33:
402:
433:), which reduces the readability of the state diagram. With Harel statecharts it is possible to model multiple cross-functional state diagrams within the statechart. Each of these cross-functional state machines can transition internally without affecting the other state machines. The current state of each cross-functional state machine defines the state of the system. The Harel statechart is equivalent to a state diagram but improves its readability.
882:
334:
118:
507:
the counter value, which is strictly increasing (until the overflow). Thus, different states are visited in sequence until the overflow occurs. After the overflow the counter becomes 0 again, so the initial state is revisited in the state space, closing a cycle in the state space (assuming the counter was initialized to 0).
186:: represent transitions from one state to another as caused by the input (identified by their symbols drawn on the edges). An edge is usually drawn as an arrow directed from the present state to the next state. This mapping describes the state transition caused by an input. This is written mathematically as
522:
An interesting extension is to allow arcs to flow from any number of states to any number of states. This only makes sense if the system is allowed to be in multiple states at once, which implies that an individual state only describes a condition or other partial aspect of the overall, global state.
499:
In the previous case, the program would be in the same state because the whole state is just the program counter. Thus, if the program counterpoints to the same position (next command) it suffices to specify that we are in the same state. However, if the state includes variables that change value, we
506:
A representative example is a do loop incrementing some counter until it overflows and becomes 0 again. Although the do loop executes the same increment command iteratively, its state space is not a cycle but a line. This results from the state being the program location (here cycling) combined with
491:
Before executing a command, the program counter is at some position (state before the command is executed). Executing the command moves the program counter to the next command. Since the program counter is the whole state, executing the command changed the state. Thus, the command itself corresponds
483:
In more detail, the source code listing represents a program graph. Executing the program graph (parsing and interpreting) results in a state graph. So each program graph induces a state graph. Conversion of the program graph to its associated state graph is called "unfolding" of the program graph.
495:
Now consider the full case, when variables exist and are affected by the program commands being executed. Not only does the program counter change between different program counter locations, but variables might also change values due to the commands executed. Consequently, even if we revisit some
513:
One can compare a flowchart to an assembly line in manufacturing because the flowchart describes the progression of some task from beginning to end (e.g., transforming source code input into object code output by a compiler). A state machine generally has no notion of such a progression. The door
441:
There are other sets of semantics available to represent state diagrams. For example, there are tools for modeling and designing logic for embedded controllers. These diagrams, like Harel's original state machines, support hierarchically nested states, orthogonal regions, state actions, and
479:
Nodes of flowcharts are edges in the induced graph of states. The reason is that each node in a flowchart represents a program command. A program command is an action to be executed. A command is not a state, but when applied to the program's state, causes a transition to another state.
514:
state machine example shown above is not in a more advanced stage in the "closed" state than in the "opened" state. Rather, it simply reacts differently to the open/close events. A state in a state machine is an efficient way of specifying a behavior, rather than a stage of processing.
288:
For example, if a state has a number of outputs (e.g. "a= motor counter-clockwise=1, b= caution light inactive=0") the diagram should reflect this : e.g. "q5/1,0" designates state q5 with outputs a=1, b=0. This designator will be written inside the state's circle.
500:
can be at the same program location with different variable values, meaning in a different state in the program's state space. The term "unfolding" originates from this multiplication of locations when producing the state graph from the program graph.
76:. This behavior is analyzed and represented by a series of events that can occur in one or more possible states. Hereby "each diagram usually represents objects of a single class and track the different states of its objects through the system".
428:
Classic state diagrams require the creation of distinct nodes for every valid combination of parameters that define the state. For all but the simplest of systems, this can lead to a very large number of nodes and transitions between nodes
697:
Alur, R., Kanade, A., Ramesh, S., & Shashidhar, K. C. (2008). Symbolic analysis for improving simulation coverage of
Simulink/Stateflow models. International Conference on Embedded Software (pp. 89–98). Atlanta, GA:
487:
The program graph is a sequence of commands. If no variables exist, then the state consists only of the program counter, which keeps track of program location during execution (what is the next command to be applied).
466:
with a flowchart. A state machine (panel (a)) performs actions in response to explicit events. In contrast, the flowchart (panel (b)) automatically transitions from node to node upon completion of activities.
