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Fixed a bug: formulas are now handled (more) correctly. Added some WLAN examples. 

Former-commit-id: 4b87ffc99f
tempestpy_adaptions
dehnert 11 years ago
parent
310a840ad5
commit
a52419652d
12 changed files with 1799 additions and 445 deletions
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  1. 41
      examples/mdp/wlan/wlan0_collide.nm
  2. 221
      examples/mdp/wlan/wlan1_collide.nm
  3. 75
      examples/mdp/wlan/wlan2_collide.nm
  4. 235
      examples/mdp/wlan/wlan3_collide.nm
  5. 252
      examples/mdp/wlan/wlan4_collide.nm
  6. 286
      examples/mdp/wlan/wlan5_collide.nm
  7. 351
      examples/mdp/wlan/wlan6_collide.nm
  8. 1
      examples/mdp/wlan/wlanX_1.cexprop
  9. 1
      examples/mdp/wlan/wlanX_4.cexprop
  10. 1
      examples/mdp/wlan/wlanX_6.cexprop
  11. 6
      src/parser/prismparser/VariableState.cpp

41
examples/mdp/wlan/wlan0_collide.nm
View File

@ -31,9 +31,9 @@ const int MAX_BACKOFF = 0;
// FORMULAE FOR THE CHANNEL
// channel is busy
// formula busy = c1>0 | c2>0;
formula busy = c1>0 | c2>0;
// channel is free
// formula free = c1=0 & c2=0;
formula free = c1=0 & c2=0;
module medium
@ -92,21 +92,21 @@ module station1
bc1 : [0..1];
// SENSE
// let time pass
[time] s1=1 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
[time] s1=1 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// ready to transmit
[] s1=1 & (x1=DIFS | x1=DIFS-1) -> (s1'=8) & (x1'=0);
// found channel busy so wait until free
[] s1=1 & (c1>0 | c2>0) -> (s1'=2) & (x1'=0);
[] s1=1 & busy -> (s1'=2) & (x1'=0);
// WAIT UNTIL FREE BEFORE SETTING BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=2 & (c1>0 | c2>0) -> (s1'=2);
[time] s1=2 & busy -> (s1'=2);
// find that channel is free so check its free for DIFS before setting backoff
[] s1=2 & (c1=0 & c2=0) -> (s1'=3);
[] s1=2 & free -> (s1'=3);
// WAIT FOR DIFS THEN SET BACKOFF
// let time pass
[time] s1=3 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
[time] s1=3 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// found channel busy so wait until free
[] s1=3 & (c1>0 | c2>0) -> (s1'=2) & (x1'=0);
[] s1=3 & busy -> (s1'=2) & (x1'=0);
// start backoff first uniformly choose slot
// backoff counter 0
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=0 -> (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF));
@ -130,27 +130,27 @@ module station1
+ 1/16 : (s1'=5) & (backoff1'=15);
// BACKOFF
// let time pass
[time] s1=5 & x1<ASLOTTIME & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
[time] s1=5 & x1<ASLOTTIME & free -> (x1'=min(x1+1,TIME_MAX));
// decrement backoff
[] s1=5 & x1=ASLOTTIME & backoff1>0 -> (s1'=5) & (x1'=0) & (backoff1'=backoff1-1);
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1>0 -> (s1'=5) & (x1'=0) & (backoff1'=15) & (slot1'=slot1-1);
// finish backoff
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1=0 -> (s1'=8) & (x1'=0);
// found channel busy
[] s1=5 & (c1>0 | c2>0) -> (s1'=6) & (x1'=0);
[] s1=5 & busy -> (s1'=6) & (x1'=0);
// WAIT UNTIL FREE IN BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=6 & (c1>0 | c2>0) -> (s1'=6);
[time] s1=6 & busy -> (s1'=6);
// find that channel is free
[] s1=6 & (c1=0 & c2=0) -> (s1'=7);
[] s1=6 & free -> (s1'=7);
// WAIT FOR DIFS THEN RESUME BACKOFF
// let time pass
[time] s1=7 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
[time] s1=7 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// resume backoff (start again from previous backoff)
[] s1=7 & (x1=DIFS | x1=DIFS-1) -> (s1'=5) & (x1'=0);
// found channel busy
[] s1=7 & (c1>0 | c2>0) -> (s1'=6) & (x1'=0);
[] s1=7 & busy -> (s1'=6) & (x1'=0);
// VULNERABLE
// let time pass
@ -168,14 +168,14 @@ module station1
// WAIT FOR SIFS i.e. c1=0
// check channel and busy: go into backoff
[] s1=10 & c1=0 & x1=0 & (c1>0 | c2>0) -> (s1'=2);
[] s1=10 & c1=0 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=10 & c1=0 & x1=0 & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
[time] s1=10 & c1=0 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
// following guard is always false as SIFS=1
// [time] s1=10 & c1=0 & x1>0 & x1<SIFS -> (x1'=min(x1+1,TIME_MAX));
// ack is sent after SIFS (since SIFS-1=0 add condition that channel is free)
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & (c1=0 & c2=0))) -> (s1'=10) & (x1'=0);
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & free)) -> (s1'=10) & (x1'=0);
// WAIT FOR ACK i.e. c1=1
// let time pass
@ -185,9 +185,9 @@ module station1
// WAIT FOR ACK_TO
// check channel and busy: go into backoff
[] s1=11 & x1=0 & (c1>0 | c2>0) -> (s1'=2);
[] s1=11 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=11 & x1=0 & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
[time] s1=11 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
[time] s1=11 & x1>0 & x1<ACK_TO -> (x1'=min(x1+1,TIME_MAX));
// no acknowledgement (go to backoff waiting DIFS first)
@ -214,5 +214,6 @@ station2=station1[x1=x2,
endmodule
// ---------------------------------------------------------------------------- //
label "oneCollision" = col=1;
label "twoCollisions" = col=2;
label "fourCollisions" = col=4;
label "sixCollisions" = col=6;

