180:
66:
25:
363:
1571:
1044:
934:
826:
1461:
1363:
716:
618:
1092:
1849:
1739:
2072:
1322:
556:
1917:
1167:
539:
454:
At the beginning, a token is produced for the source place (p = 1) and at the end, a token is consumed from the sink place (c' = c + 1). When the replay ends, the fitness value can be computed as follows:
1138:
1888:
409:
1910:
1598:
1488:
1390:
1160:
961:
853:
743:
645:
460:
1782:
1734:
1696:
1564:
1526:
1428:
1087:
1037:
999:
929:
891:
819:
781:
683:
449:
302:
it records the situations where a transition is forced to fire and the remaining tokens after the replay ends. Based on the count at each counter, we can compute the
1842:
1624:
1454:
1356:
709:
611:
1816:
1658:
2067:{\displaystyle {\frac {1}{2}}(1-{\frac {m}{c}})+{\frac {1}{2}}(1-{\frac {r}{p}})={\frac {1}{2}}(1-{\frac {1}{5}})+{\frac {1}{2}}(1-{\frac {1}{5}})=0.8}
1317:{\displaystyle {\frac {1}{2}}(1-{\frac {m}{c}})+{\frac {1}{2}}(1-{\frac {r}{p}})={\frac {1}{2}}(1-{\frac {0}{6}})+{\frac {1}{2}}(1-{\frac {0}{6}})=1}
90:
of the topic and provide significant coverage of it beyond a mere trivial mention. If notability cannot be shown, the article is likely to be
1600:
needs to be fired but there are not enough tokens. One artificial token was produced and the missing token counter is increased by one (
248:
190:
142:
220:
114:
2113:
227:
121:
38:
274:
161:
52:
234:
128:
216:
205:
110:
87:
294:
algorithm that checks how well a process conforms with its model by replaying each trace on the model (in
1103:
83:
1859:
376:
99:
1893:
1581:
1471:
1373:
1143:
944:
836:
726:
628:
44:
241:
135:
1749:
1701:
1663:
1531:
1493:
1395:
1054:
1004:
966:
896:
858:
786:
748:
650:
416:
325:
The token-replay technique uses four counters to keep track of a trace during the replaying:
201:
291:
76:
8:
2184:
1821:
1603:
1433:
1335:
688:
590:
95:
1787:
1629:
2160:
2109:
91:
2152:
2101:
534:{\displaystyle {\frac {1}{2}}(1-{\frac {m}{c}})+{\frac {1}{2}}(1-{\frac {r}{p}})}
2105:
2139:
2092:
197:
2178:
2164:
2156:
1570:
1043:
933:
825:
563:
1460:
1362:
715:
617:
1326:
300:
produced tokens, consumed tokens, missing tokens, and remaining tokens,
2140:"Conformance checking of processes based on monitoring real behavior"
549:
295:
1091:
179:
1848:
1738:
82:
Please help to demonstrate the notability of the topic by citing
1784:). The trace is complete. There is one remaining token at place
362:
1332:
Step 1: A token is initiated. There is one produced token (
587:
Step 1: A token is initiated. There is one produced token (
555:
2090:
van der Aalst, Wil (2016), van der Aalst, Wil (ed.),
1920:
1896:
1862:
1824:
1790:
1752:
1704:
1666:
1632:
1606:
1584:
1534:
1496:
1474:
1436:
1398:
1376:
1338:
1170:
1146:
1106:
1057:
1007:
969:
947:
899:
861:
839:
789:
751:
729:
691:
653:
631:
593:
463:
419:
379:
2136:
1392:
consumes 1 token to be fired and produces 2 tokens (
1327:
Example 2: Replay the trace (a, b, d) on the model M
647:
consumes 1 token to be fired and produces 2 tokens (
2138:
2091:
2066:
1904:
1882:
1836:
1810:
1776:
1728:
1690:
1652:
1618:
1592:
1558:
1520:
1482:
1448:
1422:
1384:
1350:
1316:
1154:
1132:
1081:
1031:
993:
955:
923:
885:
847:
813:
775:
737:
703:
677:
639:
605:
533:
443:
403:
2137:Rozinat, A.; van der Aalst, W.M.P. (March 2008).