626:
390:
473:
202:, so δ (the transition function) in the definition of the FA is given by both the pair of vertices connected by an edge and the symbol on an edge in a diagram representing this FA. Item
285:
the state's output is usually written inside the state's circle, also separated from the state's designator with a slash "/". There are also variants that combine these two notations.
281:, input and output are signified on each edge, separated with a slash "/": "1/0" denotes the state change upon encountering the symbol "1" causing the symbol "0" to be output. For a
530:
Another extension allows the integration of flowcharts within Harel statecharts. This extension supports the development of software that is both event driven and workflow driven.
814:
696:
270:
243:∈ Q is usually represented by an arrow with no origin pointing to the state. In older texts, the start state is not shown and must be inferred from the text.
1284:
1243:
1192:
1045:
1026:
1253:
807:
510:
The figure above attempts to show that reversal of roles by aligning the arcs of the state diagrams with the processing stages of the flowchart.
954:
92:
718:
1299:
580:
163:
The output function ω represents the mapping of ordered pairs of input symbols and states onto output symbols, denoted mathematically as
908:
800:
755:- A discontinued round-trip UML dynamic modeling/development framework and tool that ran in popular IDEs under an open-source license.
563:
is a software for modeling state diagrams (Harel statecharts, Mealy machines, Moore machines), simulation, and source code generation.
635:
472:
389:
266:
147:: a finite set of states, normally represented by circles and labeled with unique designator symbols or words written inside them
48:
and related fields to describe the behavior of systems. State diagrams require that the system is composed of a finite number of
1036:
786:
SMC: An Open Source State
Machine Compiler that generates FSM for many languages as C, Python, Lua, Scala, PHP, Java, VB, etc.
328:. Each edge is labeled with the input. This example shows an acceptor for binary numbers that contain an even number of zeros.
1279:
262:
129:
53:
1000:
1187:
944:
598:
98:
1309:
1120:
903:
32:
1212:
959:
823:
414:
1258:
1248:
1222:
1005:
913:
761:- an Open-Source-Tool for the specification and development of reactive, event-driven systems with the help of
560:
49:
552:
an XML language that provides a generic state-machine based execution environment based on Harel statecharts.
842:
752:
1304:
662:
106:
1294:
1177:
934:
646:
218:
occurs in this machine. In the diagram representing this FA, this is represented by an edge labeled by
762:
80:
686:
Harel, D. (1987). A Visual
Formalism for Complex Systems. Science of Computer Programming, 231–274.
1125:
1031:
737:
711:
Practical UML Statecharts in C/C++, Second
Edition: Event-Driven Programming for Embedded Systems
401:
1289:
1156:
1115:
714:
631:
555:
463:
452:
430:
422:
418:
333:
768:
1182:
1161:
1151:
1067:
881:
45:
746:
674:
405:
Diagram showing how Harel's
Statecharts contributed to object-oriented methods and notation
1135:
995:
969:
949:
741:
584:
496:
program command (e.g. in a loop), this does not imply the program is in the same state.
1227:
1130:
1041:
985:
939:
869:
621:
133:
122:
84:
503:
A self transition is a transition where the initial and the final state are the same.
1273:
1110:
1083:
1062:
964:
864:
617:
342:
294:
282:
278:
274:
253:. It is usually drawn as a double circle. Sometimes the accept state(s) function as "
88:
663:
Statecharts: A visual formalism for complex systems. Science of
Computer Programming
847:
250:
990:
929:
859:
685:
675:
Tiwari, A. (2002). Formal
Semantics and Analysis Methods for Simulink Stateflow.
658:
539:
410:
52:. Sometimes, this is indeed the case, while at other times this is a reasonable
774:
FSM: Open Source Finite State
Machine Generation in Java by Alexander Sakharov
56:. Many forms of state diagrams exist, which differ slightly and have different
792:
524:
458:
57:
17:
1010:
73:
413:, are gaining widespread usage since a variant has become part of the
649:, Introduction to the Theory of Switching Circuits, McGraw-Hill, 1965
544:
69:
117:
549:
31:
796:
775:
1217:
787:
758:
36:
A state diagram for a door that can only be opened and closed
249:: If used, for example for accepting automata, F ∈ Q is the
206:
in the definition of the FA means that from the state named
627:
Introduction to
Automata Theory, Languages, and Computation
450:
Newcomers to the state machine formalism often confuse
239:: (not shown in the examples below). The start state q
159:: a finite collection of output symbols or designators
83:(also called finite automata). This was introduced by
780:
153:: a finite collection of input symbols or designators
79:
State diagrams can be used to graphically represent
68:
State diagrams provide an abstract description of a
1236:
1205:
1170:
1144:
1103:
1096:
1076:
1055:
1019:
978:
922:
896:
889:
830:
630:, Addison-Wesley Publishing Company, Reading Mass,
409:Harel statecharts, invented by computer scientist
783:An efficient scxml state machine to C++ compiler.