221
examples/mdp/wlan/wlan1_collide.nm
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@ -0,0 +1,221 @@
// WLAN PROTOCOL (two stations)
// discrete time model
// gxn/jzs 20/02/02
mdp
// COLLISIONS
const int COL; // maximum number of collisions
// TIMING CONSTRAINTS
// we have used the FHSS parameters
// then scaled by the value of ASLOTTIME
const int ASLOTTIME = 1;
const int DIFS = 3; // due to scaling can be either 2 or 3 which is modelled by a non-deterministic choice
const int VULN = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
const int TRANS_TIME_MAX; // scaling up
const int TRANS_TIME_MIN = 4; // scaling down
const int ACK_TO = 6;
const int ACK = 4; // due to scaling can be either 3 or 4 which is modelled by a non-deterministic choice
const int SIFS = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
// maximum constant used in timing constraints + 1
const int TIME_MAX = max(ACK_TO,TRANS_TIME_MAX)+1;
// CONTENTION WINDOW
// CWMIN =15 & CWMAX =31
// this means that MAX_BACKOFF IS 2
const int MAX_BACKOFF = 1;
//-----------------------------------------------------------------//
// THE MEDIUM/CHANNEL
// FORMULAE FOR THE CHANNEL
// channel is busy
formula busy = c1>0 | c2>0;
// channel is free
formula free = c1=0 & c2=0;
module medium
// number of collisions
col : [0..COL];
// medium status
c1 : [0..2];
c2 : [0..2];
// ci corresponds to messages associated with station i
// 0 nothing being sent
// 1 being sent correctly
// 2 being sent garbled
// begin sending message and nothing else currently being sent
[send1] c1=0 & c2=0 -> (c1'=1);
[send2] c2=0 & c1=0 -> (c2'=1);
// begin sending message and something is already being sent
// in this case both messages become garbled
[send1] c1=0 & c2>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
[send2] c2=0 & c1>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
// finish sending message
[finish1] c1>0 -> (c1'=0);
[finish2] c2>0 -> (c2'=0);
endmodule
//-----------------------------------------------------------------//
// STATION 1
module station1
// clock for station 1
x1 : [0..TIME_MAX];
// local state
s1 : [1..12];
// 1 sense
// 2 wait until free before setting backoff
// 3 wait for DIFS then set slot
// 4 set backoff
// 5 backoff
// 6 wait until free in backoff
// 7 wait for DIFS then resume backoff
// 8 vulnerable
// 9 transmit
// 11 wait for SIFS and then ACK
// 10 wait for ACT_TO
// 12 done
// BACKOFF
// separate into slots
slot1 : [0..1];
backoff1 : [0..15];
// BACKOFF COUNTER
bc1 : [0..MAX_BACKOFF];
// SENSE
// let time pass
[time] s1=1 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// ready to transmit
[] s1=1 & (x1=DIFS | x1=DIFS-1) -> (s1'=8) & (x1'=0);
// found channel busy so wait until free
[] s1=1 & busy -> (s1'=2) & (x1'=0);
// WAIT UNTIL FREE BEFORE SETTING BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=2 & busy -> (s1'=2);
// find that channel is free so check its free for DIFS before setting backoff
[] s1=2 & free -> (s1'=3);
// WAIT FOR DIFS THEN SET BACKOFF
// let time pass
[time] s1=3 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// found channel busy so wait until free
[] s1=3 & busy -> (s1'=2) & (x1'=0);
// start backoff first uniformly choose slot
// backoff counter 0
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=0 -> (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 1
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=1 -> 1/2 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/2 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF));
// SET BACKOFF (no time can pass)
// chosen slot now set backoff
[] s1=4 -> 1/16 : (s1'=5) & (backoff1'=0 )
+ 1/16 : (s1'=5) & (backoff1'=1 )
+ 1/16 : (s1'=5) & (backoff1'=2 )
+ 1/16 : (s1'=5) & (backoff1'=3 )
+ 1/16 : (s1'=5) & (backoff1'=4 )
+ 1/16 : (s1'=5) & (backoff1'=5 )
+ 1/16 : (s1'=5) & (backoff1'=6 )
+ 1/16 : (s1'=5) & (backoff1'=7 )
+ 1/16 : (s1'=5) & (backoff1'=8 )
+ 1/16 : (s1'=5) & (backoff1'=9 )
+ 1/16 : (s1'=5) & (backoff1'=10)
+ 1/16 : (s1'=5) & (backoff1'=11)
+ 1/16 : (s1'=5) & (backoff1'=12)
+ 1/16 : (s1'=5) & (backoff1'=13)
+ 1/16 : (s1'=5) & (backoff1'=14)
+ 1/16 : (s1'=5) & (backoff1'=15);
// BACKOFF
// let time pass
[time] s1=5 & x1<ASLOTTIME & free -> (x1'=min(x1+1,TIME_MAX));
// decrement backoff
[] s1=5 & x1=ASLOTTIME & backoff1>0 -> (s1'=5) & (x1'=0) & (backoff1'=backoff1-1);
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1>0 -> (s1'=5) & (x1'=0) & (backoff1'=15) & (slot1'=slot1-1);
// finish backoff
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1=0 -> (s1'=8) & (x1'=0);
// found channel busy
[] s1=5 & busy -> (s1'=6) & (x1'=0);
// WAIT UNTIL FREE IN BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=6 & busy -> (s1'=6);
// find that channel is free
[] s1=6 & free -> (s1'=7);
// WAIT FOR DIFS THEN RESUME BACKOFF
// let time pass
[time] s1=7 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// resume backoff (start again from previous backoff)
[] s1=7 & (x1=DIFS | x1=DIFS-1) -> (s1'=5) & (x1'=0);
// found channel busy
[] s1=7 & busy -> (s1'=6) & (x1'=0);
// VULNERABLE
// let time pass
[time] s1=8 & x1<VULN -> (x1'=min(x1+1,TIME_MAX));
// move to transmit
[send1] s1=8 & (x1=VULN | x1=VULN-1) -> (s1'=9) & (x1'=0);
// TRANSMIT
// let time pass
[time] s1=9 & x1<TRANS_TIME_MAX -> (x1'=min(x1+1,TIME_MAX));
// finish transmission successful
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=1 -> (s1'=10) & (x1'=0);
// finish transmission garbled
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=2 -> (s1'=11) & (x1'=0);
// WAIT FOR SIFS THEN WAIT FOR ACK
// WAIT FOR SIFS i.e. c1=0
// check channel and busy: go into backoff
[] s1=10 & c1=0 & x1=0 & busy -> (s1'=2);
// chEck channel and free: let time pass
[time] s1=10 & c1=0 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
// following guard is always false as SIFS=1
// [time] s1=10 & c1=0 & x1>0 & x1<SIFS -> (x1'=min(x1+1,TIME_MAX));
// ack is sent after SIFS (since SIFS-1=0 add condition that channel is free)
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & free)) -> (s1'=10) & (x1'=0);
// WAIT FOR ACK i.e. c1=1
// let time pass
[time] s1=10 & c1=1 & x1<ACK -> (x1'=min(x1+1,TIME_MAX));
// get acknowledgement so packet sent correctly and move to done
[finish1] s1=10 & c1=1 & (x1=ACK | x1=ACK-1) -> (s1'=12) & (x1'=0) & (bc1'=0);
// WAIT FOR ACK_TO
// check channel and busy: go into backoff
[] s1=11 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=11 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
[time] s1=11 & x1>0 & x1<ACK_TO -> (x1'=min(x1+1,TIME_MAX));
// no acknowledgement (go to backoff waiting DIFS first)
[] s1=11 & x1=ACK_TO -> (s1'=3) & (x1'=0);
// DONE
[time] s1=12 -> (s1'=12);
endmodule
// ---------------------------------------------------------------------------- //
// STATION 2 (rename STATION 1)
module
station2=station1[x1=x2,
s1=s2,
s2=s1,
c1=c2,
c2=c1,
slot1=slot2,
backoff1=backoff2,
bc1=bc2,
send1=send2,
finish1=finish2]
endmodule
// ---------------------------------------------------------------------------- //
label "twoCollisions" = col=2;
label "fourCollisions" = col=4;
label "sixCollisions" = col=6;

