3829:) can be determined by when ?push occurs. Fig. 4. illustrates the case ?push happens at time 40 and the toaster changes into (T, 20, 0). From that time, 20 seconds later when its status becomes (T, 20, 20), the toaster gets back to (Wait, inf, 0) where we don't know when it gets back to "Toast" again. Fig. 4. shows the case that ?push occurs at time 90 so the toaster get into (T,20,0). Notice that even though there someone push again at time 97, that status (T, 20, 7) doesn't change at all because
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becomes 0 again. However, since Player B sends back the ball to Player A 0.1 second later, Player A gets back to (Send, 0.1 0) at time 0.2. From that time, 0.1 seconds later when Player A's status becomes (Send, 0.1, 0.1), Player A sends back the ball to Player B and gets into (Wait, inf, 0). Thus,
198:
Consider a toaster in which there are two slots that have their own start knobs as shown in Fig. 2(a). Each slot has the identical functionality except their toasting time. Initially, the knob is not pushed, but if one pushes the knob, the associated slot starts toasting for its toasting time: 20
202:
One can model it with FD-DEVS as shown in Fig. 2(b). Two slots are modeled as atomic FD-DEVS whose input event is "?push" and output event is "!pop", states are "Idle" (I) and "Toast" (T) with the initial state is "idle". When it is "Idle" and receives "?push" (because one pushes the knob), its
181:
To make a complete ping-pong match, one player starts as an offender whose initial state is "Send" and the other starts as a defender whose initial state is "Wait". Thus in Fig. 1. Player A is the initial offender and Player B is the initial defender. In addition, to make the game continue, each
178:. Once the player gets into "Send", it will generates "!send" and go back to "Wait" after the sending time which is 0.1 time unit. When staying at "Wait" and if it gets "?receive", it changes into "Send" again. In other words, the player model stays at "Wait" forever unless it gets "?receive".
3877:
The property of non-negative rational-valued lifespans which can be preserved or changed by input events along with finite numbers of states and events guarantees that the behavior of FD-DEVS networks can be abstracted as an equivalent finite-vertex reachability graph by abstracting the
4247:
of FD-DEVS are deterministic can be seen as somehow a limitation to model the system that has non-deterministic behaviors. For example, if a player of the ping-pong game shown in Fig. 1. has a stochastic lifespan at "Send" state, FD-DEVS doesn't capture the non-determinism effectively.
134:
where the schedule is always preserved by any input events. Due to this relaxation there is no longer OPNA problem, but there is also one limitation that a time-line abstraction which can be used for abstracting elapsed times of SP-DEVS networks is no longer useful for FD-DEVS network
2923:
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3755:
Fig. 4. shows an event segment (top) and the associated state trajectory (bottom) of the left slot of the two-slot toaster introduced in Fig. 2. Like Fig.3, the status of the left slot is described as (state, lifespan, elapsed
4119:
3583:
Fig. 3. shows an event segment (top) and the associated state trajectory (bottom) of Player A who plays the ping-pong game introduced in Fig. 1. In Fig. 3. the status of Player A is described as (state, lifespan, elapsed
2652:
199:
seconds for the left slot, 40 seconds for the right slot. After the toasting time, each slot and its knobs pop up. Notice that even though one tries to push a knob when its associated slot is toasting, nothing happens.
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4121:. Each directed arch shows how its source vertex changes into the destination vertex along with an associated event and a set of reset models. For example, the transition arc (6) to (5) is triggered by
821:
4669:, "eUDEVS: Executable UML with DEVS Theory of Modeling and Simulation", SIMULATION, Transaction of The Society for Modeling and Simulation International, Volume 85, No. 11-12, 2009, pp. 750–777,
4426:
4381:
475:
3630:) and the line segment of the bottom of Fig. 3. denotes the value of the elapsed time. Since the initial state of Player A is "Send" and its lifetime is 0.1 seconds, the height of (Send, 0.1,
2724:
4503:
4245:
4660:
4548:
3193:{\displaystyle \delta _{ext}(s,t_{s},t_{e},x)={\begin{cases}(s',t_{s}-t_{e})&{\text{if }}\delta _{x}(s,x)=(s',0)\\(s',\tau (s'))&{\text{if }}\delta _{x}(s,x)=(s',1)\\\end{cases}}}
104:
and designed to support verification analysis of its networks which had been an open problem of DEVS formalism for 30 years. In addition, it was also designated to resolve the so-called "
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Fig. 5. shows the reachability graph of two-slot toaster which was shown in Fig. 2. In the reachability graph, each vertex has its own discrete state and time zone which are ranges of
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state changes to "Toast". In other words, it stays at "Idle" forever unless it receives "?push" event. 20 (res. 40) seconds later the left (res. right) slot returns to "Idle".
520:
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649:
4285:
For standardization of DEVS, especially using FDDEVS, Dr. Saurabh Mittal together with co-workers has worked on defining of XML format of FDDEVS. We can find an article at
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As a qualitative property, safety of a FD-DEVS network is decidable by (1) generating RG of the given network and (2) checking whether some bad states are reachable or not
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4659:, "Reachability Graph of Finite & Deterministic DEVS", IEEE Transactions on Automation Science and Engineering, Volume 6, Issue 3, 2009, pp. 454–467,
4010:
218:
4661:
https://ieeexplore.ieee.org/document/5071137/;jsessionid=6E63EA120D0510F93D51D6C18728D31C?isnumber=5153598&arnumber=5071137&count=19&index=7
162:
Consider a single ping-pong match in which there are two players. Each player can be modeled by FD-DEVS such that the player model has an input event
4704:
51:
89:
in both simulation and verification ways. FD-DEVS also provides modular and hierarchical modeling features which have been inherited from
Classic
1650:
As mentioned above, FD-DEVS is an relaxation of SP-DEVS. That means, FD-DEVS is a supper class of SP-DEVS. We would give a model of FD-DEVS of a
4177:
As a qualitative property, liveness of a FD-DEVS network is decidable by (1) generating RG of the given network, (2) from RG, generating kernel
902:. The output and internal transition function defines how a state generates an output event, at the same time, how the state changes internally.
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47:
774:
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which defines how an input event changes the schedule as well as a state of the system. The internal schedule of a state
141:
which was invented by Prof. D. Dill can be applicable to obtain a finite-vertex reachability graph for FD-DEVS networks.
4606:
4386:
4336:
427:
4469:
69:
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3802:) in Fig. 4. Since the initial state of the toaster is "I" and its lifetime is infinity, the height of (Wait, inf,
4508:
4721:
2658:
4185:, and (3) checking if a vertex of KDAG contains a state transition cycle which contains a set of liveness states
4262:
830:
4270:
3878:
infinitely-many values of the elapsed times using the time abstracting technique introduced by Prof. D. Dill
86:
3510:
3348:
4645:
4623:
4601:
M.H. Hwang, "Generating Finite-State Global
Behavior of Reconfigurable Automation Systems: DEVS Approach",
4182:
713:
654:
85:(Finite & Deterministic Discrete Event System Specification) is a formalism for modeling and analyzing
912:
The formal representation of the player in the ping-pong example shown in Fig. 1 can be given as follows.
