) -> (pc1'=3) & (coin1'=0); + // decide heads + [] (pc1=2) & (counter>=right) -> (pc1'=3) & (coin1'=1); + // flip again + [] (pc1=2) & (counter>left) & (counter (pc1'=0); + // loop (all loop together when done) + [done] (pc1=3) -> (pc1'=3); + +endmodule + +// construct remaining processes through renaming +#for i=2:N# +module process#i# = process1[pc1=pc#i#,coin1=coin#i#] endmodule +#end# + +// labels +label "finished" =#& i=1:N# pc#i#=3 #end#; +label "all_coins_equal_0" =#& i=1:N# coin#i#=0 #end#; +label "all_coins_equal_1" =#& i=1:N# coin#i#=1 #end#; +label "agree" =#& i=1:N-1# coin#i#=coin#i+1# #end#; + +// rewards +rewards "steps" + true : 1; +endrewards + diff --git a/prism-examples/consensus/README b/prism-examples/consensus/README new file mode 100644 index 00000000..c7c43bc2 --- /dev/null +++ b/prism-examples/consensus/README @@ -0,0 +1,11 @@ +This case study is based on the shared coin protocol from the randomised consensus algorithm of Aspnes and Herlihy [AH90]. + +For more information, see: http://www.prismmodelchecker.org/casestudies/consensus_prism.php + +===================================================================================== + +[AH90] +J. Aspnes and M. Herlihy. +Fast randomized consensus using shared memory. +Journal of Algorithms, 15(1):441-460, 1990. + diff --git a/prism-examples/consensus/auto b/prism-examples/consensus/auto new file mode 100755 index 00000000..c24ff296 --- /dev/null +++ b/prism-examples/consensus/auto @@ -0,0 +1,16 @@ +#!/bin/csh + +prism coin2.nm coin.pctl -const K=2,k=10 -m +prism coin2.nm coin.pctl -const K=4,k=10 -m +#prism coin2.nm coin.pctl -const K=8,k=10 -m -maxiters 100000 +#prism coin2.nm coin.pctl -const K=16,k=10 -m -maxiters 100000 + +prism coin4.nm coin.pctl -const K=2,k=10 -m +prism coin4.nm coin.pctl -const K=4,k=10 -m + +#prism coin6.nm coin.pctl -const K=2,k=10 -m + +#prism coin8.nm coin.pctl -const K=2,k=10 -m + +#prism coin10.nm coin.pctl -const K=2,k=10 -m + diff --git a/prism-examples/consensus/coin.pctl b/prism-examples/consensus/coin.pctl new file mode 100644 index 00000000..e26c623e --- /dev/null +++ b/prism-examples/consensus/coin.pctl @@ -0,0 +1,25 @@ +const int k; + +// C1 (with probability 1, all N processes finish the protocol) +// (needs fairness) +P>=1 [ F "finished" ] + +// C2 (minimum probability that the protocol finishes with all coins equal to v) (v=1,2) +// (needs fairness) +// Results are same for v=1 and v=2 by symmetry +// Analytic bound is (K-1)/(2*K) +Pmin=? [ F "finished"&"all_coins_equal_0" ] +Pmin=? [ F "finished"&"all_coins_equal_1" ] + +// Max probability of finishing protocol with coins not all equal +// (no fairness needed since max. probabilities) +Pmax=? [ F "finished"&!"agree" ] + +// Min/max probability of finishing within k steps +Pmin=? [ F<=k "finished" ] +Pmax=? [ F<=k "finished" ] + +// Min/max expected steps to finish +R{"steps"}min=? [ F "finished" ] +R{"steps"}max=? [ F "finished" ] + diff --git a/prism-examples/consensus/coin10.nm b/prism-examples/consensus/coin10.nm new file mode 100644 index 00000000..7ff52a42 --- /dev/null +++ b/prism-examples/consensus/coin10.nm @@ -0,0 +1,68 @@ +// COIN FLIPPING PROTOCOL FOR POLYNOMIAL RANDOMIZED CONSENSUS [AH90] +// gxn/dxp 