75
examples/mdp/wlan/wlan2_collide.nm
View File

@ -30,10 +30,10 @@ const int MAX_BACKOFF = 2;
// THE MEDIUM/CHANNEL
// FORMULAE FOR THE CHANNEL
// channel is (c1>0 | c2>0)
// formula busy = c1>0 | c2>0;
// channel is (c1=0 & c2=0)
// formula free = c1=0 & c2=0;
// channel is busy
formula busy = c1>0 | c2>0;
// channel is free
formula free = c1=0 & c2=0;
module medium
@ -72,11 +72,11 @@ module station1
// local state
s1 : [1..12];
// 1 sense
// 2 wait until (c1=0 & c2=0) before setting backoff
// 2 wait until free before setting backoff
// 3 wait for DIFS then set slot
// 4 set backoff
// 5 backoff
// 6 wait until (c1=0 & c2=0) in backoff
// 6 wait until free in backoff
// 7 wait for DIFS then resume backoff
// 8 vulnerable
// 9 transmit
@ -92,21 +92,21 @@ module station1
bc1 : [0..MAX_BACKOFF];
// SENSE
// let time pass
[time] s1=1 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
[time] s1=1 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// ready to transmit
[] s1=1 & (x1=DIFS | x1=DIFS-1) -> (s1'=8) & (x1'=0);
// found channel (c1>0 | c2>0) so wait until (c1=0 & c2=0)
[] s1=1 & (c1>0 | c2>0) -> (s1'=2) & (x1'=0);
// WAIT UNTIL (c1=0 & c2=0) BEFORE SETTING BACKOFF
// found channel busy so wait until free
[] s1=1 & busy -> (s1'=2) & (x1'=0);
// WAIT UNTIL FREE BEFORE SETTING BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=2 & (c1>0 | c2>0) -> (s1'=2);
// find that channel is (c1=0 & c2=0) so check its (c1=0 & c2=0) for DIFS before setting backoff
[] s1=2 & (c1=0 & c2=0) -> (s1'=3);
[time] s1=2 & busy -> (s1'=2);
// find that channel is free so check its free for DIFS before setting backoff
[] s1=2 & free -> (s1'=3);
// WAIT FOR DIFS THEN SET BACKOFF
// let time pass
[time] s1=3 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// found channel (c1>0 | c2>0) so wait until (c1=0 & c2=0)
[] s1=3 & (c1>0 | c2>0) -> (s1'=2) & (x1'=0);
[time] s1=3 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// found channel busy so wait until free
[] s1=3 & busy -> (s1'=2) & (x1'=0);
// start backoff first uniformly choose slot
// backoff counter 0
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=0 -> (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF));
@ -138,27 +138,27 @@ module station1
+ 1/16 : (s1'=5) & (backoff1'=15);
// BACKOFF
// let time pass
[time] s1=5 & x1<ASLOTTIME & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
[time] s1=5 & x1<ASLOTTIME & free -> (x1'=min(x1+1,TIME_MAX));
// decrement backoff
[] s1=5 & x1=ASLOTTIME & backoff1>0 -> (s1'=5) & (x1'=0) & (backoff1'=backoff1-1);
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1>0 -> (s1'=5) & (x1'=0) & (backoff1'=15) & (slot1'=slot1-1);
// finish backoff
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1=0 -> (s1'=8) & (x1'=0);
// found channel (c1>0 | c2>0)
[] s1=5 & (c1>0 | c2>0) -> (s1'=6) & (x1'=0);
// WAIT UNTIL (c1=0 & c2=0) IN BACKOFF
// found channel busy
[] s1=5 & busy -> (s1'=6) & (x1'=0);
// WAIT UNTIL FREE IN BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=6 & (c1>0 | c2>0) -> (s1'=6);
// find that channel is (c1=0 & c2=0)
[] s1=6 & (c1=0 & c2=0) -> (s1'=7);
[time] s1=6 & busy -> (s1'=6);
// find that channel is free
[] s1=6 & free -> (s1'=7);
// WAIT FOR DIFS THEN RESUME BACKOFF
// let time pass
[time] s1=7 & x1<DIFS & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
[time] s1=7 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// resume backoff (start again from previous backoff)
[] s1=7 & (x1=DIFS | x1=DIFS-1) -> (s1'=5) & (x1'=0);
// found channel (c1>0 | c2>0)
[] s1=7 & (c1>0 | c2>0) -> (s1'=6) & (x1'=0);
// found channel busy
[] s1=7 & busy -> (s1'=6) & (x1'=0);
// VULNERABLE
// let time pass
@ -175,15 +175,15 @@ module station1
// WAIT FOR SIFS THEN WAIT FOR ACK
// WAIT FOR SIFS i.e. c1=0
// check channel and (c1>0 | c2>0): go into backoff
[] s1=10 & c1=0 & x1=0 & (c1>0 | c2>0) -> (s1'=2);
// check channel and (c1=0 & c2=0): let time pass
[time] s1=10 & c1=0 & x1=0 & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// check channel and busy: go into backoff
[] s1=10 & c1=0 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=10 & c1=0 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
// following guard is always false as SIFS=1
// [time] s1=10 & c1=0 & x1>0 & x1<SIFS -> (x1'=min(x1+1,TIME_MAX));
// ack is sent after SIFS (since SIFS-1=0 add condition that channel is (c1=0 & c2=0))
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & (c1=0 & c2=0))) -> (s1'=10) & (x1'=0);
// ack is sent after SIFS (since SIFS-1=0 add condition that channel is free)
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & free)) -> (s1'=10) & (x1'=0);
// WAIT FOR ACK i.e. c1=1
// let time pass
@ -192,10 +192,10 @@ module station1
[finish1] s1=10 & c1=1 & (x1=ACK | x1=ACK-1) -> (s1'=12) & (x1'=0) & (bc1'=0);
// WAIT FOR ACK_TO
// check channel and (c1>0 | c2>0): go into backoff
[] s1=11 & x1=0 & (c1>0 | c2>0) -> (s1'=2);
// check channel and (c1=0 & c2=0): let time pass
[time] s1=11 & x1=0 & (c1=0 & c2=0) -> (x1'=min(x1+1,TIME_MAX));
// check channel and busy: go into backoff
[] s1=11 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=11 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
[time] s1=11 & x1>0 & x1<ACK_TO -> (x1'=min(x1+1,TIME_MAX));
// no acknowledgement (go to backoff waiting DIFS first)
@ -221,5 +221,6 @@ station2=station1[x1=x2,
endmodule
// ---------------------------------------------------------------------------- //
label "oneCollision" = col=1;
label "twoCollisions" = col=2;
label "fourCollisions" = col=4;
label "sixCollisions" = col=6;