2176:
1746:Step 5: The token in the end place is consumed (
1051:Step 6: The token at the end place is consumed (
559:A process model M with the activities a, b, c, d
2100:, Berlin, Heidelberg: Springer, pp. 3–23,
1626:). The artificial token and the token at place
358:: Remaining tokens (produced but not consumed)
2089:
1847:
1737:
1569:
1459:
1361:
1090:
1042:
932:
824:
714:
616:
361:
206:introducing citations to additional sources
350:: Missing tokens (consumed while not there)
53:Learn how and when to remove these messages
1698:) and one token is produced at place end (
275:Learn how and when to remove this message
162:Learn how and when to remove this message
963:consumes 2 tokens and produces 1 token (
554:
196:Relevant discussion may be found on the
1490:consumes 1 token and produces 1 token (
855:consumes 1 token and produces 1 token (
745:consumes 1 token and produces 1 token (
2177:
2098:Process Mining: Data Science in Action
2132:
2130:
548:Suppose there is a process model in
173:
59:
18:
13:
1133:{\displaystyle \mathbf {a,b,c,d} }
306:between the trace and the model.
14:
2196:
2127:
309:
34:This article has multiple issues.
1898:
1883:{\displaystyle \mathbf {a,b,d} }
1876:
1873:
1870:
1867:
1864:
1801:
1798:
1795:
1643:
1640:
1637:
1586:
1476:
1378:
1148:
1126:
1123:
1120:
1117:
1114:
1111:
1108:
949:
841:
731:
633:
189:relies largely or entirely on a
178:
64:
23:
404:{\displaystyle p+m\geq c\geq m}
42:or discuss these issues on the
2083:
2055:
2036:
2020:
2001:
1985:
1966:
1950:
1931:
1805:
1791:
1647:
1633:
1305:
1286:
1270:
1251:
1235:
1216:
1200:
1181:
528:
509:
493:
474:
16:Conformance checking algorithm
1:
2076:
564:Example 1: Replay the trace (
1905:{\displaystyle \mathbf {M} }
1593:{\displaystyle \mathbf {d} }
1483:{\displaystyle \mathbf {b} }
1385:{\displaystyle \mathbf {a} }
1155:{\displaystyle \mathbf {M} }
956:{\displaystyle \mathbf {d} }
848:{\displaystyle \mathbf {c} }
738:{\displaystyle \mathbf {b} }
640:{\displaystyle \mathbf {a} }
77:general notability guideline
7:
2106:10.1007/978-3-662-49851-4_1
298:). Using the four counters
10:
2201:
1856:The fitness of the trace (
1100:The fitness of the trace (
543:
84:reliable secondary sources
73:The topic of this article
1089:). The trace is complete.
75:may not meet Knowledge's
2157:10.1016/j.is.2007.07.001
2093:"Data Science in Action"
1777:{\displaystyle c=4+1=5}
1729:{\displaystyle p=4+1=5}
1691:{\displaystyle c=2+2=4}
1559:{\displaystyle c=1+1=2}
1521:{\displaystyle p=3+1=4}
1423:{\displaystyle p=1+2=3}
1082:{\displaystyle c=5+1=6}
1032:{\displaystyle c=3+2=5}
994:{\displaystyle p=5+1=6}
924:{\displaystyle c=2+1=3}
886:{\displaystyle p=4+1=5}
814:{\displaystyle c=1+1=2}
776:{\displaystyle p=3+1=4}
678:{\displaystyle p=1+2=3}
444:{\displaystyle r=p+m-c}
2068:
1906:
1884:
1852:
1838:
1812:
1778:
1742:
1730:
1692:
1654:
1620:
1594:
1574:
1560:
1522:
1484:
1464:
1450:
1424:
1386:
1366:
1352:
1318:
1156:
1134:
1095:
1083:
1047:
1033:
995:
957:
937:
925:
887:
849:
829:
815:
777:
739:
719:
705:
679:
641:
621:
607:
560:
535:
445:
405:
366:
2069:
1907:
1885:
1851:
1839:
1813:
1779:
1741:
1731:
1693:
1655:
1621:
1595:
1578:Step 4: The activity
1573:
1561:
1523:
1485:
1468:Step 3: The activity
1463:
1451:
1425:
1387:
1370:Step 2: The activity
1365:
1353:
1319:
1157:
1135:
1094:
1084:
1046:
1034:
996:
958:
941:Step 5: The activity
936:
926:
888:
850:
833:Step 4: The activity
828:
816:
778:
740:
723:Step 3: The activity
718:
706:
680:
642:
625:Step 2: The activity
620:
608:
558:
552:notation as follows:
536:
446:
406:
365:
1918:
1894:
1860:
1822:
1788:
1750:
1702:
1664:
1630:
1604:
1582:
1532:
1494:
1472:
1434:
1396:
1374:
1336:
1168:
1144:
1104:
1055:
1005:
967:
945:
897:
859:
837:
787:
749:
727:
689:
651:
629:
591:
461:
417:
377:
292:conformance checking
217:"Token-based replay"
202:improve this article
111:"Token-based replay"
2145:Information Systems
1837:{\displaystyle r=1}
1619:{\displaystyle m=1}
1449:{\displaystyle c=1}
1351:{\displaystyle p=1}
704:{\displaystyle c=1}
606:{\displaystyle p=1}
2064:
1902:
1880:
1853:
1834:
1808:
1774:
1743:
1726:
1688:
1650:
1616:
1590:
1575:
1556:
1518:
1480:
1465:
1446:
1420:
1382:
1367:
1348:
1314:
1152:
1130:
1096:
1079:
1048:
1029:
991:
953:
938:
921:
883:
845:
830:
811:
773:
735:
720:
701:
675:
637:
622:
603:
561:
531:
441:
401:
367:
296:Petri net notation
288:Token-based replay
79:
2115:978-3-662-49851-4
2053:
2034:
2018:
1999:
1983:
1964:
1948:
1929:
1303:
1284:
1268:
1249:
1233:
1214:
1198:
1179:
526:
507:
491:
472:
342:: Consumed tokens
334:: Produced tokens
285:
284:
277:
267:
266:
252:
172:
171:
164:
146:
74:
57:
2192:
2169:
2168:
2142:
2134:
2125:
2124:
2123:
2122:
2095:
2087:
2073:
2071:
2070:
2065:
2054:
2046:
2035:
2027:
2019:
2011:
2000:
1992:
1984:
1976:
1965:
1957:
1949:
1941:
1930:
1922:
1911:
1909:
1908:
1903:
1901:
1889:
1887:
1886:
1881:
1879:
1843:
1841:
1840:
1835:
1817:
1815:
1814:
1811:{\displaystyle }
1809:
1804:
1783:
1781:
1780:
1775:
1735:
1733:
1732:
1727:
1697:
1695:
1694:
1689:
1659:
1657:
1656:
1653:{\displaystyle }
1651:
1646:
1625:
1623:
1622:
1617:
1599:
1597:
1596:
1591:
1589:
1565:
1563:
1562:
1557:
1527:
1525:
1524:
1519:
1489:
1487:
1486:
1481:
1479:
1455:
1453:
1452:
1447:
1429:
1427:
1426:
1421:
1391:
1389:
1388:
1383:
1381:
1357:
1355:
1354:
1349:
1323:
1321:
1320:
1315:
1304:
1296:
1285:
1277:
1269:
1261:
1250:
1242:
1234:
1226:
1215:
1207:
1199:
1191:
1180:
1172:
1161:
1159:
1158:
1153:
1151:
1139:
1137:
1136:
1131:
1129:
1088:
1086:
1085:
1080:
1038:
1036:
1035:
1030:
1000:
998:
997:
992:
962:
960:
959:
954:
952:
930:
928:
927:
922:
892:
890:
889:
884:
854:
852:
851:
846:
844:
820:
818:
817:
812:
782:
780:
779:
774:
744:
742:
741:
736:
734:
710:
708:
707:
702:
684:
682:
681:
676:
646:
644:
643:
638:
636:
612:
610:
609:
604:
582:) on the model M
581:
540:
538:
537:
532:
527:
519:
508:
500:
492:
484:
473:
465:
450:
448:
447:
442:
410:
408:
407:
402:
357:
349:
341:
333:
322:
321:
317:
280:
273:
262:
259:
253:
251:
210:
182:
174:
167:
160:
156:
153:
147:
145:
104:
68:
67:
60:
49:
27:
26:
19:
2200:
2199:
2195:
2194:
2193:
2191:
2190:
2189:
2175:
2174:
2173:
2172:
2135:
2128:
2120:
2118:
2116:
2088:
2084:
2079:
2045:
2026:
2010:
1991:
1975:
1956:
1940:
1921:
1919:
1916:
1915:
1897:
1895:
1892:
1891:
1890:) on the model
1863:
1861:
1858:
1857:
1855:
1823:
1820:
1819:
1794:
1789:
1786:
1785:
1751:
1748:
1747:
1703:
1700:
1699:
1665:
1662:
1661:
1636:
1631:
1628:
1627:
1605:
1602:
1601:
1585:
1583:
1580:
1579:
1533:
1530:
1529:
1495:
1492:
1491:
1475:
1473:
1470:
1469:
1435:
1432:
1431:
1397:
1394:
1393:
1377:
1375:
1372:
1371:
1337:
1334:
1333:
1329:
1295:
1276:
1260:
1241:
1225:
1206:
1190:
1171:
1169:
1166:
1165:
1147:
1145:
1142:
1141:
1140:) on the model
1107:
1105:
1102:
1101:
1056:
1053:
1052:
1006:
1003:
1002:
968:
965:
964:
948:
946:
943:
942:
898:
895:
894:
860:
857:
856:
840:
838:
835:
834:
788:
785:
784:
750:
747:
746:
730:
728:
725:
724:
690:
687:
686:
652:
649:
648:
632:
630:
627:
626:
592:
589:
588:
584:
580:
576:
572:
568:
565:
546:
518:
499:
483:
464:
462:
459:
458:
418:
415:
414:
378:
375:
374:
356:
353:
348:
345:
340:
337:
332:
329:
323:
319:
315:
313:
312:
290:technique is a
281:
270:
269:
268:
263:
257:
254:
211:
209:
195:
183:
168:
157:
151:
148:
105:
103:
81:
69:
65:
28:
24:
17:
12:
11:
5:
2198:
2188:
2187:
2171:
2170:
2126:
2114:
2081:
2080:
2078:
2075:
2063:
2060:
2057:
2052:
2049:
2044:
2041:
2038:
2033:
2030:
2025:
2022:
2017:
2014:
2009:
2006:
2003:
1998:
1995:
1990:
1987:
1982:
1979:
1974:
1971:
1968:
1963:
1960:
1955:
1952:
1947:
1944:
1939:
1936:
1933:
1928:
1925:
1900:
1878:
1875:
1872:
1869:
1866:
1846:
1845:
1833:
1830:
1827:
1807:
1803:
1800:
1797:
1793:
1773:
1770:
1767:
1764:
1761:
1758:
1755:
1744:
1725:
1722:
1719:
1716:
1713:
1710:
1707:
1687:
1684:
1681:
1678:
1675:
1672:
1669:
1660:are consumed (
1649:
1645:
1642:
1639:
1635:
1615:
1612:
1609:
1588:
1568:
1567:
1555:
1552:
1549:
1546:
1543:
1540:
1537:
1517:
1514:
1511:
1508:
1505:
1502:
1499:
1478:
1458:
1457:
1445:
1442:
1439:
1419:
1416:
1413:
1410:
1407:
1404:
1401:
1380:
1360:
1359:
1347:
1344:
1341:
1328:
1325:
1313:
1310:
1307:
1302:
1299:
1294:
1291:
1288:
1283:
1280:
1275:
1272:
1267:
1264:
1259:
1256:
1253:
1248:
1245:
1240:
1237:
1232:
1229:
1224:
1221:
1218:
1213:
1210:
1205:
1202:
1197:
1194:
1189:
1186:
1183:
1178:
1175:
1150:
1128:
1125:
1122:
1119:
1116:
1113:
1110:
1098:
1097:
1078:
1075:
1072:
1069:
1066:
1063:
1060:
1041:
1040:
1028:
1025:
1022:
1019:
1016:
1013:
1010:
990:
987:
984:
981:
978:
975:
972:
951:
939:
920:
917:
914:
911:
908:
905:
902:
882:
879:
876:
873:
870:
867:
864:
843:
823:
822:
810:
807:
804:
801:
798:
795:
792:
772:
769:
766:
763:
760:
757:
754:
733:
713:
712:
700:
697:
694:
674:
671:
668:
665:
662:
659:
656:
635:
615:
614:
602:
599:
596:
583:
578:
574:
570:
566:
562:
545:
542:
530:
525:
522:
517:
514:
511:
506:
503:
498:
495:
490:
487:
482:
479:
476:
471:
468:
452:
451:
440:
437:
434:
431:
428:
425:
422:
411:
400:
397:
394:
391:
388:
385:
382:
360:
359:
354:
351:
346:
343:
338:
335:
330:
311:
310:The algorithm
308:
283:
282:
265:
264:
200:. Please help
186:
184:
177:
170:
169:
72:
70:
63:
58:
32:
31:
29:
22:
15:
9:
6:
4:
3:
2:
2197:
2186:
2183:
2182:
2180:
2166:
2162:
2158:
2154:
2150:
2146:
2141:
2133:
2131:
2117:
2111:
2107:
2103:
2099:
2094:
2086:
2082:
2074:
2061:
2058:
2050:
2047:
2042:
2039:
2031:
2028:
2023:
2015:
2012:
2007:
2004:
1996:
1993:
1988:
1980:
1977:
1972:
1969:
1961:
1958:
1953:
1945:
1942:
1937:
1934:
1926:
1923:
1913:
1850:
1831:
1828:
1825:
1771:
1768:
1765:
1762:
1759:
1756:
1753:
1745:
1740:
1723:
1720:
1717:
1714:
1711:
1708:
1705:
1685:
1682:
1679:
1676:
1673:
1670:
1667:
1613:
1610:
1607:
1577:
1576:
1572:
1553:
1550:
1547:
1544:
1541:
1538:
1535:
1515:
1512:
1509:
1506:
1503:
1500:
1497:
1467:
1466:
1462:
1443:
1440:
1437:
1417:
1414:
1411:
1408:
1405:
1402:
1399:
1369:
1368:
1364:
1345:
1342:
1339:
1331:
1330:
1324:
1311:
1308:
1300:
1297:
1292:
1289:
1281:
1278:
1273:
1265:
1262:
1257:
1254:
1246:
1243:
1238:
1230:
1227:
1222:
1219:
1211:
1208:
1203:
1195:
1192:
1187:
1184:
1176:
1173:
1163:
1093:
1076:
1073:
1070:
1067:
1064:
1061:
1058:
1050:
1049:
1045:
1026:
1023:
1020:
1017:
1014:
1011:
1008:
988:
985:
982:
979:
976:
973:
970:
940:
935:
918:
915:
912:
909:
906:
903:
900:
880:
877:
874:
871:
868:
865:
862:
832:
831:
827:
808:
805:
802:
799:
796:
793:
790:
770:
767:
764:
761:
758:
755:
752:
722:
721:
717:
698:
695:
692:
672:
669:
666:
663:
660:
657:
654:
624:
623:
619:
600:
597:
594:
586:
585:
557:
553:
551:
541:
523:
520:
515:
512:
504:
501:
496:
488:
485:
480:
477:
469:
466:
456:
438:
435:
432:
429:
426:
423:
420:
412:
398:
395:
392:
389:
386:
383:
380:
373:At any time:
372:
371:
370:
364:
352:
344:
336:
328:
327:
326:
318:
307:
305:
304:fitness value
301:
297:
293:
289:
279:
276:
261:
258:November 2021
250:
247:
243:
240:
236:
233:
229:
226:
222:
219: –
218:
214:
213:Find sources:
207:
203:
199:
193:
192:
191:single source
187:This article
185:
181:
176:
175:
166:
163:
155:
152:November 2021
144:
141:
137:
134:
130:
127:
123:
120:
116:
113: –
112:
108:
107:Find sources:
101:
97:
93:
89:
85:
78:
71:
62:
61:
56:
54:
47:
46:
41:
40:
35:
30:
21:
20:
2151:(1): 64–95.