20/11/00 + +mdp + +// constants +const int N=10; +const int K; +const int range = 2*(K+1)*N; +const int counter_init = (K+1)*N; +const int left = N; +const int right = 2*(K+1)*N - N; + +// shared coin +global counter : [0..range] init counter_init; + +module process1 + + // program counter + pc1 : [0..3]; + // 0 - flip + // 1 - write + // 2 - check + // 3 - finished + + // local coin + coin1 : [0..1]; + + // flip coin + [] (pc1=0) -> 0.5 : (coin1'=0) & (pc1'=1) + 0.5 : (coin1'=1) & (pc1'=1); + // write tails -1 (reset coin to add regularity) + [] (pc1=1) & (coin1=0) & (counter>0) -> (counter'=counter-1) & (pc1'=2) & (coin1'=0); + // write heads +1 (reset coin to add regularity) + [] (pc1=1) & (coin1=1) & (counter (counter'=counter+1) & (pc1'=2) & (coin1'=0); + // check + // decide tails + [] (pc1=2) & (counter<=left) -> (pc1'=3) & (coin1'=0); + // decide heads + [] (pc1=2) & (counter>=right) -> (pc1'=3) & (coin1'=1); + // flip again + [] (pc1=2) & (counter>left) & (counter (pc1'=0); + // loop (all loop together when done) + [done] (pc1=3) -> (pc1'=3); + +endmodule + +// construct remaining processes through renaming +module process2 = process1[pc1=pc2,coin1=coin2] endmodule +module process3 = process1[pc1=pc3,coin1=coin3] endmodule +module process4 = process1[pc1=pc4,coin1=coin4] endmodule +module process5 = process1[pc1=pc5,coin1=coin5] endmodule +module process6 = process1[pc1=pc6,coin1=coin6] endmodule +module process7 = process1[pc1=pc7,coin1=coin7] endmodule +module process8 = process1[pc1=pc8,coin1=coin8] endmodule +module process9 = process1[pc1=pc9,coin1=coin9] endmodule +module process10 = process1[pc1=pc10,coin1=coin10] endmodule + +// labels +label "finished" = pc1=3 & pc2=3 & pc3=3 & pc4=3 & pc5=3 & pc6=3 & pc7=3 & pc8=3 & pc9=3 & pc10=3 ; +label "all_coins_equal_0" = coin1=0 & coin2=0 & coin3=0 & coin4=0 & coin5=0 & coin6=0 & coin7=0 & coin8=0 & coin9=0 & coin10=0 ; +label "all_coins_equal_1" = coin1=1 & coin2=1 & coin3=1 & coin4=1 & coin5=1 & coin6=1 & coin7=1 & coin8=1 & coin9=1 & coin10=1 ; +label "agree" = coin1=coin2 & coin2=coin3 & coin3=coin4 & coin4=coin5 & coin5=coin6 & coin6=coin7 & coin7=coin8 & coin8=coin9 & coin9=coin10 ; + +// rewards +rewards "steps" + true : 1; +endrewards + diff --git a/prism-examples/consensus/coin2.nm b/prism-examples/consensus/coin2.nm new file mode 100644 index 00000000..07ec59e1 --- /dev/null +++ b/prism-examples/consensus/coin2.nm @@ -0,0 +1,60 @@ +// COIN FLIPPING PROTOCOL FOR POLYNOMIAL RANDOMIZED CONSENSUS [AH90] +// gxn/dxp 20/11/00 + +mdp + +// constants +const int N=2; +const int K; +const int range = 2*(K+1)*N; +const int counter_init = (K+1)*N; +const int left = N; +const int right = 2*(K+1)*N - N; + +// shared coin +global counter : [0..range] init counter_init; + +module process1 + + // program counter + pc1 : [0..3]; + // 0 - flip + // 1 - write + // 2 - check + // 3 - finished + + // local coin + coin1 : [0..1]; + + // flip coin + [] (pc1=0) -> 0.5 : (coin1'=0) & (pc1'=1) + 0.5 : (coin1'=1) & (pc1'=1); + // write tails -1 (reset coin to add regularity) + [] (pc1=1) & (coin1=0) & (counter>0) -> (counter'=counter-1) & (pc1'=2) & (coin1'=0); + // write heads +1 (reset coin to add regularity) + [] (pc1=1) & (coin1=1) & (counter (counter'=counter+1) & (pc1'=2) & (coin1'=0); + // check + // decide tails + [] (pc1=2) & (counter<=left) -> (pc1'=3) & (coin1'=0); + // decide heads + [] (pc1=2) & (counter>=right) -> (pc1'=3) & (coin1'=1); + // flip again + [] (pc1=2) & (counter>left) & (counter (pc1'=0); + // loop (all loop together when done) + [done] (pc1=3) -> (pc1'=3); + +endmodule + +// construct remaining processes through renaming +module process2 = process1[pc1=pc2,coin1=coin2] endmodule + +// labels +label "finished" = pc1=3 & pc2=3 ; +label "all_coins_equal_0" = coin1=0 & coin2=0 ; +label "all_coins_equal_1" = coin1=1 & coin2=1 ; +label "agree" = coin1=coin2 ; + +// rewards +rewards "steps" + true : 1; +endrewards + diff --git a/prism-examples/consensus/coin4.nm b/prism-examples/consensus/coin4.nm new file mode 100644 index 00000000..8639b867 --- /dev/null +++ b/prism-examples/consensus/coin4.nm @@ -0,0 +1,62 @@ +// COIN FLIPPING PROTOCOL FOR POLYNOMIAL RANDOMIZED CONSENSUS [AH90] +// gxn/dxp 20/11/00 + +mdp + +// constants +const int N=4; +const int K; +const int range = 2*(K+1)*N; +const int counter_init = (K+1)*N; +const int left = N; +const int right = 2*(K+1)*N - N; + +// shared coin +global counter : [0..range] init counter_init; + +module process1 + + // program counter + pc1 : [0..3]; + // 0 - flip + // 1 - write + // 2 - check + // 3 - finished + + // local coin + coin1 : [0..1]; + + // flip coin + [] (pc1=0) -> 0.5 : (coin1'=0) & (pc1'=1) + 0.5 : (coin1'=1) & (pc1'=1); + // write tails -1 (reset coin to add regularity) + [] (pc1=1) & (coin1=0) & (counter>0) -> (counter'=counter-1) & (pc1'=2) & (coin1'=0); + // write heads +1 (reset coin to add regularity) + [] (pc1=1) & (coin1=1) & (counter (counter'=counter+1) & (pc1'=2) & (coin1'=0); + // check + // decide tails + [] (pc1=2) & (counter<=left) -> (pc1'=3) & (coin1'=0); + // decide heads + [] (pc1=2) & (counter>=right) -> (pc1'=3) & (coin1'=1); + // flip again + [] (pc1=2) & (counter>left) & (counter (pc1'=0); + // loop (all loop together when done) + [done] (pc1=3) -> (pc1'=3); + +endmodule + +// construct remaining processes through renaming +module process2 = process1[pc1=pc2,coin1=coin2] endmodule +module process3 = process1[pc1=pc3,coin1=coin3] endmodule +module process4 = process1[pc1=pc4,coin1=coin4] endmodule + +// labels +label "finished" = pc1=3 & pc2=3 & pc3=3 & pc4=3 ; +label "all_coins_equal_0" = coin1=0 & coin2=0 & coin3=0 & coin4=0 ; +label "all_coins_equal_1" = coin1=1 & coin2=1 & coin3=1 & coin4=1 ; +label "agree" = coin1=coin2 & coin2=coin3 & coin3=coin4 ; + +// rewards +rewards "steps" + true : 1; +endrewards + diff --git a/prism-examples/consensus/coin6.nm b/prism-examples/consensus/coin6.nm new file mode 100644 index 00000000..b373c40d --- /dev/null +++ b/prism-examples/consensus/coin6.nm @@ -0,0 +1,64 @@ +// COIN FLIPPING PROTOCOL FOR POLYNOMIAL RANDOMIZED CONSENSUS [AH90] +// gxn/dxp 20/11/00 + +mdp + +// constants +const int N=6; +const int K; +const int range = 2*(K+1)*N; +const int counter_init = (K+1)*N; +const int left = N; +const int right = 2*(K+1)*N - N; + +// shared coin +global counter : [0..range] init counter_init; + +module process1 + + // program counter + pc1 : [0..3]; + // 0 - flip + // 1 - write + // 2 - check + // 3 - finished + + // local coin + coin1 : [0..1]; + + // flip coin + [] (pc1=0) -> 0.5 : (coin1'=0) & (pc1'=1) + 0.5 : (coin1'=1) & (pc1'=1); + // write tails -1 (reset coin to add regularity) + [] (pc1=1) & (coin1=0) & (counter>0) -> (counter'=counter-1) & (pc1'=2) & (coin1'=0); + // write heads +1 (reset coin to add regularity) + [] (pc1=1) & (coin1=1) & (counter (counter'=counter+1) & (pc1'=2) & (coin1'=0); + // check + // decide tails + [] (pc1=2) & (counter<=left) -> (pc1'=3) & (coin1'=0); + // decide heads + [] (pc1=2) & (counter>=right) -> (pc1'=3) & (coin1'=1); + // flip again + [] (pc1=2) & (counter>left) & (counter (pc1'=0); + // loop (all loop together when done) + [done] (pc1=3) -> (pc1'=3); + +endmodule + +// construct remaining processes through renaming +module process2 = process1[pc1=pc2,coin1=coin2] endmodule +module process3 = process1[pc1=pc3,coin1=coin3] endmodule +module process4 = process1[pc1=pc4,coin1=coin4] endmodule +module process5 = process1[pc1=pc5,coin1=coin5] endmodule +module process6 = process1[pc1=pc6,coin1=coin6] endmodule + +// labels +label "finished" = pc1=3 & pc2=3 & pc3=3 & pc4=3 & pc5=3 & pc6=3 ; +label "all_coins_equal_0" = coin1=0 & coin2=0 & coin3=0 & coin4=0 & coin5=0 & coin6=0 ; +label "all_coins_equal_1" = coin1=1 & coin2=1 & coin3=1 & coin4=1 & coin5=1 & coin6=1 ; +label "agree" = coin1=coin2 & coin2=coin3 & coin3=coin4 & coin4=coin5 & coin5=coin6 ; + +// rewards +rewards "steps" + true : 1; +endrewards + diff --git a/prism-examples/consensus/coin8.nm b/prism-examples/consensus/coin8.nm new file mode 100644 index 00000000..7af13794 --- /dev/null +++ b/prism-examples/consensus/coin8.nm @@ -0,0 +1,66 @@ +// COIN FLIPPING PROTOCOL FOR POLYNOMIAL RANDOMIZED CONSENSUS [AH90] +// gxn/dxp 20/11/00 + +mdp + +// constants +const int N=8; +const int K; +const int range = 2*(K+1)*N; +const int counter_init = (K+1)*N; +const int left = N; +const int right = 2*(K+1)*N - N; + +// shared coin +global counter : [0..range] init counter_init; + +module process1 + + // program counter + pc1 : [0..3]; + // 0 - flip + // 1 - write + // 2 - check + // 3 - finished + + // local coin + coin1 : [0..1]; + + // flip coin + [] (pc1=0) -> 0.5 : (coin1'=0) & (pc1'=1) + 0.5 : (coin1'=1) & (pc1'=1); + // write tails -1 (reset coin to add regularity) + [] (pc1=1) & (coin1=0) & (counter>0) -> (counter'=counter-1) & (pc1'=2) & (coin1'=0); + // write heads +1 (reset coin to add regularity) + [] (pc1=1) & (coin1=1) & (counter (counter'=counter+1) & (pc1'=2) & (coin1'=0); + // check + // decide tails + [] (pc1=2) & (counter<=left) -> (pc1'=3) & (coin1'=0); + // decide heads + [] (pc1=2) & (counter>=right) -> (pc1'=3) & (coin1'=1); + // flip again + [] (pc1=2) & (counter>left) & (counter (pc1'=0); + // loop (all loop together when done) + [done] (pc1=3) -> (pc1'=3); + +endmodule + +// construct remaining processes through renaming +module process2 = process1[pc1=pc2,coin1=coin2] endmodule +module process3 = process1[pc1=pc3,coin1=coin3] endmodule +module process4 = process1[pc1=pc4,coin1=coin4] endmodule +module process5 = process1[pc1=pc5,coin1=coin5] endmodule +module process6 = process1[pc1=pc6,coin1=coin6] endmodule +module process7 = process1[pc1=pc7,coin1=coin7] endmodule +module process8 = process1[pc1=pc8,coin1=coin8] endmodule + +// labels +label "finished" = pc1=3 & pc2=3 & pc3=3 & pc4=3 & pc5=3 & pc6=3 & pc7=3 & pc8=3 ; +label "all_coins_equal_0" = coin1=0 & coin2=0 & coin3=0 & coin4=0 & coin5=0 & coin6=0 & coin7=0 & coin8=0 ; +label "all_coins_equal_1" = coin1=1 & coin2=1 & coin3=1 & coin4=1 & coin5=1 & coin6=1 & coin7=1 & coin8=1 ; +label "agree" = coin1=coin2 & coin2=coin3 & coin3=coin4 & coin4=coin5 & coin5=coin6 & coin6=coin7 & coin7=coin8 ; + +// rewards +rewards "steps" + true : 1; +endrewards + diff --git a/prism-examples/wlan/auto b/prism-examples/wlan/auto index d1a74ccb..745f5a54 100755 --- a/prism-examples/wlan/auto +++ b/prism-examples/wlan/auto @@ -4,9 +4,9 @@ prism wlan0.nm wlan.pctl -const TRANS_TIME_MAX=10,k=2 prism wlan1.nm wlan.pctl -const TRANS_TIME_MAX=10,k=2 prism wlan2.nm wlan.pctl -const TRANS_TIME_MAX=10,k=2 prism wlan3.nm wlan.pctl -const TRANS_TIME_MAX=10,k=2 -prism wlan4.nm wlan.pctl -const TRANS_TIME_MAX=10,k=2 -prism wlan5.nm wlan.pctl -const TRANS_TIME_MAX=10,k=2 -prism wlan6.nm wlan.pctl -const TRANS_TIME_MAX=10,k=2 +#prism wlan4.nm wlan.pctl -const TRANS_TIME_MAX=10,k=2 +#prism wlan5.nm wlan.pctl -const TRANS_TIME_MAX=10,k=2 +#prism wlan6.nm wlan.pctl -const TRANS_TIME_MAX=10,k=2 # probability collide @@ -14,16 +14,16 @@ prism wlan0_collide.nm wlan_collide.pctl -const COL=2,TRANS_TIME_MAX=10,k=2 prism wlan1_collide.nm wlan_collide.pctl -const COL=2,TRANS_TIME_MAX=10,k=2 prism wlan2_collide.nm wlan_collide.pctl -const COL=2,TRANS_TIME_MAX=10,k=2 prism wlan3_collide.nm wlan_collide.pctl -const COL=2,TRANS_TIME_MAX=10,k=2 -prism wlan4_collide.nm wlan_collide.pctl -const COL=2,TRANS_TIME_MAX=10,k=2 -prism wlan5_collide.nm wlan_collide.pctl -const COL=2,TRANS_TIME_MAX=10,k=2 -prism wlan6_collide.nm wlan_collide.pctl -const COL=2,TRANS_TIME_MAX=10,k=2 +#prism wlan4_collide.nm wlan_collide.pctl -const COL=2,TRANS_TIME_MAX=10,k=2 +#prism wlan5_collide.nm wlan_collide.pctl -const COL=2,TRANS_TIME_MAX=10,k=2 +#prism wlan6_collide.nm wlan_collide.pctl -const COL=2,TRANS_TIME_MAX=10,k=2 # time bounded prism wlan0_time_bounded.nm wlan_time_bounded.pctl -const TRANS_TIME_MAX=10,DEADLINE=100 -nopre -m -prop 3 prism wlan1_time_bounded.nm wlan_time_bounded.pctl -const TRANS_TIME_MAX=10,DEADLINE=100 -nopre -m -prop 3 prism wlan2_time_bounded.nm wlan_time_bounded.pctl -const TRANS_TIME_MAX=10,DEADLINE=100 -nopre -m -prop 3 prism wlan3_time_bounded.nm wlan_time_bounded.pctl -const TRANS_TIME_MAX=10,DEADLINE=100 -nopre -m -prop 3 -prism wlan4_time_bounded.nm wlan_time_bounded.pctl -const TRANS_TIME_MAX=10,DEADLINE=100 -nopre -m -prop 3 -prism wlan5_time_bounded.nm wlan_time_bounded.pctl -const TRANS_TIME_MAX=10,DEADLINE=100 -nopre -m -prop 3 -prism wlan6_time_bounded.nm wlan_time_bounded.pctl -const TRANS_TIME_MAX=10,DEADLINE=100 -nopre -m -prop 3 +#prism wlan4_time_bounded.nm wlan_time_bounded.pctl -const TRANS_TIME_MAX=10,DEADLINE=100 -nopre -m -prop 3 +#prism wlan5_time_bounded.nm wlan_time_bounded.pctl -const TRANS_TIME_MAX=10,DEADLINE=100 -nopre -m -prop 3 +#prism wlan6_time_bounded.nm wlan_time_bounded.pctl -const TRANS_TIME_MAX=10,DEADLINE=100 -nopre -m -prop 3