235
examples/mdp/wlan/wlan3_collide.nm
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@ -0,0 +1,235 @@
// WLAN PROTOCOL (two stations)
// discrete time model
// gxn/jzs 20/02/02
mdp
// COLLISIONS
const int COL; // maximum number of collisions
// TIMING CONSTRAINTS
// we have used the FHSS parameters
// then scaled by the value of ASLOTTIME
const int ASLOTTIME = 1;
const int DIFS = 3; // due to scaling can be either 2 or 3 which is modelled by a non-deterministic choice
const int VULN = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
const int TRANS_TIME_MAX; // scaling up
const int TRANS_TIME_MIN = 4; // scaling down
const int ACK_TO = 6;
const int ACK = 4; // due to scaling can be either 3 or 4 which is modelled by a non-deterministic choice
const int SIFS = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
// maximum constant used in timing constraints + 1
const int TIME_MAX = max(ACK_TO,TRANS_TIME_MAX)+1;
// CONTENTION WINDOW
// CWMIN =15 & CWMAX =127
// this means that MAX_BACKOFF IS 3
const int MAX_BACKOFF = 3;
//-----------------------------------------------------------------//
// THE MEDIUM/CHANNEL
// FORMULAE FOR THE CHANNEL
// channel is busy
formula busy = c1>0 | c2>0;
// channel is free
formula free = c1=0 & c2=0;
module medium
// number of collisions
col : [0..COL];
// medium status
c1 : [0..2];
c2 : [0..2];
// ci corresponds to messages associated with station i
// 0 nothing being sent
// 1 being sent correctly
// 2 being sent garbled
// begin sending message and nothing else currently being sent
[send1] c1=0 & c2=0 -> (c1'=1);
[send2] c2=0 & c1=0 -> (c2'=1);
// begin sending message and something is already being sent
// in this case both messages become garbled
[send1] c1=0 & c2>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
[send2] c2=0 & c1>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
// finish sending message
[finish1] c1>0 -> (c1'=0);
[finish2] c2>0 -> (c2'=0);
endmodule
//-----------------------------------------------------------------//
// STATION 1
module station1
// clock for station 1
x1 : [0..TIME_MAX];
// local state
s1 : [1..12];
// 1 sense
// 2 wait until free before setting backoff
// 3 wait for DIFS then set slot
// 4 set backoff
// 5 backoff
// 6 wait until free in backoff
// 7 wait for DIFS then resume backoff
// 8 vulnerable
// 9 transmit
// 11 wait for SIFS and then ACK
// 10 wait for ACT_TO
// 12 done
// BACKOFF
// separate into slots
slot1 : [0..7];
backoff1 : [0..15];
// BACKOFF COUNTER
bc1 : [0..MAX_BACKOFF];
// SENSE
// let time pass
[time] s1=1 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// ready to transmit
[] s1=1 & (x1=DIFS | x1=DIFS-1) -> (s1'=8) & (x1'=0);
// found channel busy so wait until free
[] s1=1 & busy -> (s1'=2) & (x1'=0);
// WAIT UNTIL FREE BEFORE SETTING BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=2 & busy -> (s1'=2);
// find that channel is free so check its free for DIFS before setting backoff
[] s1=2 & free -> (s1'=3);
// WAIT FOR DIFS THEN SET BACKOFF
// let time pass
[time] s1=3 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// found channel busy so wait until free
[] s1=3 & busy -> (s1'=2) & (x1'=0);
// start backoff first uniformly choose slot
// backoff counter 0
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=0 -> (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 1
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=1 -> 1/2 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/2 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 2
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=2 -> 1/4 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 3
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=3 -> 1/8 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=4) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=5) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=6) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=7) & (bc1'=min(bc1+1,MAX_BACKOFF));
// SET BACKOFF (no time can pass)
// chosen slot now set backoff
[] s1=4 -> 1/16 : (s1'=5) & (backoff1'=0 )
+ 1/16 : (s1'=5) & (backoff1'=1 )
+ 1/16 : (s1'=5) & (backoff1'=2 )
+ 1/16 : (s1'=5) & (backoff1'=3 )
+ 1/16 : (s1'=5) & (backoff1'=4 )
+ 1/16 : (s1'=5) & (backoff1'=5 )
+ 1/16 : (s1'=5) & (backoff1'=6 )
+ 1/16 : (s1'=5) & (backoff1'=7 )
+ 1/16 : (s1'=5) & (backoff1'=8 )
+ 1/16 : (s1'=5) & (backoff1'=9 )
+ 1/16 : (s1'=5) & (backoff1'=10)
+ 1/16 : (s1'=5) & (backoff1'=11)
+ 1/16 : (s1'=5) & (backoff1'=12)
+ 1/16 : (s1'=5) & (backoff1'=13)
+ 1/16 : (s1'=5) & (backoff1'=14)
+ 1/16 : (s1'=5) & (backoff1'=15);
// BACKOFF
// let time pass
[time] s1=5 & x1<ASLOTTIME & free -> (x1'=min(x1+1,TIME_MAX));
// decrement backoff
[] s1=5 & x1=ASLOTTIME & backoff1>0 -> (s1'=5) & (x1'=0) & (backoff1'=backoff1-1);
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1>0 -> (s1'=5) & (x1'=0) & (backoff1'=15) & (slot1'=slot1-1);
// finish backoff
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1=0 -> (s1'=8) & (x1'=0);
// found channel busy
[] s1=5 & busy -> (s1'=6) & (x1'=0);
// WAIT UNTIL FREE IN BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=6 & busy -> (s1'=6);
// find that channel is free
[] s1=6 & free -> (s1'=7);
// WAIT FOR DIFS THEN RESUME BACKOFF
// let time pass
[time] s1=7 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// resume backoff (start again from previous backoff)
[] s1=7 & (x1=DIFS | x1=DIFS-1) -> (s1'=5) & (x1'=0);
// found channel busy
[] s1=7 & busy -> (s1'=6) & (x1'=0);
// VULNERABLE
// let time pass
[time] s1=8 & x1<VULN -> (x1'=min(x1+1,TIME_MAX));
// move to transmit
[send1] s1=8 & (x1=VULN | x1=VULN-1) -> (s1'=9) & (x1'=0);
// TRANSMIT
// let time pass
[time] s1=9 & x1<TRANS_TIME_MAX -> (x1'=min(x1+1,TIME_MAX));
// finish transmission successful
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=1 -> (s1'=10) & (x1'=0);
// finish transmission garbled
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=2 -> (s1'=11) & (x1'=0);
// WAIT FOR SIFS THEN WAIT FOR ACK
// WAIT FOR SIFS i.e. c1=0
// check channel and busy: go into backoff
[] s1=10 & c1=0 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=10 & c1=0 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
// following guard is always false as SIFS=1
// [time] s1=10 & c1=0 & x1>0 & x1<SIFS -> (x1'=min(x1+1,TIME_MAX));
// ack is sent after SIFS (since SIFS-1=0 add condition that channel is free)
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & free)) -> (s1'=10) & (x1'=0);
// WAIT FOR ACK i.e. c1=1
// let time pass
[time] s1=10 & c1=1 & x1<ACK -> (x1'=min(x1+1,TIME_MAX));
// get acknowledgement so packet sent correctly and move to done
[finish1] s1=10 & c1=1 & (x1=ACK | x1=ACK-1) -> (s1'=12) & (x1'=0) & (bc1'=0);
// WAIT FOR ACK_TO
// check channel and busy: go into backoff
[] s1=11 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=11 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
[time] s1=11 & x1>0 & x1<ACK_TO -> (x1'=min(x1+1,TIME_MAX));
// no acknowledgement (go to backoff waiting DIFS first)
[] s1=11 & x1=ACK_TO -> (s1'=3) & (x1'=0);
// DONE
[time] s1=12 -> (s1'=12);
endmodule
// ---------------------------------------------------------------------------- //
// STATION 2 (rename STATION 1)
module
station2=station1[x1=x2,
s1=s2,
s2=s1,
c1=c2,
c2=c1,
slot1=slot2,
backoff1=backoff2,
bc1=bc2,
send1=send2,
finish1=finish2]
endmodule
// ---------------------------------------------------------------------------- //
label "twoCollisions" = col=2;
label "fourCollisions" = col=4;
label "sixCollisions" = col=6;

