Knowledge (XXG)

Calculus of communicating systems

Source đź“ť

1490: 33: 389: 157:
According to Milner, "There is nothing canonical about the choice of the basic combinators, even though they were chosen with great attention to economy. What characterises our calculus is not the exact choice of combinators, but rather the choice of interpretation and of mathematical framework".
145:
around 1980 and the title of a book describing the calculus. Its actions model indivisible communications between exactly two participants. The formal language includes primitives for describing parallel composition, choice between actions and scope restriction. CCS is useful for evaluating the
1257:. Combined Proceedings of the Second International Workshop on Coordination and Organization (CoOrg 2006) and the Second International Workshop on Methods and Tools for Coordinating Concurrent, Distributed and Mobile Systems (MTCoord 2006). 187: 561: 1078:, Joachim Parrow, and David Walker in the late 80's extends CCS with mobility of communication links, by allowing processes to communicate the names of communication channels themselves. 983: 1239:
A Philippou, M Toro, M Antonaki. Simulation and Verification in a Process Calculus for Spatially-Explicit Ecological Models. Scientific Annals of Computer Science 23 (1). 2014
50: 774: 674: 458: 1010: 904: 877: 828: 801: 728: 701: 608: 505: 1311: 1030: 944: 924: 628: 581: 478: 419: 384:{\displaystyle P::=0\,\,\,|\,\,\,a.P_{1}\,\,\,|\,\,\,A\,\,\,|\,\,\,P_{1}+P_{2}\,\,\,|\,\,\,P_{1}|P_{2}\,\,\,|\,\,\,P_{1}\,\,\,|\,\,\,P_{1}{\backslash }a\,\,\,} 1399: 1112: 1361: 97: 1118: 1088:
introduces activity timing in terms of exponentially distributed rates and probabilistic choice, allowing performance metrics to be evaluated.
69: 1213: 76: 515: 1394: 1384: 1304: 1052: 1041: 1176: 1161: 116: 83: 1107: 1193: 65: 1334: 54: 1460: 1494: 1297: 1124: 1470: 1455: 1450: 147: 1515: 43: 1445: 1344: 1520: 90: 1475: 162: 953: 1349: 1320: 1339: 1092: 1096: 737: 639: 17: 1121:(PALPS) is an extension of CCS with probabilistic choice, locations and attributes for locations 1272: 1209: 1172: 1157: 1064: 430: 1409: 1376: 1262: 1201: 138: 988: 882: 838: 806: 779: 706: 679: 586: 483: 1366: 1356: 1060: 1465: 1249:
Montesi, Fabrizio; Guidi, Claudio; Lucchi, Roberto; Zavattaro, Gianluigi (2007-06-27).
1135: 1015: 929: 909: 613: 566: 463: 404: 1509: 1424: 1404: 1219: 1085: 1414: 1099:, and others, introduces (partial) reversibility in the execution of CCS processes. 1075: 1056: 166: 142: 177:
Given a set of action names, the set of CCS processes is defined by the following
1200:. Lecture Notes in Computer Science. Vol. 4486. Springer. pp. 318–370. 1440: 1267: 1250: 1140: 1071: 178: 32: 1205: 1045: 1276: 151: 1289: 556:{\displaystyle A{\overset {\underset {\mathrm {def} }{}}{=}}P_{1}} 1091:
Reversible Communicating Concurrent Systems (RCCS) introduced by
1419: 1081: 1293: 26: 1131:
Models that have been used in the study of CCS-like systems:
968: 371: 1171:, Prentice Hall, International Series in Computer Science, 1048:, is a formal language that arose at a similar time to CCS. 146:
qualitative correctness of properties of a system such as
1251:"JOLIE: a Java Orchestration Language Interpreter Engine" 1119:
Process Calculus for Spatially-Explicit Ecological Models
1063:
in 1982, and uses an axiomatic approach (in the style of
