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// Firewire protocol (PTA model)
// dxp/gxn 08/07/09
pta
// 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 = 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;
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 : clock;
y2 : clock;
// clock invariant
invariant
(w12=1 => y2<=delay)
& (w12=2 => y1<=delay)
& (w12=3 => y2<=delay)
& (w12=4 => y1<=delay)
& (w12=5 => y2<=delay)
& (w12=6 => y1<=delay)
& (w12=7 => y1<=delay)
& (w12=8 => y1<=delay)
& (w12=9 => y1<=delay)
endinvariant
// 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);
// 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);
// rec_req_ack
[snd_ack12] w12=2 -> (w12'=2);
[rec_req12] w12=2 -> (w12'=3);
// 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);
// rec_ack_idle
[snd_idle12] w12=4 -> (w12'=4);
[rec_ack12] w12=4 -> (w12'=5);
// 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);
// rec_idle_req
[snd_req12] w12=6 -> (w12'=6);
[rec_idle12] w12=6 -> (w12'=1);
// rec_ack_req
[snd_req12] w12=7 -> (w12'=7);
[rec_ack12] w12=7 -> (w12'=1);
// rec_req_idle
[snd_idle12] w12=8 -> (w12'=8);
[rec_req12] w12=8 -> (w12'=5);
// rec_idle_ack
[snd_ack12] w12=9 -> (w12'=9);
[rec_idle12] w12=9 -> (w12'=3);
endmodule
module node1
// clock for node1
x1 : clock;
// 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
// clock invariant
invariant
(s1=2 => x1<=rc_fast_max)
& (s1=3 => x1<=rc_slow_max)
& (s1=4 => x1<=rc_fast_max)
& (s1=5 => x1<=rc_slow_max)
// urgency:
& (s1=0 => x1<=0)
& (s1=1 => x1<=0)
endinvariant
// 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);
// rec_req_slow
[rec_idle21] s1=3 -> (s1'=5);
[snd_ack12] s1=3 & x1>=rc_slow_min -> (s1'=7) & (x1'=0);
// rec_idle_fast
[rec_req21] s1=4 -> (s1'=2);
[snd_req12] s1=4 & x1>=rc_fast_min -> (s1'=6) & (x1'=0);
// rec_idle_slow
[rec_req21] s1=5 -> (s1'=3);
[snd_req12] s1=5 & x1>=rc_slow_min -> (s1'=6) & (x1'=0);
// 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);
// almost root or almost child (immediate)
// loop in final states to remove deadlock
[loop] s1=7 -> true;
[loop] s1=8 -> true;
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]
endmodule
// labels
label "done" = (s1=8 & s2=7) | (s1=7 & s2=8);
// reward structures
// time
rewards "time"
true : 1;
endrewards
// time nodes sending
rewards "time_sending"
(w12>0 | w21>0) : 1;
endrewards