417:(UML). The diagram type allows the modeling of
808:
271:generalized nondeterministic finite automaton
8:
738:Introduction to UML 2 State Machine Diagrams
462:. The figure below shows a comparison of a
277:, the input is denoted on each edge. For a
27:Diagram of behavior of finite state systems
1100:
893:
815:
801:
793:
136:with the following elements (Q, Σ, Z, δ, q
105:. Another possible representation is the
492:to a transition between the two states.
400:
116:
94:The Mathematical Theory of Communication
1254:List of Unified Modeling Language tools
613:
611:
603:Sequential Machines and Automata Theory
594:
592:
573:
368:are states. Each edge is labeled with "
103:Sequential Machines and Automata Theory
769:Understanding and Using State Machines
747:UML 2 State Machine Diagram Guidelines
523:The resulting formalism is known as a
128:A classic form of state diagram for a
425:, and activities as part of a state.
7:
222:pointing from the vertex labeled by
909:Object-oriented analysis and design
771:MATLAB Tech Talks on State Machines
1285:Unified Modeling Language diagrams
25:
1213:Systems Modeling Language (SysML)
267:nondeterministic finite automaton
880:
605:, John Wiley and Sons, New York.
471:
446:State diagrams versus flowcharts
388:
332:
753:Intelliwizard - UML StateWizard
1223:XML Metadata Interchange (XMI)
431:state and transition explosion
263:deterministic finite automaton
214:, the transition to the state
1:
257:inal" (halt, trapped) states.
293:Example: DFA, NFA, GNFA, or
1300:Application-specific graphs
904:Object-oriented programming
1326:
665:, 8(3):231–274, June 1987.
1218:UML eXchange Format (UXF)
878:
824:Unified Modeling Language
415:Unified Modeling Language
226:to the vertex labeled by
1259:Object Modeling in Color
1249:Rational Unified Process
914:Object-oriented modeling
759:YAKINDU Statechart Tools
561:YAKINDU Statechart Tools
843:Object Management Group
713:. Newnes. p. 728.
406:
125:
107:state-transition table
37:
1280:Models of computation
1244:Glossary of UML terms
1228:Executable UML (xUML)
437:Alternative semantics
404:
120:
81:finite-state machines
35:
1188:Interaction overview
709:Samek, Miro (2008).
442:transition actions.
247:Accepting state(s) F
97:. Another source is
1121:Composite structure
210:under input symbol
91:in their 1949 book
1310:Modeling languages
749:by Scott W. Ambler
647:Edward J. McClusky
423:orthogonal regions
407:
126:
38:
1267:
1266:
1206:Derived languages
1201:
1200:
1092:
1091:
720:978-0-7506-8706-5
556:UML state machine
380:is the input and
101:in his 1967 book
16:(Redirected from
1317:
1101:
894:
884:
817:
810:
803:
794:
725:
724:
706:
700:
694:
688:
683:
677:
672:
666:
656:
650:
644:
638:
615:
606:
596:
587:
578:
518:Other extensions
475:
397:Harel statechart
392:
336:
157:Output symbols Z
130:finite automaton
46:computer science
21:
1325:
1324:
1320:
1319:
1318:
1316:
1315:
1314:
1270:
1269:
1268:
1263:
1232:
1197:
1166:
1140:
1088:
1072:
1051:
1015:
974:
970:Profile diagram
918:
897:Object oriented
885:
876:
826:
821:
742:Scott W. Ambler
734:
729:
728:
721:
708:
707:
703:
695:
691:
684:
680:
673:
669:
657:
653:
645:
641:
616:
609:
597:
590:
585:Wayback Machine
579:
575:
570:
536:
520:
448:
439:
399:
384:is the output.