1194:"Tackling Large State Spaces in Performance Modelling" 1067:) to reason about a similar class of processes as CCS. 394:
The parts of the syntax are, in the order given above
1018: 991: 956: 932: 912: 885: 841: 809: 782: 740: 709: 682: 642: 616: 589: 569: 518: 486: 466: 433: 407: 190: 161:
The expressions of the language are interpreted as a
1433: 1375: 1327: 57:. Unsourced material may be challenged and removed. 1024: 1004: 977: 938: 918: 898: 871: 822: 795: 768: 722: 695: 668: 622: 602: 575: 555: 499: 472: 452: 413: 383: 1255:Electronic Notes in Theoretical Computer Science 630:itself, i.e., recursive definitions are allowed) 1125:Java Orchestration Language Interpreter Engine 1305: 8: 1113:Language Of Temporal Ordering Specification 1312: 1298: 1290: 1266: 1198:Formal Methods for Performance Evaluation 1017: 996: 990: 967: 961: 955: 931: 911: 890: 884: 858: 846: 840: 814: 808: 787: 781: 760: 751: 745: 739: 714: 708: 687: 681: 660: 647: 641: 615: 594: 588: 568: 547: 529: 522: 517: 491: 485: 465: 444: 432: 406: 380: 379: 378: 370: 364: 359: 358: 357: 352: 351: 350: 349: 338: 326: 321: 320: 319: 314: 313: 312: 311: 305: 296: 290: 285: 284: 283: 278: 277: 276: 275: 269: 256: 251: 250: 249: 244: 243: 242: 241: 237: 236: 235: 230: 229: 228: 227: 221: 210: 209: 208: 203: 202: 201: 200: 189: 117:Learn how and when to remove this message 1184: 1036:Related calculi, models, and languages 7: 55:adding citations to reliable sources 1154:A Calculus of Communicating Systems 1103:Some other languages based on CCS: 978:{\displaystyle P_{1}{\backslash }a} 169:is used as a semantic equivalence. 66:"Calculus of communicating systems" 1053:Algebra of Communicating Processes 1042:Communicating sequential processes 676:can proceed either as the process 610:(which may contain the identifier 536: 533: 530: 25: 131:calculus of communicating systems 18:Calculus of Communicating Systems 1489: 1488: 1192:Herzog, Ulrich, ed. (May 2007). 1108:Calculus of broadcasting systems 31: 42:needs additional citations for 1495:Category: Concurrent computing 866: 852: 752: 353: 346: 332: 315: 297: 279: 245: 231: 204: 1: 1169:Communication and Concurrency 480:and continue as the process 1456:Dining philosophers problem 1268:10.1016/j.entcs.2007.01.051 769:{\displaystyle P_{1}|P_{2}} 669:{\displaystyle P_{1}+P_{2}} 1537: 1345:Concurrent data structures 163:labelled transition system 1484: 1461:Producer–consumer problem 1446:Cigarette smokers problem 1206:10.1007/978-3-540-72522-0 583:to refer to the process 165:. Between these models, 1476:Sleeping barber problem 1471:Readers–writers problem 1055:(ACP) was developed by 906:with all actions named 453:{\displaystyle a.P_{1}} 1350:Concurrent hash tables 1026: 1006: 979: 940: 920: 900: 873: 824: 797: 770: 724: 697: 670: 624: 604: 577: 563:to use the identifier 557: 501: 474: 460:can perform an action 454: 421:is a valid CCS process 415: 385: 1027: 1007: 1005:{\displaystyle P_{1}} 980: 941: 921: 901: 899:{\displaystyle P_{1}} 874: 872:{\displaystyle P_{1}} 825: 823:{\displaystyle P_{2}} 798: 796:{\displaystyle P_{1}} 776:tells that processes 771: 725: 723:{\displaystyle P_{2}} 698: 696:{\displaystyle P_{1}} 671: 625: 605: 603:{\displaystyle P_{1}} 578: 558: 502: 500:{\displaystyle P_{1}} 475: 455: 416: 401:the inactive process 386: 1321:Concurrent computing 1044:(CSP), developed