252
examples/mdp/wlan/wlan4_collide.nm
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@ -0,0 +1,252 @@
// WLAN PROTOCOL (two stations)
// discrete time model
// gxn/jzs 20/02/02
mdp
// COLLISIONS
const int COL; // maximum number of collisions
// TIMING CONSTRAINTS
// we have used the FHSS parameters
// then scaled by the value of ASLOTTIME
const int ASLOTTIME = 1;
const int DIFS = 3; // due to scaling can be either 2 or 3 which is modelled by a non-deterministic choice
const int VULN = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
const int TRANS_TIME_MAX; // scaling up
const int TRANS_TIME_MIN = 4; // scaling down
const int ACK_TO = 6;
const int ACK = 4; // due to scaling can be either 3 or 4 which is modelled by a non-deterministic choice
const int SIFS = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
// maximum constant used in timing constraints + 1
const int TIME_MAX = max(ACK_TO,TRANS_TIME_MAX)+1;
// CONTENTION WINDOW
// CWMIN =15 & CWMAX =255
// this means that MAX_BACKOFF IS 4
const int MAX_BACKOFF = 4;
//-----------------------------------------------------------------//
// THE MEDIUM/CHANNEL
// FORMULAE FOR THE CHANNEL
// channel is busy
formula busy = c1>0 | c2>0;
// channel is free
formula free = c1=0 & c2=0;
module medium
// number of collisions
col : [0..COL];
// medium status
c1 : [0..2];
c2 : [0..2];
// ci corresponds to messages associated with station i
// 0 nothing being sent
// 1 being sent correctly
// 2 being sent garbled
// begin sending message and nothing else currently being sent
[send1] c1=0 & c2=0 -> (c1'=1);
[send2] c2=0 & c1=0 -> (c2'=1);
// begin sending message and something is already being sent
// in this case both messages become garbled
[send1] c1=0 & c2>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
[send2] c2=0 & c1>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
// finish sending message
[finish1] c1>0 -> (c1'=0);
[finish2] c2>0 -> (c2'=0);
endmodule
//-----------------------------------------------------------------//
// STATION 1
module station1
// clock for station 1
x1 : [0..TIME_MAX];
// local state
s1 : [1..12];
// 1 sense
// 2 wait until free before setting backoff
// 3 wait for DIFS then set slot
// 4 set backoff
// 5 backoff
// 6 wait until free in backoff
// 7 wait for DIFS then resume backoff
// 8 vulnerable
// 9 transmit
// 11 wait for SIFS and then ACK
// 10 wait for ACT_TO
// 12 done
// BACKOFF
// separate into slots
slot1 : [0..15];
backoff1 : [0..15];
// BACKOFF COUNTER
bc1 : [0..MAX_BACKOFF];
// SENSE
// let time pass
[time] s1=1 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// ready to transmit
[] s1=1 & (x1=DIFS | x1=DIFS-1) -> (s1'=8) & (x1'=0);
// found channel busy so wait until free
[] s1=1 & busy -> (s1'=2) & (x1'=0);
// WAIT UNTIL FREE BEFORE SETTING BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=2 & busy -> (s1'=2);
// find that channel is free so check its free for DIFS before setting backoff
[] s1=2 & free -> (s1'=3);
// WAIT FOR DIFS THEN SET BACKOFF
// let time pass
[time] s1=3 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// found channel busy so wait until free
[] s1=3 & busy -> (s1'=2) & (x1'=0);
// start backoff first uniformly choose slot
// backoff counter 0
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=0 -> (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 1
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=1 -> 1/2 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/2 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 2
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=2 -> 1/4 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 3
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=3 -> 1/8 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=4) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=5) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=6) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=7) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 4
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=4 -> 1/16 : (s1'=4) & (x1'=0) & (slot1'=0 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=1 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=2 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=3 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=4 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=5 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=6 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=7 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=8 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=9 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=10) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=11) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=12) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=13) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=14) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=15) & (bc1'=min(bc1+1,MAX_BACKOFF));
// SET BACKOFF (no time can pass)
// chosen slot now set backoff
[] s1=4 -> 1/16 : (s1'=5) & (backoff1'=0 )
+ 1/16 : (s1'=5) & (backoff1'=1 )
+ 1/16 : (s1'=5) & (backoff1'=2 )
+ 1/16 : (s1'=5) & (backoff1'=3 )
+ 1/16 : (s1'=5) & (backoff1'=4 )
+ 1/16 : (s1'=5) & (backoff1'=5 )
+ 1/16 : (s1'=5) & (backoff1'=6 )
+ 1/16 : (s1'=5) & (backoff1'=7 )
+ 1/16 : (s1'=5) & (backoff1'=8 )
+ 1/16 : (s1'=5) & (backoff1'=9 )
+ 1/16 : (s1'=5) & (backoff1'=10)
+ 1/16 : (s1'=5) & (backoff1'=11)
+ 1/16 : (s1'=5) & (backoff1'=12)
+ 1/16 : (s1'=5) & (backoff1'=13)
+ 1/16 : (s1'=5) & (backoff1'=14)
+ 1/16 : (s1'=5) & (backoff1'=15);
// BACKOFF
// let time pass
[time] s1=5 & x1<ASLOTTIME & free -> (x1'=min(x1+1,TIME_MAX));
// decrement backoff
[] s1=5 & x1=ASLOTTIME & backoff1>0 -> (s1'=5) & (x1'=0) & (backoff1'=backoff1-1);
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1>0 -> (s1'=5) & (x1'=0) & (backoff1'=15) & (slot1'=slot1-1);
// finish backoff
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1=0 -> (s1'=8) & (x1'=0);
// found channel busy
[] s1=5 & busy -> (s1'=6) & (x1'=0);
// WAIT UNTIL FREE IN BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=6 & busy -> (s1'=6);
// find that channel is free
[] s1=6 & free -> (s1'=7);
// WAIT FOR DIFS THEN RESUME BACKOFF
// let time pass
[time] s1=7 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// resume backoff (start again from previous backoff)
[] s1=7 & (x1=DIFS | x1=DIFS-1) -> (s1'=5) & (x1'=0);
// found channel busy
[] s1=7 & busy -> (s1'=6) & (x1'=0);
// VULNERABLE
// let time pass
[time] s1=8 & x1<VULN -> (x1'=min(x1+1,TIME_MAX));
// move to transmit
[send1] s1=8 & (x1=VULN | x1=VULN-1) -> (s1'=9) & (x1'=0);
// TRANSMIT
// let time pass
[time] s1=9 & x1<TRANS_TIME_MAX -> (x1'=min(x1+1,TIME_MAX));
// finish transmission successful
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=1 -> (s1'=10) & (x1'=0);
// finish transmission garbled
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=2 -> (s1'=11) & (x1'=0);
// WAIT FOR SIFS THEN WAIT FOR ACK
// WAIT FOR SIFS i.e. c1=0
// check channel and busy: go into backoff
[] s1=10 & c1=0 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=10 & c1=0 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
// following guard is always false as SIFS=1
// [time] s1=10 & c1=0 & x1>0 & x1<SIFS -> (x1'=min(x1+1,TIME_MAX));
// ack is sent after SIFS (since SIFS-1=0 add condition that channel is free)
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & free)) -> (s1'=10) & (x1'=0);
// WAIT FOR ACK i.e. c1=1
// let time pass
[time] s1=10 & c1=1 & x1<ACK -> (x1'=min(x1+1,TIME_MAX));
// get acknowledgement so packet sent correctly and move to done
[finish1] s1=10 & c1=1 & (x1=ACK | x1=ACK-1) -> (s1'=12) & (x1'=0) & (bc1'=0);
// WAIT FOR ACK_TO
// check channel and busy: go into backoff
[] s1=11 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=11 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
[time] s1=11 & x1>0 & x1<ACK_TO -> (x1'=min(x1+1,TIME_MAX));
// no acknowledgement (go to backoff waiting DIFS first)
[] s1=11 & x1=ACK_TO -> (s1'=3) & (x1'=0);
// DONE
[time] s1=12 -> (s1'=12);
endmodule
// ---------------------------------------------------------------------------- //
// STATION 2 (rename STATION 1)
module
station2=station1[x1=x2,
s1=s2,
s2=s1,
c1=c2,
c2=c1,
slot1=slot2,
backoff1=backoff2,
bc1=bc2,
send1=send2,
finish1=finish2]
endmodule
// ---------------------------------------------------------------------------- //
label "twoCollisions" = col=2;
label "fourCollisions" = col=4;
label "sixCollisions" = col=6;