3462:
4155:
is reset by 0 when transition (6) to (5) occurs. For more detailed information, the reader can refer to
2781:
4277:
that support some reachability graph-based verification algorithms for finding safeness and liveness.
3412:
3206:
2844:
2731:
1281:
The formal representation of the slot of Two-slot
Toaster Fig. 2(a) and (b) can be given as follows.
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player's "?send" event should be coupled to the other player's "?receive" as shown in Fig. 1.
4565:
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1128:
4128:
2894:
2476:{\displaystyle {\mathcal {M}}=<X,Y,S',s_{0}',ta,\delta _{ext},\delta _{int},\lambda >}
594:
4596:
Proceedings of the
Workshop on Computer Aided Verification Methods for Finite State Systems
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this cyclic state transitions which move "Send" to "Wait" back and forth will go forever.
8:
2489:
4594:
D.L. Dill, "Timing
Assumptions and Verification of Finite-State Concurrent Systems", In
3881:. An algorithm generating a finite-vertex reachability graph (RG)has been introduced in
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event. At that time, the set {1} of the arc denotes that elapsed time of 1 (that is
4114:{\displaystyle 0\leq t_{e1}\leq 40,0\leq t_{e2}\leq 40,-20\leq t_{e1}-t_{21}\leq 0}
4649:
4627:
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105:
123:
the lifespan of a state can be scheduled by a rational number or infinity, and
4715:
194:
Fig. 2: (a) Two-slot toaster (b) FD-DEVS coupled diagram for two-slot toaster
4615:, "A Modular Verification Framework using Finite and Deterministic DEVS",
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4429:
4290:
4186:
4167:
4156:
3885:
3882:
3879:
139:
136:
102:
126:
the internal schedule can be either preserved or updated by an input event.
3987:. For example, for node (6) of Fig. 5, discrete state information is ((E,
2647:{\displaystyle S'=\{(s,t_{s}):s\in S,t_{s}\in \mathbb {T} ^{\infty }\}}
2262:
4196:
3742:
4637:, "A Reachable Graph of Finite and Deterministic DEVS Networks",
4274:
2354:{\displaystyle M=<X,Y,S,s_{0},\tau ,\delta _{x},\delta _{y}>}
1737:{\displaystyle M=<X,Y,S,s_{0},\tau ,\delta _{x},\delta _{y}>}
1360:{\displaystyle M=<X,Y,S,s_{0},\tau ,\delta _{x},\delta _{y}>}
991:{\displaystyle M=<X,Y,S,s_{0},\tau ,\delta _{x},\delta _{y}>}
294:{\displaystyle M=<X,Y,S,s_{0},\tau ,\delta _{x},\delta _{y}>}
154:
190:
1655:
131:
109:
580:{\displaystyle \delta _{x}:S\times X\rightarrow S\times \{0,1\}}
4665:
José L. Risco-Martín, Jesús M. de la Cruz, Saurabh Mittal and
4642:
4620:
101:
FD-DEVS was originally named as "Schedule-Controllable DEVS"
3746:
Fig. 4. an Event
Segment and a State Trajectory of a Toaster
130:
The third restriction can be also seen as a relaxation from
3186:
2362:
2266:
Fig. 3. an Event
Segment and a State Trajectory of Player A
113:
90:
816:{\displaystyle \delta _{y}:S\rightarrow Y^{\phi }\times S}
522:
is the set of non-negative rational numbers plus infinity.
3872:
3864:
3572:
For details of DEVS behavior, the readers can refer to
4289:. This standard XML format was used for UML execution
4568:
4511:
4472:
4445:
4389:
4339:
4312:
4261:
There are two open source libraries DEVS# written in
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3338:{\displaystyle \delta _{int}(s,t_{s})=(s',\tau (s'))}
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221:
4641:, pp48–56, Huntsville, Alabama, USA, (Available at
4619:, pp57–65, Huntsville, Alabama, USA, (Available at
1646:
42:
may be too technical for most readers to understand
4574:
4542:
4497:
4458:
4421:{\displaystyle \delta _{x}:S\times X\rightarrow S}
4420:
4376:{\displaystyle \rho :S\times X\rightarrow \{0,1\}}
4375:
4325:
4287:http://www.duniptechnologies.com/research/xfddevs/
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470:{\displaystyle \tau :S\rightarrow \mathbb {Q} _{}}
469:
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371:
345:
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293:
158:Fig. 1: FD-DEVS coupled diagram for ping-pong game
4671:http://sim.sagepub.com/content/85/11-12/750.short
4197:Weak Expressiveness for describing nondeterminism
1474:(T)=20 for the left slot, 40 for the right slot,
4713:
4605:, Edmonton, Canada, Aug. 1-2, 2005(Available at
4498:{\displaystyle \lambda :S\rightarrow Y^{\phi }}
4201:The features that all characteristic functions,
3868:Fig. 5. Reachability Graph of Two-slot Toaster
2257:
4683:(second ed.). Academic Press, New York.
4240:{\displaystyle \tau ,\delta _{x},\delta _{y}}
481:which defines the lifespan of a state where
4703:: CS1 maint: multiple names: authors list (
4543:{\displaystyle \delta _{int}:S\rightarrow S}
4370:
4358:
4267:http://xsy-csharp.sourceforge.net/DEVSsharp/
2641:
2576:
859:
853:
574:
562:
4172:
2719:{\displaystyle s_{0}'=(s_{0},\tau (s_{0}))}
825:the output and internal transition function
3711:is reset by 0, Player A doesn't know when
3684:. After changing into (Wait, inf, 0) when
4679:, Tag Gon Kim, Herbert Praehofer (2000).
4280:
4161:
2631:
1277:Formal Representation of One Slot Toaster
908:Formal Representation of Ping-Pong Player
865:{\displaystyle Y^{\phi }=Y\cup \{\phi \}}
490:
445:
70:Learn how and when to remove this message
54:, without removing the technical details.