by 1016: 989: 954: 930: 910: 883: 839: 830:exist simultaneously 807: 780: 738: 732:parallel composition 707: 680: 640: 614: 587: 567: 516: 484: 464: 431: 405: 188: 51:improve this article 1340:Concurrency control 1156:, Springer Verlag, 1022: 1002: 975: 936: 916: 896: 869: 820: 793: 766: 720: 693: 666: 620: 600: 573: 553: 540: 509:process identifier 497: 470: 450: 411: 381: 1516:1980 in computing 1503: 1502: 1215:978-3-540-72482-7 1065:Universal algebra 1025:{\displaystyle a} 939:{\displaystyle b} 919:{\displaystyle a} 623:{\displaystyle A} 576:{\displaystyle A} 541: 528: 527: 473:{\displaystyle a} 414:{\displaystyle 0} 127: 126: 119: 101: 16:(Redirected from 1528: 1492: 1491: 1434:Classic problems 1410:Ambient calculus 1357:Concurrent users 1314: 1307: 1300: 1291: 1281: 1280: 1270: 1246: 1240: 1237: 1231: 1230: 1228: 1227: 1218:. Archived from 1189: 1031: 1029: 1028: 1023: 1011: 1009: 1008: 1003: 1001: 1000: 984: 982: 981: 976: 971: 966: 965: 945: 943: 942: 937: 925: 923: 922: 917: 905: 903: 902: 897: 895: 894: 878: 876: 875: 870: 862: 851: 850: 829: 827: 826: 821: 819: 818: 802: 800: 799: 794: 792: 791: 775: 773: 772: 767: 765: 764: 755: 750: 749: 729: 727: 726: 721: 719: 718: 702: 700: 699: 694: 692: 691: 675: 673: 672: 667: 665: 664: 652: 651: 629: 627: 626: 621: 609: 607: 606: 601: 599: 598: 582: 580: 579: 574: 562: 560: 559: 554: 552: 551: 542: 539: 523: 506: 504: 503: 498: 496: 495: 479: 477: 476: 471: 459: 457: 456: 451: 449: 448: 420: 418: 417: 412: 398:inactive process 390: 388: 387: 382: 374: 369: 368: 356: 342: 331: 330: 318: 310: 309: 300: 295: 294: 282: 274: 273: 261: 260: 248: 234: 226: 225: 207: 139:process calculus 122: 115: 111: 108: 102: 100: 59: 35: 27: 21: 1536: 1535: 1531: 1530: 1529: 1527: 1526: 1525: 1521:Process calculi 1506: 1505: 1504: 1499: 1480: 1429: 1377:Process calculi 1371: 1367:Linearizability 1323: 1318: 1287: 1285: 1284: 1248: 1247: 1243: 1238: 1234: 1225: 1223: 1216: 1191: 1190: 1186: 1149: 1084:, developed by 1074:, developed by 1061:Jan Willem Klop 1038: 1014: 1013: 1012:without action 992: 987: 986: 985:is the process 957: 952: 951: 928: 927: 908: 907: 886: 881: 880: 879:is the process 842: 837: 836: 810: 805: 804: 783: 778: 777: 756: 741: 736: 735: 710: 705: 704: 703:or the process 683: 678: 677: 656: 643: 638: 637: 612: 611: 590: 585: 584: 565: 564: 543: 514: 513: 487: 482: 481: 462: 461: 440: 429: 428: 403: 402: 360: 322: 301: 286: 265: 252: 217: 186: 185: 175: 123: 112: 106: 103: 60: 58: 48: 36: 23: 22: 15: 12: 11: 5: 1534: 1532: 1524: 1523: 1518: 1508: 1507: 1501: 1500: 1498: 1497: 1485: 1482: 1481: 1479: 1478: 1473: 1468: 1466:Race condition 1463: 1458: 1453: 1448: 1443: 1437: 1435: 1431: 1430: 1428: 1427: 1422: 1417: 1412: 1407: 1402: 1397: 1392: 1387: 1381: 1379: 1373: 1372: 1370: 1369: 1364: 1359: 1354: 1353: 1352: 1342: 1337: 1331: 1329: 1325: 1324: 1319: 1317: 1316: 1309: 1302: 1294: 1283: 1282: 1241: 1232: 1214: 1183: 1182: 1181: 1180: 1167:Robin Milner, 1165: 1152:Robin Milner: 1148: 1145: 1144: 1143: 1138: 1136:History monoid 1129: 1128: 1122: 1116: 1110: 1101: 1100: 1089: 1079: 1068: 1049: 1037: 1034: 1033: 1032: 1021: 999: 995: 974: 970: 964: 960: 949: 946: 935: 915: 893: 889: 868: 865: 861: 857: 854: 849: 845: 834: 831: 817: 813: 790: 786: 763: 759: 754: 748: 744: 733: 730: 717: 713: 690: 686: 663: 659: 655: 650: 646: 634: 631: 619: 597: 593: 572: 