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examples/mdp/wlan/wlan5_collide.nm
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// WLAN PROTOCOL (two stations)
// discrete time model
// gxn/jzs 20/02/02
mdp
// COLLISIONS
const int COL; // maximum number of collisions
// TIMING CONSTRAINTS
// we have used the FHSS parameters
// then scaled by the value of ASLOTTIME
const int ASLOTTIME = 1;
const int DIFS = 3; // due to scaling can be either 2 or 3 which is modelled by a non-deterministic choice
const int VULN = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
const int TRANS_TIME_MAX; // scaling up
const int TRANS_TIME_MIN = 4; // scaling down
const int ACK_TO = 6;
const int ACK = 4; // due to scaling can be either 3 or 4 which is modelled by a non-deterministic choice
const int SIFS = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
// maximum constant used in timing constraints + 1
const int TIME_MAX = max(ACK_TO,TRANS_TIME_MAX)+1;
// CONTENTION WINDOW
// CWMIN =15 & CWMAX =511
// this means that MAX_BACKOFF IS 5
const int MAX_BACKOFF = 5;
//-----------------------------------------------------------------//
// THE MEDIUM/CHANNEL
// FORMULAE FOR THE CHANNEL
// channel is busy
formula busy = c1>0 | c2>0;
// channel is free
formula free = c1=0 & c2=0;
module medium
// number of collisions
col : [0..COL];
// medium status
c1 : [0..2];
c2 : [0..2];
// ci corresponds to messages associated with station i
// 0 nothing being sent
// 1 being sent correctly
// 2 being sent garbled
// begin sending message and nothing else currently being sent
[send1] c1=0 & c2=0 -> (c1'=1);
[send2] c2=0 & c1=0 -> (c2'=1);
// begin sending message and something is already being sent
// in this case both messages become garbled
[send1] c1=0 & c2>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
[send2] c2=0 & c1>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
// finish sending message
[finish1] c1>0 -> (c1'=0);
[finish2] c2>0 -> (c2'=0);
endmodule
//-----------------------------------------------------------------//
// STATION 1
module station1
// clock for station 1
x1 : [0..TIME_MAX];
// local state
s1 : [1..12];
// 1 sense
// 2 wait until free before setting backoff
// 3 wait for DIFS then set slot
// 4 set backoff
// 5 backoff
// 6 wait until free in backoff
// 7 wait for DIFS then resume backoff
// 8 vulnerable
// 9 transmit
// 11 wait for SIFS and then ACK
// 10 wait for ACT_TO
// 12 done
// BACKOFF
// separate into slots
slot1 : [0..31];
backoff1 : [0..15];
// BACKOFF COUNTER
bc1 : [0..MAX_BACKOFF];
// SENSE
// let time pass
[time] s1=1 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// ready to transmit
[] s1=1 & (x1=DIFS | x1=DIFS-1) -> (s1'=8) & (x1'=0);
// found channel busy so wait until free
[] s1=1 & busy -> (s1'=2) & (x1'=0);
// WAIT UNTIL FREE BEFORE SETTING BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=2 & busy -> (s1'=2);
// find that channel is free so check its free for DIFS before setting backoff
[] s1=2 & free -> (s1'=3);
// WAIT FOR DIFS THEN SET BACKOFF
// let time pass
[time] s1=3 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// found channel busy so wait until free
[] s1=3 & busy -> (s1'=2) & (x1'=0);
// start backoff first uniformly choose slot
// backoff counter 0
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=0 -> (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 1
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=1 -> 1/2 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/2 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 2
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=2 -> 1/4 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 3
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=3 -> 1/8 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=4) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=5) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=6) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=7) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 4
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=4 -> 1/16 : (s1'=4) & (x1'=0) & (slot1'=0 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=1 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=2 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=3 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=4 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=5 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=6 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=7 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=8 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=9 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=10) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=11) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=12) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=13) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=14) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=15) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 5
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=5 -> 1/32 : (s1'=4) & (x1'=0) & (slot1'=0 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=1 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=2 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=3 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=4 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=5 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=6 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=7 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=8 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=9 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=10) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=11) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=12) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=13) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=14) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=15) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=16) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=17) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=18) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=19) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=20) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=21) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=22) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=23) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=24) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=25) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=26) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=27) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=28) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=29) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=30) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=31) & (bc1'=min(bc1+1,MAX_BACKOFF));
// SET BACKOFF (no time can pass)
// chosen slot now set backoff
[] s1=4 -> 1/16 : (s1'=5) & (backoff1'=0 )
+ 1/16 : (s1'=5) & (backoff1'=1 )
+ 1/16 : (s1'=5) & (backoff1'=2 )
+ 1/16 : (s1'=5) & (backoff1'=3 )
+ 1/16 : (s1'=5) & (backoff1'=4 )
+ 1/16 : (s1'=5) & (backoff1'=5 )
+ 1/16 : (s1'=5) & (backoff1'=6 )
+ 1/16 : (s1'=5) & (backoff1'=7 )
+ 1/16 : (s1'=5) & (backoff1'=8 )
+ 1/16 : (s1'=5) & (backoff1'=9 )
+ 1/16 : (s1'=5) & (backoff1'=10)
+ 1/16 : (s1'=5) & (backoff1'=11)
+ 1/16 : (s1'=5) & (backoff1'=12)
+ 1/16 : (s1'=5) & (backoff1'=13)
+ 1/16 : (s1'=5) & (backoff1'=14)
+ 1/16 : (s1'=5) & (backoff1'=15);
// BACKOFF
// let time pass
[time] s1=5 & x1<ASLOTTIME & free -> (x1'=min(x1+1,TIME_MAX));
// decrement backoff
[] s1=5 & x1=ASLOTTIME & backoff1>0 -> (s1'=5) & (x1'=0) & (backoff1'=backoff1-1);
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1>0 -> (s1'=5) & (x1'=0) & (backoff1'=15) & (slot1'=slot1-1);
// finish backoff
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1=0 -> (s1'=8) & (x1'=0);
// found channel busy
[] s1=5 & busy -> (s1'=6) & (x1'=0);
// WAIT UNTIL FREE IN BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=6 & busy -> (s1'=6);
// find that channel is free
[] s1=6 & free -> (s1'=7);
// WAIT FOR DIFS THEN RESUME BACKOFF
// let time pass
[time] s1=7 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// resume backoff (start again from previous backoff)
[] s1=7 & (x1=DIFS | x1=DIFS-1) -> (s1'=5) & (x1'=0);
// found channel busy
[] s1=7 & busy -> (s1'=6) & (x1'=0);
// VULNERABLE
// let time pass
[time] s1=8 & x1<VULN -> (x1'=min(x1+1,TIME_MAX));
// move to transmit
[send1] s1=8 & (x1=VULN | x1=VULN-1) -> (s1'=9) & (x1'=0);
// TRANSMIT
// let time pass
[time] s1=9 & x1<TRANS_TIME_MAX -> (x1'=min(x1+1,TIME_MAX));
// finish transmission successful
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=1 -> (s1'=10) & (x1'=0);
// finish transmission garbled
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=2 -> (s1'=11) & (x1'=0);
// WAIT FOR SIFS THEN WAIT FOR ACK
// WAIT FOR SIFS i.e. c1=0
// check channel and busy: go into backoff
[] s1=10 & c1=0 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=10 & c1=0 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
// following guard is always false as SIFS=1
// [time] s1=10 & c1=0 & x1>0 & x1<SIFS -> (x1'=min(x1+1,TIME_MAX));
// ack is sent after SIFS (since SIFS-1=0 add condition that channel is free)
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & free)) -> (s1'=10) & (x1'=0);
// WAIT FOR ACK i.e. c1=1
// let time pass
[time] s1=10 & c1=1 & x1<ACK -> (x1'=min(x1+1,TIME_MAX));
// get acknowledgement so packet sent correctly and move to done
[finish1] s1=10 & c1=1 & (x1=ACK | x1=ACK-1) -> (s1'=12) & (x1'=0) & (bc1'=0);
// WAIT FOR ACK_TO
// check channel and busy: go into backoff
[] s1=11 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=11 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
[time] s1=11 & x1>0 & x1<ACK_TO -> (x1'=min(x1+1,TIME_MAX));
// no acknowledgement (go to backoff waiting DIFS first)
[] s1=11 & x1=ACK_TO -> (s1'=3) & (x1'=0);
// DONE
[time] s1=12 -> (s1'=12);
endmodule
// ---------------------------------------------------------------------------- //
// STATION 2 (rename STATION 1)
module
station2=station1[x1=x2,
s1=s2,
s2=s1,
c1=c2,
c2=c1,
slot1=slot2,
backoff1=backoff2,
bc1=bc2,
send1=send2,
finish1=finish2]
endmodule
// ---------------------------------------------------------------------------- //
label "twoCollisions" = col=2;
label "fourCollisions" = col=4;
label "sixCollisions" = col=6;