3863:
3741:
2261:
1085:=Send for Player A, Wait for Player B;
189:
153:
120:finiteness of event sets and state set,
14:
4714:
3873:Applicability of Time-Zone Abstraction
3562:{\displaystyle \delta _{y}(s)=(y,s').}
3400:{\displaystyle \delta _{y}(s)=(y,s').}
138:. But another time abstraction method
3890:
762:{\displaystyle \delta _{x}(s)=(s',0)}
703:{\displaystyle \delta _{x}(s)=(s',1)}
52:make it understandable to non-experts
4598:, pp 197–212, Grenoble, France, 1989
211:
26:
4466:can be divided into two functions:
4333:can be divided into two functions:
4256:
3500:{\displaystyle \lambda (s,t_{s})=y}
185:
24:
4639:Proceedings of 2006 DEVS Symposium
4617:Proceedings of 2006 DEVS Symposium
4569:
3994:
2832:{\displaystyle ta(s,t_{s})=t_{s}.}
2636:
2521:
2373:
1501:
1132:
504:
459:
25:
4733:
4681:Theory of Modeling and Simulation
206:
149:
116:, FD-DEVS has three restrictions
4275:https://code.google.com/p/x-s-y/
4191:
589:the external transition function
112:. From the viewpoint of Classic
31:
3657:) is 0.1 which is the value of
3452:{\displaystyle (s,t_{s})\in S'}
3246:{\displaystyle (s,t_{s})\in S'}
2884:{\displaystyle (s,t_{s})\in S'}
2771:{\displaystyle (s,t_{s})\in S'}
515:{\displaystyle \mathbb {Q} _{}}
4556:
4534:
4482:
4434:
4412:
4355:
4301:
3579:Behavior of Ping-Pong Player A
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2579:
2529:{\displaystyle {\mathcal {M}}}
2271:FD-DEVS is a sub-class of DEVS
794:
756:
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87:discrete event dynamic systems
13:
1:
4603:Proceedings of 2005 IEEE-CASE
4588:
3980:{\displaystyle t_{e1}-t_{e2}}
3934:{\displaystyle t_{e1},t_{e2}}
3859:
3795:{\displaystyle s,t_{s},t_{e}}
3623:{\displaystyle s,t_{s},t_{e}}
891:{\displaystyle \phi \notin Y}
769:), the schedule is preserved.
355:a finite set of output events
4643:http://www.acims.arizona.edu
4621:http://www.acims.arizona.edu
4295:
4183:strongly connected component
4181:(KDAG) in which a vertex is
4007:),(T,40)), and time zone is
329:a finite set of input events
7:
4459:{\displaystyle \delta _{y}}
4326:{\displaystyle \delta _{x}}
3849:{\displaystyle \delta _{x}}
2258:Behaviors of FD-DEVS Models
2247:{\displaystyle \delta _{y}}
2220:{\displaystyle \delta _{y}}
2193:{\displaystyle \delta _{y}}
2166:{\displaystyle \delta _{y}}
2119:{\displaystyle \delta _{y}}
2092:{\displaystyle \delta _{y}}
2065:{\displaystyle \delta _{y}}
2018:{\displaystyle \delta _{x}}
1991:{\displaystyle \delta _{x}}
1804:={BG, BW, G, GR, R, W, D};
1784:={!g:0, !g:1, !w:0, !w:1};
1615:{\displaystyle \delta _{y}}
1588:{\displaystyle \delta _{y}}
1561:{\displaystyle \delta _{x}}
1534:{\displaystyle \delta _{x}}
1246:{\displaystyle \delta _{y}}
1219:{\displaystyle \delta _{y}}
1192:{\displaystyle \delta _{x}}
1165:{\displaystyle \delta _{x}}
144:
10:
4738:
1652:crosswalk light controller
1199:(Send,?receive)=(Send,0);
1172:(Wait,?receive)=(Send,1),
411:{\displaystyle s_{0}\in S}
96:
2536:are the same as those of
644:{\displaystyle \tau (s')}
479:the time advance function
170:, and it has two states:
4173:Decidability of Liveness
4575:{\displaystyle \infty }
4251:
4000:{\displaystyle \infty }
3574:Behavior of Atomic DEVS
1507:{\displaystyle \infty }
1138:{\displaystyle \infty }
4722:Automata (computation)
4576:
4544:
4499:
4460:
4422:
4377:
4327:
4281:For Simulation via XML
4241:
4179:directed acyclic graph
4162:Decidability of Safety
4149:
4148:{\displaystyle t_{e1}}
4115:
4001:
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3747:
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2911:
2910:{\displaystyle x\in X}
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1247:
1226:(Send)=(!send, Wait),
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1079:
1052:
1032:
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992:
905:
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866:
817:
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645:
611:
610:{\displaystyle s\in S}
581:
516:
471:
412:
381:a finite set of states
373:
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321:
295:
195:
159:
4577:
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4500:
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4002:
3982:
3936:
3867:
3851:
3824:
3822:{\displaystyle t_{e}}
3797:
3751:Behavior of a Toaster
3745:
3733:
3731:{\displaystyle t_{e}}
3706:
3704:{\displaystyle t_{e}}
3679:
3677:{\displaystyle t_{s}}
3652:
3650:{\displaystyle t_{e}}
3625:
3564:
3502:
3454:
3402:
3340:
3248:
3195:
2912:
2886:
2834:
2773:
2721:
2649:
2551:
2531:
2507:
2478:
2356:
2265:
2249:
2222:
2195:
2168:
2141:
2139:{\displaystyle \phi }
2121:
2094:
2067:
2040:
2038:{\displaystyle \neq }
2020:
1993:
1966:
1964:{\displaystyle \tau }
1946:
1944:{\displaystyle \tau }
1926:
1924:{\displaystyle \tau }
1906:
1904:{\displaystyle \tau }
1886:
1884:{\displaystyle \tau }
1866:
1864:{\displaystyle \tau }
1846:
1844:{\displaystyle \tau }
1826:
1824:{\displaystyle s_{0}}
1799:
1779:
1759:
1739:
1637:
1635:{\displaystyle \phi }
1617:
1590:
1563:
1536:
1509:
1489:
1487:{\displaystyle \tau }
1469:
1467:{\displaystyle \tau }
1449:
1447:{\displaystyle s_{0}}
1422:
1402:
1382:
1362:
1268:
1266:{\displaystyle \phi }
1248:
1221:
1194:
1167:
1140:
1120:
1118:{\displaystyle \tau }
1100:
1098:{\displaystyle \tau }
1080:
1078:{\displaystyle s_{0}}
1053:
1033:
1013:
993:
893:
867:
818:
764:
705:
646:
612:
582:
517:
472:
413:
374:
348:
322:
305:
296:
193:
157:
4566:
4562:inf in Fig 3. means
4509:
4470:
4443:
4387:
4337:
4310:
4205:
4129:
4011:
3991:
3945:
3899:
3833:
3806:
3760:
3715:
3688:
3661:
3634:
3588:
3511:
3463:
3413:
3349:
3257:
3207:
2924:
2895:
2845:
2782:
2732:
2659:
2562:
2540:
2516:
2490:
2368:
2279:
2231:
2204:
2177:
2150:
2130:
2103:
2076:
2049:
2029:
2002:
1975:
1955:
1935:
1915:
1895:
1875:
1855:
1835:
1808:
1788:
1768:
1748:
1662:
1626:
1599:
1572:
1545:
1518:
1498:
1478:
1458:
1431:
1411:
1391:
1371:
1285:
1257:
1230:
1203:
1176:
1149:
1129:
1109:
1089:
1062:
1042:
1022:
1002:
916:
876:
831:
775:
714:
655:
621:
595:
528:
485:
428:
389:
363:
337:
311:
219:
166:and an output event
4269:and XSY written in
2891:and an input event
2674:
2505:{\displaystyle X,Y}
2416:
1658:in this Knowledge.