2148:
2144:
2119:, retrieved
2097:
2085:
1914:
1854:
1164:
1099:
547:
457:
453:
413:At the end:
369:Invariants:
368:
324:
303:
299:
287:
286:
271:
255:
245:
238:
231:
224:
212:
188:
158:
149:
139:
132:
125:
118:
106:
50:
43:
37:
36:Please help
33:
88:independent
2185:Algorithms
2121:2021-11-16
2077:References
228:newspapers
122:newspapers
96:redirected
39:improve it
2165:0306-4379
2043:−
2008:−
1973:−
1938:−
1293:−
1258:−
1223:−
1188:−
550:Petri net
516:−
481:−
436:−
396:≥
390:≥
198:talk page
86:that are
45:talk page
2179:Category
544:Example
242:scholar
136:scholar
100:deleted
2163:
2112:
314:": -->
244:
237:
230:
223:
215:
138:
131:
124:
117:
109:
92:merged
249:JSTOR
235:books
143:JSTOR
129:books
98:, or
2161:ISSN
2110:ISBN
1912:is:
1528:and
1430:and
1162:is:
893:and
783:and
685:and
316:edit
221:news
115:news
2153:doi
2102:doi
2062:0.8
204:by
2181::
2159:.
2149:33
2147:.
2143:.
2129:^
2108:,
2096:,
1844:).
1736:).
1566:).
1456:).
1358:).
1039:).
1001:,
931:).
821:).
711:).
613:).
577:,
573:,
569:,
94:,
48:.
2167:.
2155::
2104::
2059:=
2056:)
2051:5
2048:1
2040:1
2037:(
2032:2
2029:1
2024:+
2021:)
2016:5
2013:1
2005:1
2002:(
1997:2
1994:1
1989:=
1986:)
1981:p
1978:r
1970:1
1967:(
1962:2
1959:1
1954:+
1951:)
1946:c
1943:m
1935:1
1932:(
1927:2
1924:1
1899:M
1877:d
1874:,
1871:b
1868:,
1865:a
1832:1
1829:=
1826:r
1818:(
1806:]
1802:c
1799:,
1796:a
1792:[
1772:5
1769:=
1766:1
1763:+
1760:4
1757:=
1754:c
1724:5
1721:=
1718:1
1715:+
1712:4
1709:=
1706:p
1686:4
1683:=
1680:2
1677:+
1674:2
1671:=
1668:c
1648:]
1644:d
1641:,
1638:b
1634:[
1614:1
1611:=
1608:m
1587:d
1554:2
1551:=
1548:1
1545:+
1542:1
1539:=
1536:c
1516:4
1513:=
1510:1
1507:+
1504:3
1501:=
1498:p
1477:b
1444:1
1441:=
1438:c
1418:3
1415:=
1412:2
1409:+
1406:1
1403:=
1400:p
1379:a
1346:1
1343:=
1340:p
1312:1
1309:=
1306:)
1301:6
1298:0
1290:1
1287:(
1282:2
1279:1
1274:+
1271:)
1266:6
1263:0
1255:1
1252:(
1247:2
1244:1
1239:=
1236:)
1231:p
1228:r
1220:1
1217:(
1212:2
1209:1
1204:+
1201:)
1196:c
1193:m
1185:1
1182:(
1177:2
1174:1
1149:M
1127:d
1124:,
1121:c
1118:,
1115:b
1112:,
1109:a
1077:6
1074:=
1071:1
1068:+
1065:5
1062:=
1059:c
1027:5
1024:=
1021:2
1018:+
1015:3
1012:=
1009:c
989:6
986:=
983:1
980:+
977:5
974:=
971:p
950:d
919:3
916:=
913:1
910:+
907:2
904:=
901:c
881:5
878:=
875:1
872:+
869:4
866:=
863:p
842:c
809:2
806:=
803:1
800:+
797:1
794:=
791:c
771:4
768:=
765:1
762:+
759:3
756:=
753:p
732:b
699:1
696:=
693:c
673:3
670:=
667:2
664:+
661:1
658:=
655:p
634:a
601:1
598:=
595:p
579:d
575:c
571:b
567:a
529:)
524:p
521:r
513:1
510:(
505:2
502:1
497:+
494:)
489:c
486:m
478:1
475:(
470:2
467:1
439:c
433:m
430:+
427:p
424:=
421:r
399:m
393:c
387:m
384:+
381:p
355:r
347:m
339:c
331:p
320:]
278:)
272:(
260:)
256:(
246:·
239:·
232:·
225:·
208:.
194:.
165:)
159:(
154:)
150:(
140:·
133:·
126:·
119:·
102:.
80:.
55:)
51:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