367:
360:
353:
346:
322:accepting state
319:
313:are states and
312:
305:
298:
251:accepting state
242:
237:
151:Input symbols Σ
139:
115:
66:
28:
23:
22:
15:
12:
11:
5:
1323:
1321:
1313:
1312:
1307:
1302:
1297:
1292:
1287:
1282:
1272:
1271:
1265:
1264:
1262:
1261:
1256:
1251:
1246:
1240:
1238:
1234:
1233:
1231:
1230:
1225:
1220:
1215:
1209:
1207:
1203:
1202:
1199:
1198:
1196:
1195:
1190:
1185:
1180:
1178:Communications
1174:
1172:
1168:
1167:
1165:
1164:
1159:
1154:
1148:
1146:
1142:
1141:
1139:
1138:
1133:
1128:
1123:
1118:
1113:
1107:
1105:
1098:
1094:
1093:
1090:
1089:
1087:
1086:
1080:
1078:
1074:
1073:
1071:
1070:
1065:
1059:
1057:
1053:
1052:
1050:
1049:
1042:Generalization
1039:
1034:
1029:
1023:
1021:
1017:
1016:
1014:
1013:
1008:
1003:
998:
993:
988:
982:
980:
976:
975:
973:
972:
967:
962:
957:
952:
947:
942:
937:
932:
926:
924:
920:
919:
917:
916:
911:
906:
900:
898:
891:
887:
886:
879:
877:
875:
874:
873:
872:
870:James Rumbaugh
867:
862:
852:
851:
850:
845:
834:
832:
828:
827:
822:
820:
819:
812:
805:
797:
791:
790:
784:
778:
772:
766:
763:state machines
756:
750:
744:
733:
732:External links
730:
727:
726:
719:
701:
689:
678:
667:
651:
639:
622:Jeffrey Ullman
607:
588:
572:
571:
569:
566:
565:
564:
558:
553:
547:
542:
535:
532:
519:
516:
477:
476:
453:state diagrams
447:
444:
438:
435:
398:
395:
394:
393:
365:
358:
351:
345:
339:
338:
337:
317:
310:
303:
297:
291:
259:
258:
244:
240:
235:
231:
161:
160:
154:
148:
137:
134:directed graph
123:directed graph
114:
113:Directed graph
111:
85:Claude Shannon
65:
62:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1322:
1311:
1308:
1306:
1305:Graph drawing
1303:
1301:
1298:
1296:
1293:
1291:
1288:
1286:
1283:
1281:
1278:
1277:
1275:
1260:
1257:
1255:
1252:
1250:
1247:
1245:
1242:
1241:
1239:
1235:
1229:
1226:
1224:
1221:
1219:
1216:
1214:
1211:
1210:
1208:
1204:
1194:
1191:
1189:
1186:
1184:
1181:
1179:
1176:
1175:
1173:
1169:
1163:
1160:
1158:
1157:State Machine
1155:
1153:
1150:
1149:
1147:
1143:
1137:
1134:
1132:
1129:
1127:
1124:
1122:
1119:
1117:
1114:
1112:
1109:
1108:
1106:
1102:
1099:
1095:
1085:
1082:
1081:
1079:
1075:
1069:
1066:
1064:
1061:
1060:
1058:
1056:Extensibility
1054:
1047:
1043:
1040:
1038:
1035:
1033:
1030:
1028:
1025:
1024:
1022:
1020:Relationships
1018:
1012:
1009:
1007:
1004:
1002:
999:
997:
994:
992:
989:
987:
984:
983:
981:
977:
971:
968:
966:
963:
961:
958:
956:
953:
951:
948:
946:
943:
941:
938:
936:
933:
931:
928:
927:
925:
921:
915:
912:
910:
907:
905:
902:
901:
899:
895:
892:
888:
883:
871:
868:
866:
865:Ivar Jacobson
863:
861:
858:
857:
856:
853:
849:
846:
844:
841:
840:
839:
838:Organizations
836:
835:
833:
829:
825:
818:
813:
811:
806:
804:
799:
798:
795:
789:
785:
782:
779:
777:
773:
770:
767:
764:
760:
757:
754:
751:
748:
745:
743:
739:
736:
735:
731:
722:
716:
712:
705:
702:
699:
693:
690:
687:
682:
679:
676:
671:
668:
664:
660:
655:
652:
648:
643:
640:
637:
636:0-201-02988-X
633:
629:
628:
623:
619:
618:John Hopcroft