4648:2012-07-26 at the
4626:2012-07-26 at the
4572:
4540:
4495:
4456:
4418:
4373:
4323:
4237:
4145:
4111:
3997:
3977:
3931:
3891:Reachability Graph
3870:
3846:
3819:
3792:
3748:
3728:
3701:
3674:
3647:
3620:
3559:
3497:
3449:
3397:
3335:
3243:
3190:
3185:
2907:
2881:
2829:
2768:
2716:
2662:
2644:
2546:
2526:
2502:
2473:
2404:
2351:
2268:
2244:
2217:
2190:
2163:
2136:
2116:
2089:
2062:
2035:
2025:(s,?p)=(s,0) if s
2015:
1988:
1961:
1941:
1921:
1901:
1881:
1861:
1841:
1821:
1794:
1774:
1754:
1734:
1654:which is used for
1632:
1612:
1585:
1558:
1541:(I, ?push)=(T,1),
1531:
1504:
1484:
1464:
1444:
1417:
1397:
1377:
1357:
1263:
1243:
1216:
1189:
1162:
1135:
1115:
1095:
1075:
1048:
1028:
1008:
988:
888:
862:
813:
759:
710:, otherwise(i.e.,
700:
641:
607:
577:
512:
467:
408:
369:
343:
317:
291:
196:
160:
4690:978-0-12-778455-7
4611:M. H. Hwang and
3856:(T,?push)=(T,1).
3133:
3040:
2549:{\displaystyle M}
2275:A FD-DEVS model,
2072:(BG)=(!g:1, BW),
1797:{\displaystyle S}
1777:{\displaystyle Y}
1757:{\displaystyle X}
1568:(T,?push)=(T,0);
1420:{\displaystyle S}
1400:{\displaystyle Y}
1380:{\displaystyle X}
1051:{\displaystyle S}
1031:{\displaystyle Y}
1011:{\displaystyle X}
420:the initial state
372:{\displaystyle S}
346:{\displaystyle Y}
320:{\displaystyle X}
212:Formal Definition
80:
79:
72:
16:(Redirected from
4729:
4708:
4702:
4694:
4633:M. H. Hwang and
4583:
4581:
4579:
4578:
4573:
4560:
4554:
4549:
4547:
4546:
4541:
4527:
4526:
4504:
4502:
4501:
4496:
4494:
4493:
4465:
4463:
4462:
4457:
4455:
4454:
4438:
4432:
4427:
4425:
4424:
4419:
4399:
4398:
4382:
4380:
4379:
4374:
4332:
4330:
4329:
4324:
4322:
4321:
4305:
4257:For Verification
4246:
4244:
4243:
4238:
4236:
4235:
4223:
4222:
4154:
4152:
4151:
4146:
4144:
4143:
4120:
4118:
4117:
4112:
4104:
4103:
4091:
4090:
4060:
4059:
4032:
4031:
4006:
4004:
4003:
3998:
3986:
3984:
3983:
3978:
3976:
3975:
3960:
3959:
3940:
3938:
3937:
3932:
3930:
3929:
3914:
3913:
3855:
3853:
3852:
3847:
3845:
3844:
3828:
3826:
3825:
3820:
3818:
3817:
3801:
3799:
3798:
3793:
3791:
3790:
3778:
3777:
3737:
3735:
3734:
3729:
3727:
3726:
3710:
3708:
3707:
3702:
3700:
3699:
3683:
3681:
3680:
3675:
3673:
3672:
3656:
3654:
3653:
3648:
3646:
3645:
3629:
3627:
3626:
3621:
3619:
3618:
3606:
3605:
3568:
3566:
3565:
3560:
3552:
3523:
3522:
3506:
3504:
3503:
3498:
3487:
3486:
3458:
3456:
3455:
3450:
3448:
3434:
3433:
3406:
3404:
3403:
3398:
3390:
3361:
3360:
3344:
3342:
3341:
3336:
3328:
3311:
3294:
3293:
3275:
3274:
3252:
3250:
3249:
3244:
3242:
3228:
3227:
3199:
3197:
3196:
3191:
3189:
3188:
3173:
3144:
3143:
3134:
3131:
3121:
3104:
3080:
3051:
3050:
3041:
3038:
3031:
3030:
3018:
3017:
3005:
2974:
2973:
2961:
2960:
2942:
2941:
2916:
2914:
2913:
2908:
2890:
2888:
2887:
2882:
2880:
2866:
2865:
2838:
2836:
2835:
2830:
2825:
2824:
2809:
2808:
2777:
2775:
2774:
2769:
2767:
2753:
2752:
2725:
2723:
2722:
2717:
2709:
2708:
2690:
2689:
2670:
2653:
2651:
2650:
2645:
2640:
2639:
2634:
2625:
2624:
2597:
2596:
2572:
2555:
2553:
2552:
2547:
2535:
2533:
2532:
2527:
2525:
2524:
2511:
2509:
2508:
2503:
2482:
2480:
2479:
2474:
2463:
2462:
2444:
2443:
2412:
2400:
2377:
2376:
2360:
2358:
2357:
2352:
2347:
2346:
2334:
2333:
2315:
2314:
2253:
2251:
2250:
2245:
2243:
2242:
2226:
2224:
2223:
2218:
2216:
2215:
2199:
2197:
2196:
2191:
2189:
2188:
2173:(GR)=(!g:0, R),
2172:
2170:
2169:
2164:
2162:
2161:
2145:
2143:
2142:
2137:
2125:
2123:
2122:
2117:
2115:
2114:
2098:
2096:
2095:
2090:
2088:
2087:
2071:
2069:
2068:
2063:
2061:
2060:
2044:
2042:
2041:
2036:
2024:
2022:
2021:
2016:
2014:
2013:
1997:
1995:
1994:
1989:
1987:
1986:
1970:
1968:
1967:
1962:
1950:
1948:
1947:
1942:
1930:
1928:
1927:
1922:
1910:
1908:
1907:
1902:
1890:
1888:
1887:
1882:
1870:
1868:
1867:
1862:
1850:
1848:
1847:
1842:
1830:
1828:
1827:
1822:
1820:
1819:
1803:
1801:
1800:
1795:
1783:
1781:
1780:
1775:
1763:
1761:
1760:
1755:
1743:
1741:
1740:
1735:
1730:
1729:
1717:
1716:
1698:
1697:
1641:
1639:
1638:
1633:
1621:
1619:
1618:
1613:
1611:
1610:
1594:
1592:
1591:
1586:
1584:
1583:
1567:
1565:
1564:
1559:
1557:
1556:
1540:
1538:
1537:
1532:
1530:
1529:
1513:
1511:
1510:
1505:
1493:
1491:
1490:
1485:
1473:
1471:
1470:
1465:
1453:
1451:
1450:
1445:
1443:
1442:
1426:
1424:
1423:
1418:
1406:
1404:
1403:
1398:
1386:
1384:
1383:
1378:
1366:
1364:
1363:
1358:
1353:
1352:
1340:
1339:
1321:
1320:
1272:
1270:
1269:
1264:
1252:
1250:
1249:
1244:
1242:
1241:
1225:
1223:
1222:
1217:
1215:
1214:
1198:
1196:
1195:
1190:
1188:
1187:
1171:
1169:
1168:
1163:
1161:
1160:
1144:
1142:
1141:
1136:
1124:
1122:
1121:
1116:
1104:
1102:
1101:
1096:
1084:
1082:
1081:
1076:
1074:
1073:
1057:
1055:
1054:
1049:
1037:
1035:
1034:
1029:
1017:
1015:
1014:
1009:
997:
995:
994:
989:
984:
983:
971:
970:
952:
951:
900:the silent event
897:
895:
894:
889:
871:
869:
868:
863:
843:
842:
822:
820:
819:
814:
806:
805:
787:
786:
768:
766:
765:
760:
749:
726:
725:
709:
707:
706:
701:
690:
667:
666:
650:
648:
647:
642:
637:
616:
614:
613:
608:
586:
584:
583:
578:
540:
539:
521:
519:
518:
513:
511:
510:
493:
476:
474:
473:
468:
466:
465:
448:
417:
415:
414:
409:
401:
400:
378:
376:
375:
370:
352:
350:
349:
344:
326:
324:
323:
318:
300:
298:
297:
292:
287:
286:
274:
273:
255:
254:
186:Two-slot toaster
75:
68:
64:
61:
55:
35:
34:
27:
21:
4737:
4736:
4732:
4731:
4730:
4728:
4727:
4726:
4712:
4711:
4696:
4695:
4691:
4677:Bernard Zeigler
4667:Bernard Zeigler
4657:Bernard Zeigler
4655:M.H. Hwang and
4650:Wayback Machine
4635:Bernard Zeigler
4628:Wayback Machine
4613:Bernard Zeigler
4591:
4586:
4567:
4564:
4563:
4561:
4557:
4516:
4512:
4510:
4507:
4506:
4489:
4485:
4471:
4468:
4467:
4450:
4446:
4444:
4441:
4440:
4439:
4435:
4394:
4390:
4388:
4385:
4384:
4338:
4335:
4334:
4317:
4313:
4311:
4308:
4307:
4306:
4302:
4298:
4283:
4259:
4254:
4231:
4227:
4218:
4214:
4206:
4203:
4202:
4199:
4194:
4175:
4164:
4136:
4132:
4130:
4127:
4126:
4099:
4095:
4083:
4079:
4052:
4048:
4024:
4020:
4012:
4009:
4008:
3992:
3989:
3988:
3968:
3964:
3952:
3948:
3946:
3943:
3942:
3922:
3918:
3906:
3902:
3900:
3897:
3896:
3893:
3875:
3862:
3840:
3836:
3834:
3831:
3830:
3813:
3809:
3807:
3804:
3803:
3786:
3782:
3773:
3769:
3761:
3758:
3757:
3722:
3718:
3716:
3713:
3712:
3695:
3691:
3689:
3686:
3685:
3668:
3664:
3662:
3659:
3658:
3641:
3637:
3635:
3632:
3631:
3614:
3610:
3601:
3597:
3589:
3586:
3585:
3545:
3518:
3514:
3512:
3509:
3508:
3482:
3478:
3464:
3461:
3460:
3441:
3429:
3425:
3414:
3411:
3410:
3383:
3356:
3352:
3350:
3347:
3346:
3321:
3304:
3289:
3285:
3264:
3260:
3258:
3255:
3254:
3235:
3223:
3219:
3208:
3205:
3204:
3184:
3183:
3166:
3139:
3135:
3130:
3128:
3114:
3097:
3091:
3090:
3073:
3046:
3042:
3037:
3035:
3026:
3022:
3013:
3009:
2998:
2988:
2987:
2969:
2965:
2956:
2952:
2931:
2927:
2925:
2922:
2921:
2896:
2893:
2892:
2873:
2861:
2857:
2846:
2843:
2842:
2820:
2816:
2804:
2800:
2783:
2780:
2779:
2760:
2748:
2744:
2733:
2730:
2729:
2704:
2700:
2685:
2681:
2666:
2660:
2657:
2656:
2635:
2630:
2629:
2620:
2616:
2592:
2588:
2565:
2563:
2560:
2559:
2541:
2538:
2537:
2520:
2519:
2517:
2514:
2513:
2491:
2488:
2487:
2452:
2448:
2433:
2429:
2408:
2393:
2372:
2371:
2369:
2366:
2365:
2342:
2338:
2329:
2325:
2310:
2306:
2280:
2277:
2276:
2260:
2254:(D)=(!g:1, G);
2238:
2234:
2232:
2229:
2228:
2227:(W)=(!w:0, D),
2211:
2207:
2205:
2202:
2201:
2200:(R)=(!w:1, W),
2184:
2180:
2178:
2175:
2174:
2157:
2153:
2151:
2148:
2147:
2131:
2128:
2127:
2110:
2106:
2104:
2101:
2100:
2099:(BW)=(!w:0, G),
2083:
2079:
2077:
2074:
2073:
2056:
2052:
2050:
2047:
2046:
2030:
2027:
2026:
2009:
2005:
2003:
2000:
1999:
1998:(G,?p)=(GR,0),
1982:
1978:
1976:
1973:
1972:
1956:
1953:
1952:
1936:
1933:
1932:
1916:
1913:
1912:
1896:
1893:
1892:
1876:
1873:
1872:
1856:
1853:
1852:
1836:
1833:
1832:
1815:
1811:
1809:
1806:
1805:
1789:
1786:
1785:
1769:
1766:
1765:
1749:
1746:
1745:
1725:
1721:
1712:
1708:
1693:
1689:
1663:
1660:
1659:
1627:
1624:
1623:
1606:
1602:
1600:
1597:
1596:
1595:(T)=(!pop, I),
1579:
1575:
1573:
1570:
1569:
1552:
1548:
1546:
1543:
1542:
1525:
1521:
1519:
1516:
1515:
1499:
1496:
1495:
1479:
1476:
1475:
1459:
1456:
1455:
1438:
1434:
1432:
1429:
1428:
1412:
1409:
1408:
1392:
1389:
1388:
1372:
1369:
1368:
1348:
1344:
1335:
1331:
1316:
1312:
1286:
1283:
1282:
1258:
1255:
1254:
1237:
1233:
1231:
1228:
1227:
1210:
1206:
1204:
1201:
1200:
1183:
1179:
1177:
1174:
1173:
1156:
1152:
1150:
1147:
1146:
1130:
1127:
1126:
1110:
1107:
1106:
1090:
1087:
1086:
1069:
1065:
1063:
1060:
1059:
1058:={Send, Wait};
1043:
1040:
1039:
1023:
1020:
1019:
1003:
1000:
999:
979:
975:
966:
962:
947:
943:
917:
914:
913:
877:
874:
873:
838:
834:
832:
829:
828:
801:
797:
782:
778:
776:
773:
772:
742:
721:
717:
715:
712:
711:
683:
662:
658:
656:
653:
652:
630:
622:
619:
618:
596:
593:
592:
535:
531:
529:
526:
525:
494:
489:
488:
486:
483:
482:
449:
444:
443:
429:
426:
425:
396:
392:
390:
387:
386:
364:
361:
360:
338:
335:
334:
312:
309:
308:
282:
278:
269:
265:
250:
246:
220:
217:
216:
214:
209:
188:
152:
147:
99:
76:
65:
59:
56:
48:help improve it
45:
36:
32:
23:
22:
15:
12:
11:
5:
4735:
4725:
4724:
4710:
4709:
4689:
4673:
4663:
4653:
4631:
4609:
4599:
4590:
4587:
4585:
4584:
4571:
4555:
4539:
4536:
4533:
4530:
4525:
4522:
4519:
4515:
4492:
4488:
4484:
4481:
4478:
4475:
4453:
4449:
4433:
4417:
4414:
4411:
4408:
4405:
4402:
4397:
4393:
4372:
4369:
4366:
4363:
4360:
4357:
4354:
4351:
4348:
4345:
4342:
4320:
4316:
4299:
4297:
4294:
4282:
4279:
4258:
4255:
4253:
4250:
4234:
4230:
4226:
4221:
4217:
4213:
4210:
4198:
4195:
4193:
4190:
4174:
4171:
4163:
4160:
4142:
4139:
4135:
4110:
4107:
4102:
4098:
4094:
4089:
4086:
4082:
4078:
4075:
4072:
4069:
4066:
4063:
4058:
4055:
4051:
4047:
4044:
4041:
4038:
4035:
4030:
4027:
4023:
4019:
4016:
3996:
3974:
3971:
3967:
3963:
3958:
3955:
3951:
3928:
3925:
3921:
3917:
3912:
3909:
3905:
3892:
3889:
3874:
3871:
3861:
3858:
3843:
3839:
3816:
3812:
3789:
3785:
3781:
3776:
3772:
3768:
3765:
3753:
3752:
3725:
3721:
3698:
3694:
3671:
3667:
3644:
3640:
3617:
3613:
3609:
3604:
3600:
3596:
3593:
3581:
3580:
3570:
3569:
3558:
3555:
3551:
3548:
3544:
3541:
3538:
3535:
3532:
3529:
3526:
3521:
3517:
3496:
3493:
3490:
3485:
3481:
3477:
3474:
3471:
3468:
3447:
3444:
3440:
3437:
3432:
3428:
3424:
3421:
3418:
3409:Given a state
3407:
3396:
3393:
3389:
3386:
3382:
3379:
3376:
3373:
3370:
3367:
3364:
3359:
3355:
3334:
3331:
3327:
3324:
3320:
3317:
3314:
3310:
3307:
3303:
3300:
3297:
3292:
3288:
3284:
3281:
3278:
3273:
3270:
3267:
3263:
3241:
3238:
3234:
3231:
3226:
3222:
3218:
3215:
3212:
3203:Given a state
3187:
3182:
3179:
3176:
3172:
3169:
3165:
3162:
3159:
3156:
3153:
3150:
3147:
3142:
3138:
3129:
3127:
3124:
3120:
3117:
3113:
3110:
3107:
3103:
3100:
3096:
3093:
3092:
3089:
3086:
3083:
3079:
3076:
3072:
3069:
3066:
3063:
3060:
3057:
3054:
3049:
3045:
3036:
3034:
3029:
3025:
3021:
3016:
3012:
3008:
3004:
3001:
2997:
2994:
2993:
2991:
2986:
2983:
2980:
2977:
2972:
2968:
2964:
2959:
2955:
2951:
2948:
2945:
2940:
2937:
2934:
2930:
2919:
2918:
2906:
2903:
2900:
2879:
2876:
2872:
2869:
2864:
2860:
2856:
2853:
2850:
2841:Given a state
2839:
2828:
2823:
2819:
2815:
2812:
2807:
2803:
2799:
2796:
2793:
2790:
2787:
2766:
2763:
2759:
2756:
2751:
2747:
2743:
2740:
2737:
2728:Given a state
2726:
2715:
2712:
2707:
2703:
2699:
2696:
2693:
2688:
2684:
2680:
2677:
2673:
2669:
2665:
2654:
2643:
2638:
2633:
2628:
2623:
2619:
2615:
2612:
2609:
2606:
2603:
2600:
2595:
2591:
2587:
2584:
2581:
2578:
2575:
2571:
2568:
2557:
2545:
2523:
2501:
2498:
2495:
2472:
2469:
2466:
2461:
2458:
2455:
2451:
2447:
2442:
2439:
2436:
2432:
2428:
2425:
2422:
2419:
2415:
2411:
2407:
2403:
2399:
2396:
2392:
2389:
2386:
2383:
2380:
2375:
2350:
2345:
2341:
2337:
2332:
2328:
2324:
2321:
2318:
2313:
2309:
2305:
2302:
2299:
2296:
2293:
2290:
2287:
2284:
2273:
2272:
2259:
2256:
2241:
2237:
2214:
2210:
2187:
2183:
2160:
2156:
2135:
2113:
2109:
2086:
2082:
2059:
2055:
2034:
2012:
2008:
1985:
1981:
1960:
1940:
1920:
1900:
1880:
1860:
1840:
1818:
1814:
1793:
1773:
1753:
1733:
1728:
1724:
1720:
1715:
1711:
1707:
1704:
1701:
1696:
1692:
1688:
1685:
1682:
1679:
1676:
1673:
1670:
1667:
1648:
1647:
1631:
1609:
1605:
1582:
1578:
1555:
1551:
1528:
1524:
1503:
1483:
1463:
1441:
1437:
1416:
1396:
1376:
1356:
1351:
1347:
1343:
1338:
1334:
1330:
1327:
1324:
1319:
1315:
1311:
1308:
1305:
1302:
1299:
1296:
1293:
1290:
1279:
1278:
1262:
1240:
1236:
1213:
1209:
1186:
1182:
1159:
1155:
1134:
1114:
1094:
1072:
1068:
1047:
1027:
1007:
987:
982:
978:
974:
969:
965:
961:
958:
955:
950:
946:
942:
939:
936:
933:
930:
927:
924:
921:
910:
909:
904:
903:
887:
884:
881:
861:
858:
855:
852:
849:
846:
841:
837:
812:
809:
804:
800:
796:
793:
790:
785:
781:
770:
758:
755:
752:
748:
745:
741:
738:
735:
732:
729:
724:
720:
699:
696:
693:
689:
686:
682:
679:
676:
673:
670:
665:
661:
640:
636:
633:
629:
626:
617:is updated by
606:
603:
600:
576:
573:
570:
567:
564:
561:
558:
555:
552:
549:
546:
543:
538:
534:
523:
509:
506:
503:
500:
497:
492:
464:
461:
458:
455:
452:
447:
442:
439:
436:
433:
423:
407:
404:
399:
395:
384:
368:
358:
342:
332:
316:
290:
285:
281:
277:
272:
268:
264:
261:
258:
253:
249:
245:
242:
239:
236:
233:
230:
227:
224:
213:
210:
208:
207:Atomic FD-DEVS
205:
187:
184:
151:
150:Ping-pong game
148:
146:
143:
128:
127:
124:
121:
98:
95:
78:
77:
39:
37:
30:
9:
6:
4:
3:
2:
4734:
4723:
4720:
4719:
4717:
4706:
4700:
4692:
4686:
4682:
4678:
4674:
4672:
4668:
4664:
4662:
4658:
4654:
4651:
4647:
4644:
4640:
4636:
4632:
4629:
4625:
4622:
4618:
4614:
4610:
4607:
4604:
4600:
4597:
4593:
4592:
4559:
4552:
4537:
4531:
4528:
4523:
4520:
4517:
4513:
4490:
4486:
4479:
4476:
4473:
4451:
4447:
4437:
4430:
4415:
4409:
4406:
4403:
4400:
4395:
4391:
4367:
4364:
4361:
4352:
4349:
4346:
4343:
4340:
4318:
4314:
4304:
4300:
4293:
4291:
4288:
4278:
4276:
4272:
4268:
4264:
4249:
4232:
4228:
4224:
4219:
4215:
4211:
4208:
4192:Disadvantages
4189:
4187:
4184:
4180:
4170:
4168:
4159:
4157:
4140:
4137:
4133:
4124:
4108:
4105:
4100:
4096:
4092:
4087:
4084:
4080:
4076:
4073:
4070:
4067:
4064:
4061:
4056:
4053:
4049:
4045:
4042:
4039:
4036:
4033:
4028:
4025:
4021:
4017:
4014:
3972:
3969:
3965:
3961:
3956:
3953:
3949:
3926:
3923:
3919:
3915:
3910:
3907:
3903:
3888:
3886:
3883:
3880:
3866:
3857:
3841:
3837:
3814:
3810:
3787:
3783:
3779:
3774:
3770:
3766:
3763:
3750:
3749:
3744:
3740:
3723:
3719:
3696:
3692:
3669:
3665:
3642:
3638:
3615:
3611:
3607:
3602:
3598:
3594:
3591:
3578:
3577:
3576:
3575:
3556:
3549:
3546:
3542:
3539:
3533:
3527:
3519:
3515:
3494:
3491:
3483:
3479:
3475:
3472:
3466:
3445:
3442:
3438:
3430:
3426:
3422:
3419:
3408:
3394:
3387:
3384:
3380:
3377:
3371:
3365:
3357:
3353:
3325:
3322:
3315:
3312:
3308:
3305:
3298:
3290:
3286:
3282:
3279:
3271:
3268:
3265:
3261:
3239:
3236:
3232:
3224:
3220:
3216:
3213:
3202:
3201:
3200:
3177:
3174:
3170:
3167:
3160:
3154:
3151:
3148:
3140:
3136:
3118:
3115:
3108:
3105:
3101:
3098:
3084:
3081:
3077:
3074:
3067:
3061:
3058:
3055:
3047:
3043:
3027:
3023:
3019:
3014:
3010:
3006:
3002:
2999:
2989:
2984:
2978:
2975:
2970:
2966:
2962:
2957:
2953:
2949:
2946:
2938:
2935:
2932:
2928:
2904:
2901:
2898:
2877:
2874:
2870:
2862:
2858:
2854:
2851:
2840:
2826:
2821:
2817:
2813:
2805:
2801:
2797:
2794:
2788:
2785:
2764:
2761:
2757:
2749:
2745:
2741:
2738:
2727:
2705:
2701:
2694:
2691:
2686:
2682:
2675:
2671:
2667:
2663:
2655:
2626:
2621:
2617:
2613:
2610:
2607:
2604:
2601:
2593:
2589:
2585:
2582:
2573:
2569:
2566:
2558:
2543:
2499:
2496:
2493:
2486:
2485:
2484:
2470:
2467:
2464:
2459:
2456:
2453:
2449:
2445:
2440:
2437:
2434:
2430:
2426:
2423:
2420:
2417:
2413:
2409:
2405:
2401:
2397:
2394:
2390:
2387:
2384:
2381:
2378:
2364:
2348:
2343:
2339:
2335:
2330:
2326:
2322:
2319:
2316:
2311:
2307:
2303:
2300:
2297:
2294:
2291:
2288:
2285:
2282:
2270:
2269:
2264:
2255:
2239:
2235:
2212:
2208:
2185:
2181:
2158:
2154:
2133:
2111:
2107:
2084:
2080:
2057:
2053:
2032:
2010:
2006:
1983:
1979:
1958:
1938:
1918:
1898:
1878:
1858:
1838:
1816:
1812:
1791:
1771:
1751:
1731:
1726:
1722:
1718:
1713:
1709:
1705:
1702:
1699:
1694:
1690:
1686:
1683:
1680:
1677:
1674:
1671:
1668:
1665:
1657:
1653:
1645:
1644:
1643:
1629:
1607:
1603:
1580:
1576:
1553:
1549:
1526:
1522:
1481:
1461:
1439:
1435:
1414:
1394:
1374:
1354:
1349:
1345:
1341:
1336:
1332:
1328:
1325:
1322:
1317:
1313:
1309:
1306:
1303:
1300:
1297:
1294:
1291:
1288:
1276:
1275:
1274:
1260:
1238:
1234:
1211:
1207:
1184:
1180:
1157:
1153:
1112:
1092:
1070:
1066:
1045:
1025:
1018:={?receive};
1005:
985:
980:
976:
972:
967:
963:
959:
956:
953:
948:
944:
940:
937:
934:
931:
928:
925:
922:
919:
907:
906:
901:
885:
882:
879:
856:
850:
847:
844:
839:
835:
826:
810:
807:
802:
798:
791:
788:
783:
779:
771:
753:
750:
746:
743:
736:
730:
722:
718:
694:
691:
687:
684:
677:
671:
663:
659:
634:
631:
624:
604:
601:
598:
590:
571:
568:
565:
559:
556:
550:
547:
544:
541:
536:
532:
524:
501:
498:
480:
456:
453:
437:
434:
431:
424:
421:
405:
402:
397:
393:
385:
382:
366:
359:
356:
340:
333:
330:
314:
307:
306:
304:
301:
288:
283:
279:
275:
270:
266:
262:
259:
256:
251:
247:
243:
240:
237:
234:
231:
228:
225:
222:
204:
200:
192:
183:
179:
177:
173:
169:
165:
156:
142:
140:
137:
133:
125:
122:
119:
118:
117:
115:
111:
108:" problem of
107:
103:
94:
92:
88:
84:
74:
71:
63:
53:
49:
43:
40:This article
38:
29:
28:
19:
4680:
4638:
4616:
4602:
4595:
4558:
4436:
4303:
4284:
4260:
4200:
4176:
4165:
4122:
3894:
3876:
3754:
3582:
3571:
2920:
2274:
1649:
1280:
911:
899:
824:
588:
478:
419:
380:
354:
328:
302:
215:
201:
197:
180:
175:
171:
167:
163:
161:
129:
100:
82:
81:
66:
60:January 2019
57:
41:
1105:(Send)=0.1,
4589:References
3860:Advantages
1871:(BW)=0.5,
1387:={?push};
1038:={!send};
4699:cite book
4570:∞
4535:→
4514:δ
4491:ϕ
4483:→
4474:λ
4448:δ
4413:→
4407:×
4392:δ
4356:→
4350:×
4341:ρ
4315:δ
4296:Footnotes
4229:δ
4216:δ
4209:τ
4106:≤
4093:−
4077:≤
4071:−
4062:≤
4046:≤
4034:≤
4018:≤
3995:∞
3962:−
3838:δ
3516:δ
3467:λ
3439:∈
3354:δ
3316:τ
3262:δ
3233:∈
3137:δ
3109:τ
3044:δ
3020:−
2929:δ
2902:∈
2871:∈
2758:∈
2695:τ
2637:∞
2627:∈
2608:∈
2468:λ
2450:δ
2431:δ
2340:δ
2327:δ
2320:τ
2236:δ
2209:δ
2182:δ
2155:δ
2134:ϕ
2108:δ
2081:δ
2054:δ
2033:≠
2007:δ
1980:δ
1959:τ
1939:τ
1919:τ
1899:τ
1879:τ
1859:τ
1851:(BG)=0.5,
1839:τ
1723:δ
1710:δ
1703:τ
1630:ϕ
1604:δ
1577:δ
1550:δ
1523:δ
1502:∞
1482:τ
1462:τ
1427:={I, T};
1407:={!pop};
1346:δ
1333:δ
1326:τ
1273:, Wait).