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// WLAN PROTOCOL (two stations)
// discrete time model
// gxn/jzs 20/02/02
mdp
// COLLISIONS
const int COL; // maximum number of collisions
// TIMING CONSTRAINTS
// we have used the FHSS parameters
// then scaled by the value of ASLOTTIME
const int ASLOTTIME = 1;
const int DIFS = 3; // due to scaling can be either 2 or 3 which is modelled by a non-deterministic choice
const int VULN = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
const int TRANS_TIME_MAX; // scaling up
const int TRANS_TIME_MIN = 4; // scaling down
const int ACK_TO = 6;
const int ACK = 4; // due to scaling can be either 3 or 4 which is modelled by a non-deterministic choice
const int SIFS = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice
// maximum constant used in timing constraints + 1
const int TIME_MAX = max(ACK_TO,TRANS_TIME_MAX)+1;
// CONTENTION WINDOW
// CWMIN =15 & CWMAX =1023
// this means that MAX_BACKOFF IS 6
const int MAX_BACKOFF = 6;
//-----------------------------------------------------------------//
// THE MEDIUM/CHANNEL
// FORMULAE FOR THE CHANNEL
// channel is busy
formula busy = c1>0 | c2>0;
// channel is free
formula free = c1=0 & c2=0;
module medium
// number of collisions
col : [0..COL];
// medium status
c1 : [0..2];
c2 : [0..2];
// ci corresponds to messages associated with station i
// 0 nothing being sent
// 1 being sent correctly
// 2 being sent garbled
// begin sending message and nothing else currently being sent
[send1] c1=0 & c2=0 -> (c1'=1);
[send2] c2=0 & c1=0 -> (c2'=1);
// begin sending message and something is already being sent
// in this case both messages become garbled
[send1] c1=0 & c2>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
[send2] c2=0 & c1>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL));
// finish sending message
[finish1] c1>0 -> (c1'=0);
[finish2] c2>0 -> (c2'=0);
endmodule
//-----------------------------------------------------------------//
// STATION 1
module station1
// clock for station 1
x1 : [0..TIME_MAX];
// local state
s1 : [1..12];
// 1 sense
// 2 wait until free before setting backoff
// 3 wait for DIFS then set slot
// 4 set backoff
// 5 backoff
// 6 wait until free in backoff
// 7 wait for DIFS then resume backoff
// 8 vulnerable
// 9 transmit
// 11 wait for SIFS and then ACK
// 10 wait for ACT_TO
// 12 done
// BACKOFF
// separate into slots
slot1 : [0..63];
backoff1 : [0..15];
// BACKOFF COUNTER
bc1 : [0..MAX_BACKOFF];
// SENSE
// let time pass
[time] s1=1 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// ready to transmit
[] s1=1 & (x1=DIFS | x1=DIFS-1) -> (s1'=8) & (x1'=0);
// found channel busy so wait until free
[] s1=1 & busy -> (s1'=2) & (x1'=0);
// WAIT UNTIL FREE BEFORE SETTING BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=2 & busy -> (s1'=2);
// find that channel is free so check its free for DIFS before setting backoff
[] s1=2 & free -> (s1'=3);
// WAIT FOR DIFS THEN SET BACKOFF
// let time pass
[time] s1=3 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// found channel busy so wait until free
[] s1=3 & busy -> (s1'=2) & (x1'=0);
// start backoff first uniformly choose slot
// backoff counter 0
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=0 -> (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 1
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=1 -> 1/2 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/2 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 2
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=2 -> 1/4 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/4 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 3
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=3 -> 1/8 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=4) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=5) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=6) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/8 : (s1'=4) & (x1'=0) & (slot1'=7) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 4
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=4 -> 1/16 : (s1'=4) & (x1'=0) & (slot1'=0 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=1 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=2 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=3 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=4 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=5 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=6 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=7 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=8 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=9 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=10) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=11) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=12) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=13) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=14) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/16 : (s1'=4) & (x1'=0) & (slot1'=15) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 5
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=5 -> 1/32 : (s1'=4) & (x1'=0) & (slot1'=0 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=1 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=2 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=3 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=4 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=5 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=6 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=7 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=8 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=9 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=10) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=11) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=12) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=13) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=14) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=15) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=16) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=17) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=18) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=19) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=20) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=21) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=22) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=23) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=24) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=25) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=26) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=27) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=28) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=29) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=30) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/32 : (s1'=4) & (x1'=0) & (slot1'=31) & (bc1'=min(bc1+1,MAX_BACKOFF));
// backoff counter 6
[] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=6 -> 1/64 : (s1'=4) & (x1'=0) & (slot1'=0 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=1 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=2 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=3 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=4 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=5 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=6 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=7 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=8 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=9 ) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=10) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=11) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=12) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=13) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=14) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=15) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=16) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=17) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=18) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=19) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=20) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=21) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=22) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=23) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=24) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=25) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=26) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=27) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=28) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=29) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=30) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=31) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=32) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=33) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=34) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=35) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=36) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=37) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=38) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=39) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=40) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=41) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=42) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=43) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=44) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=45) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=46) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=47) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=48) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=49) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=50) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=51) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=52) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=53) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=54) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=55) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=56) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=57) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=58) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=59) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=60) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=61) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=62) & (bc1'=min(bc1+1,MAX_BACKOFF))
+ 1/64 : (s1'=4) & (x1'=0) & (slot1'=63) & (bc1'=min(bc1+1,MAX_BACKOFF));
// SET BACKOFF (no time can pass)
// chosen slot now set backoff
[] s1=4 -> 1/16 : (s1'=5) & (backoff1'=0 )
+ 1/16 : (s1'=5) & (backoff1'=1 )
+ 1/16 : (s1'=5) & (backoff1'=2 )
+ 1/16 : (s1'=5) & (backoff1'=3 )
+ 1/16 : (s1'=5) & (backoff1'=4 )
+ 1/16 : (s1'=5) & (backoff1'=5 )
+ 1/16 : (s1'=5) & (backoff1'=6 )
+ 1/16 : (s1'=5) & (backoff1'=7 )
+ 1/16 : (s1'=5) & (backoff1'=8 )
+ 1/16 : (s1'=5) & (backoff1'=9 )
+ 1/16 : (s1'=5) & (backoff1'=10)
+ 1/16 : (s1'=5) & (backoff1'=11)
+ 1/16 : (s1'=5) & (backoff1'=12)
+ 1/16 : (s1'=5) & (backoff1'=13)
+ 1/16 : (s1'=5) & (backoff1'=14)
+ 1/16 : (s1'=5) & (backoff1'=15);
// BACKOFF
// let time pass
[time] s1=5 & x1<ASLOTTIME & free -> (x1'=min(x1+1,TIME_MAX));
// decrement backoff
[] s1=5 & x1=ASLOTTIME & backoff1>0 -> (s1'=5) & (x1'=0) & (backoff1'=backoff1-1);
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1>0 -> (s1'=5) & (x1'=0) & (backoff1'=15) & (slot1'=slot1-1);
// finish backoff
[] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1=0 -> (s1'=8) & (x1'=0);
// found channel busy
[] s1=5 & busy -> (s1'=6) & (x1'=0);
// WAIT UNTIL FREE IN BACKOFF
// let time pass (no need for the clock x1 to change)
[time] s1=6 & busy -> (s1'=6);
// find that channel is free
[] s1=6 & free -> (s1'=7);
// WAIT FOR DIFS THEN RESUME BACKOFF
// let time pass
[time] s1=7 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX));
// resume backoff (start again from previous backoff)
[] s1=7 & (x1=DIFS | x1=DIFS-1) -> (s1'=5) & (x1'=0);
// found channel busy
[] s1=7 & busy -> (s1'=6) & (x1'=0);
// VULNERABLE
// let time pass
[time] s1=8 & x1<VULN -> (x1'=min(x1+1,TIME_MAX));
// move to transmit
[send1] s1=8 & (x1=VULN | x1=VULN-1) -> (s1'=9) & (x1'=0);
// TRANSMIT
// let time pass
[time] s1=9 & x1<TRANS_TIME_MAX -> (x1'=min(x1+1,TIME_MAX));
// finish transmission successful
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=1 -> (s1'=10) & (x1'=0);
// finish transmission garbled
[finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=2 -> (s1'=11) & (x1'=0);
// WAIT FOR SIFS THEN WAIT FOR ACK
// WAIT FOR SIFS i.e. c1=0
// check channel and busy: go into backoff
[] s1=10 & c1=0 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=10 & c1=0 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
// following guard is always false as SIFS=1
// [time] s1=10 & c1=0 & x1>0 & x1<SIFS -> (x1'=min(x1+1,TIME_MAX));
// ack is sent after SIFS (since SIFS-1=0 add condition that channel is free)
[send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & free)) -> (s1'=10) & (x1'=0);
// WAIT FOR ACK i.e. c1=1
// let time pass
[time] s1=10 & c1=1 & x1<ACK -> (x1'=min(x1+1,TIME_MAX));
// get acknowledgement so packet sent correctly and move to done
[finish1] s1=10 & c1=1 & (x1=ACK | x1=ACK-1) -> (s1'=12) & (x1'=0) & (bc1'=0);
// WAIT FOR ACK_TO
// check channel and busy: go into backoff
[] s1=11 & x1=0 & busy -> (s1'=2);
// check channel and free: let time pass
[time] s1=11 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX));
// let time pass
[time] s1=11 & x1>0 & x1<ACK_TO -> (x1'=min(x1+1,TIME_MAX));
// no acknowledgement (go to backoff waiting DIFS first)
[] s1=11 & x1=ACK_TO -> (s1'=3) & (x1'=0);
// DONE
[time] s1=12 -> (s1'=12);
endmodule
// ---------------------------------------------------------------------------- //
// STATION 2 (rename STATION 1)
module
station2=station1[x1=x2,
s1=s2,
s2=s1,
c1=c2,
c2=c1,
slot1=slot2,
backoff1=backoff2,
bc1=bc2,
send1=send2,
finish1=finish2]
endmodule
// ---------------------------------------------------------------------------- //
label "twoCollisions" = col=2;
label "fourCollisions" = col=4;
label "sixCollisions" = col=6;

1
examples/mdp/wlan/wlanX_1.cexprop
View File

@ -1 +0,0 @@
P<0.5 [ F oneCollision ]

1
examples/mdp/wlan/wlanX_4.cexprop
View File

@ -0,0 +1 @@
P<0.1 [ F fourCollisions ]

1
examples/mdp/wlan/wlanX_6.cexprop
View File

@ -0,0 +1 @@
P<0.1 [ F sixCollisions ]

6
src/parser/prismparser/VariableState.cpp
View File

@ -175,6 +175,12 @@ namespace storm {
booleanConstants_.clear();
doubleConstants_.clear();
allConstantNames_.clear();
constantBooleanFormulas_.clear();
booleanFormulas_.clear();
constantIntegerFormulas_.clear();
integerFormulas_.clear();
constantDoubleFormulas_.clear();
doubleFormulas_.clear();
this->firstRun = false;
nextGlobalCommandIndex = 0;
nextGlobalUpdateIndex = 0;

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