614:
612:
608:
604:
600:
595:
593:
589:
586:
582:
581:Archive index
577:
574:
567:
562:
559:
557:
554:
551:
548:
546:
543:
541:
538:
537:
533:
531:
528:
526:
517:
515:
511:
508:
504:
501:
497:
493:
489:
485:
481:
474:
470:
469:
468:
465:
464:state diagram
461:
460:
455:
454:
445:
443:
436:
434:
432:
426:
424:
420:
416:
412:
403:
396:
391:
387:
386:
385:
383:
379:
375:
371:
364:
357:
350:
344:
343:Mealy machine
340:
335:
331:
330:
329:
327:
323:
316:
309:
302:
296:
295:Moore machine
292:
290:
286:
284:
283:Moore machine
280:
279:Mealy machine
276:
275:Moore machine
272:
268:
264:
256:
252:
248:
245:
238:
234:Start state q
232:
229:
225:
221:
217:
213:
209:
205:
201:
197:
193:
189:
185:
182:
181:
180:
178:
174:
170:
166:
158:
155:
152:
149:
146:
143:
142:
141:
135:
131:
124:
119:
112:
110:
108:
104:
100:
96:
95:
90:
89:Warren Weaver
86:
82:
77:
75:
71:
63:
61:
59:
55:
51:
47:
43:
42:state diagram
34:
30:
19:
1295:Infographics
1237:Other topics
1084:Multiplicity
854:
848:UML Partners
837:
710:
704:
692:
681:
670:
654:
642:
625:
602:
599:Taylor Booth
576:
529:
521:
512:
509:
505:
502:
498:
494:
490:
486:
482:
478:
457:
451:
449:
440:
427:
408:
381:
377:
373:
369:
362:
355:
348:
347:
325:
321:
314:
307:
300:
299:
287:
260:
254:
246:
233:
227:
223:
219:
215:
211:
207:
203:
199:
195:
191:
187:
183:
176:
172:
168:
164:
162:
156:
150:
144:
127:
102:
99:Taylor Booth
93:
78:
67:
41:
39:
29:
1171:Interaction
1046:Inheritance
1032:Composition
1027:Association
860:Grady Booch
659:David Harel
540:David Harel
419:superstates
411:David Harel
326:final state
273:(GNFA), or
204:δ(q, a) = p
54:abstraction
44:is used in
1274:Categories
1126:Deployment
1068:Stereotype
1037:Dependency
568:References
459:flowcharts
145:Vertices Q
132:(FA) is a
18:Statechart
1145:Behaviour
1116:Component
1104:Structure
955:Interface
950:Component
935:Attribute
923:Structure
525:Petri net
341:Example:
58:semantics
1290:Diagrams
1183:Sequence
1162:Use case
1152:Activity
1097:Diagrams
1011:Use case
986:Activity
979:Behavior
940:Artifact
890:Concepts
534:See also
376:" where
190: :
167: :
74:behavior
64:Overview
1136:Package
1063:Profile
996:Message
965:Package
855:Persons
781:scxmlcc
624:(1979)
601:(1967)
583:at the
269:(NFA),
265:(DFA),
184:Edges δ
1193:Timing
1131:Object
1001:Method
960:Object
831:Actors
717:
634:
545:DRAKON
361:, and
320:is an
261:For a
140:, F):
70:system
50:states
1111:Class
1077:Other
1006:State
991:Event
945:Class
930:Actor
550:SCXML
456:with
324:or a
1044:(or
715:ISBN
698:ACM.
632:ISBN
620:and
306:and
198:→
87:and
788:SMC
776:FSM
740:by
72:'s
1276::
661:,
610:^
591:^
527:.
421:,
372:/
354:,
194:×
179:.
175:→
171:×
121:A
109:.
60:.
40:A
1048:)
816:e
809:t
802:v
765:.
723:.
429:(
382:k
378:j
374:k
370:j
366:2
363:S
359:1
356:S
352:0
349:S
318:1
315:S
311:2
308:S
304:1
301:S
255:F
241:0
236:0
230:.
228:p
224:q
220:a
216:p
212:a
208:q
200:Q
196:Σ
192:Q
188:δ
177:Z
173:Q
169:Σ
165:ω
138:0
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