1261:ϕ
1235:δ
1208:δ
1181:δ
1154:δ
1133:∞
1113:τ
1093:τ
977:δ
964:δ
957:τ
883:∉
880:ϕ
857:ϕ
851:∪
840:ϕ
808:×
803:ϕ
795:→
780:δ
719:δ
660:δ
625:τ
602:∈
560:×
554:→
548:×
533:δ
505:∞
460:∞
441:→
432:τ
403:∈
280:δ
267:δ
260:τ
4716:Category
4646:Archived
4624:Archived
3550:′
3446:′
3388:′
3326:′
3309:′
3240:′
3171:′
3132:if
3119:′
3102:′
3078:′
3039:if
3003:′
2878:′
2765:′
2672:′
2570:′
2414:′
2398:′
1951:(W)=26,
1911:(GR)=30,
1891:(G)=30,
1253:(Wait)=(
898:denotes
747:′
688:′
635:′
164:?receive
145:Examples
3756:time)=(
3584:time)=(
1971:(D)=2;
1931:(R)=2,
1764:={?p};
1656:SP-DEVS
1125:(Wait)=
132:SP-DEVS
110:SP-DEVS
97:History
83:FD-DEVS
46:Please
18:FD-DEVS
4687:
4550:as in
4428:as in
4271:Python
2483:where
2146:, G),
1744:where
1642:, I).
1367:where
998:where
827:where
303:where
4123:push1
2379:=<
2286:=<
2126:(G)=(
1831:=BG,
1669:=<
1622:(I)=(
1454:=I;
1292:=<
923:=<
226:=<
168:!send
4705:link
4685:ISBN
4505:and
4383:and
4252:Tool
3941:and
2471:>
2363:DEVS
2349:>
1732:>
1494:(I)=
1355:>
986:>
872:and
289:>
176:Wait
174:and
172:Send
114:DEVS
106:OPNA
91:DEVS
4273:at
4265:at
3507:if
3459:,
3345:if
3253:,
2778:,
2512:of
2361:is
2045:G;
823:is
651:if
587:is
477:is
418:is
379:is
353:is
327:is
50:to
4718::
4701:}}
4697:{{
4292:.
4263:C#
4188:.
4169:.
4158:.
4101:21
4074:20
4065:40
4037:40
3887:.
3884:,
1514:;
1145:;
93:.
4707:)
4693:.
4652:)
4630:)
4608:)
4582:.
4553:.
4538:S
4532:S
4529::
4524:t
4521:n
4518:i
4487:Y
4480:S
4477::
4452:y
4431:.
4416:S
4410:X
4404:S
4401::
4396:x
4371:}
4368:1
4365:,
4362:0
4359:{
4353:X
4347:S
4344::
4319:x
4233:y
4225:,
4220:x
4212:,
4141:1
4138:e
4134:t
4109:0
4097:t
4088:1
4085:e
4081:t
4068:,
4057:2
4054:e
4050:t
4043:0
4040:,
4029:1
4026:e
4022:t
4015:0
3973:2
3970:e
3966:t
3957:1
3954:e
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3927:2
3924:e
3920:t
3916:,
3911:1
3908:e
3904:t
3842:x
3815:e
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3788:e
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3775:s
3771:t
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3643:e
3639:t
3616:e
3612:t
3608:,
3603:s
3599:t
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3592:s
3557:.
3554:)
3547:s
3543:,
3540:y
3537:(
3534:=
3531:)
3528:s
3525:(
3520:y
3495:y
3492:=
3489:)
3484:s
3480:t
3476:,
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3470:(
3443:S
3436:)
3431:s
3427:t
3423:,
3420:s
3417:(
3395:.
3392:)
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3378:y
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3372:=
3369:)
3366:s
3363:(
3358:y
3333:)
3330:)
3323:s
3319:(
3313:,
3306:s
3302:(
3299:=
3296:)
3291:s
3287:t
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3272:t
3269:n
3266:i
3237:S
3230:)
3225:s
3221:t
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3181:)
3178:1
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3168:s
3164:(
3161:=
3158:)
3155:x
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3141:x
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3065:)
3062:x
3059:,
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3011:t
3007:,
3000:s
2996:(
2990:{
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2982:)
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2806:s
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2714:)
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2664:s
2642:}
2632:T
2622:s
2618:t
2614:,
2611:S
2605:s
2602::
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2577:{
2574:=
2567:S
2556:.
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2522:M
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2410:0
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2402:,
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2159:y
2112:y
2085:y
2058:y
2011:x
1984:x
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1727:y
1719:,
1714:x
1706:,
1700:,
1695:0
1691:s
1687:,
1684:S
1681:,
1678:Y
1675:,
1672:X
1666:M
1608:y
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1415:S
1395:Y
1375:X
1350:y
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949:0
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920:M
886:Y
860:}
854:{
848:Y
845:=
836:Y
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789::
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754:0
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744:s
740:(
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734:)
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599:s
575:}
572:1
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566:0
563:{
557:S
551:X
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542::
537:x
508:]
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491:Q
463:]
457:,
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446:Q
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435::
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398:0
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383:;
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341:Y
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271:x
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248:s
244:,
241:S
238:,
235:Y
232:,
229:X
223:M
73:)
67:(
62:)
58:(
44:.
20:)
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