550: 546: 538: 535: 532: 526: 521: 510: 507: 494: 490: 469: 447: 443: 439: 436: 425: 422: 410: 399: 392: 391: 377: 373: 367: 363: 355: 348: 345: 341: 337: 334: 329: 325: 317: 308: 304: 299: 293: 289: 281: 272: 268: 264: 259: 255: 247: 240: 233: 224: 220: 216: 213: 206: 199: 196: 193: 174: 171: 141:introduced by 125: 124: 39: 37: 30: 24: 14: 13: 10: 9: 6: 4: 3: 2: 1533: 1522: 1519: 1517: 1514: 1513: 1511: 1496: 1487: 1486: 1483: 1477: 1474: 1472: 1469: 1467: 1464: 1462: 1459: 1457: 1454: 1452: 1449: 1447: 1444: 1442: 1439: 1438: 1436: 1432: 1426: 1425:Join-calculus 1423: 1421: 1418: 1416: 1413: 1411: 1408: 1406: 1403: 1401: 1398: 1396: 1393: 1391: 1388: 1386: 1383: 1382: 1380: 1378: 1374: 1368: 1365: 1363: 1362:Indeterminacy 1360: 1358: 1355: 1351: 1348: 1347: 1346: 1343: 1341: 1338: 1336: 1333: 1332: 1330: 1326: 1322: 1315: 1310: 1308: 1303: 1301: 1296: 1295: 1292: 1288: 1278: 1274: 1269: 1264: 1260: 1256: 1252: 1245: 1242: 1236: 1233: 1222:on 2008-04-12 1221: 1217: 1211: 1207: 1203: 1199: 1195: 1188: 1185: 1178: 1177:0-13-115007-3 1174: 1170: 1166: 1163: 1162:0-387-10235-3 1159: 1155: 1151: 1150: 1146: 1142: 1139: 1137: 1134: 1133: 1132: 1126: 1123: 1120: 1117: 1114: 1111: 1109: 1106: 1105: 1104: 1098: 1094: 1093:Vincent Danos 1090: 1087: 1086:Jane Hillston 1083: 1080: 1077: 1073: 1069: 1066: 1062: 1058: 1054: 1050: 1047: 1043: 1040: 1039: 1035: 1019: 997: 993: 972: 962: 958: 950: 947: 933: 913: 891: 887: 863: 859: 855: 847: 843: 835: 832: 815: 811: 788: 784: 761: 757: 746: 742: 734: 731: 715: 711: 688: 684: 661: 657: 653: 648: 644: 635: 632: 617: 595: 591: 570: 548: 544: 524: 519: 511: 508: 492: 488: 467: 445: 441: 437: 434: 426: 423: 408: 400: 397: 396: 395: 375: 365: 361: 343: 339: 335: 327: 323: 306: 302: 291: 287: 270: 266: 262: 257: 253: 238: 222: 218: 214: 211: 197: 194: 191: 184: 183: 182: 180: 172: 170: 168: 164: 159: 155: 153: 149: 144: 140: 136: 132: 121: 118: 110: 107:November 2011 99: 96: 92: 89: 85: 82: 78: 75: 71: 68: â€“  67: 63: 62:Find sources: 56: 52: 46: 45: 40:This article 38: 34: 29: 28: 19: 1415:API-Calculus 1389: 1286: 1258: 1254: 1244: 1235: 1224:. Retrieved 1220:the original 1197: 1187: 1168: 1153: 1130: 1102: 1097:Jean Krivine 1076:Robin Milner 1057:Jan Bergstra 636:the process 427:the process 393: 176: 167:bisimilarity 160: 156: 143:Robin Milner 134: 130: 128: 113: 104: 94: 87: 80: 73: 61: 49:Please help 44:verification 41: 1441:ABA problem 1335:Concurrency 1141:Actor model 1072:pi-calculus 948:restriction 926:renamed as 179:BNF grammar 1510:Categories 1405:Ď€-calculus 1226:2009-04-21 1147:References 1046:Tony Hoare 77:newspapers 1277:1571-0661 1261:: 19–33. 969:∖ 633:summation 372:∖ 1451:Deadlock 833:renaming 152:livelock 148:deadlock 1328:General 1164:. 1980. 1127:(Jolie) 1115:(LOTOS) 137:) is a 91:scholar 1493:  1275:  1212:  1179:. 1989 1175:  1160:  512:write 424:action 173:Syntax 93:  86:  79:  72:  64:  1400:LOTOS 98:JSTOR 84:books 1420:PEPA 1273:ISSN 1210:ISBN 1173:ISBN 1158:ISBN 1082:PEPA 1070:The 1059:and 1051:The 803:and 129:The 70:news 1395:ACP 1390:CCS 1385:CSP 1263:doi 1259:181 1202:doi 195:::= 150:or 135:CCS 53:by 1512:: 1271:. 1253:. 1208:. 1196:. 1095:, 181:: 154:. 1313:e 1306:t 1299:v 1279:. 1265:: 1229:. 1204:: 1020:a 998:1 994:P 973:a 963:1 959:P 934:b 914:a 892:1 888:P 867:] 864:a 860:/ 856:b 853:[ 848:1 844:P 816:2 812:P 789:1 785:P 762:2 758:P 753:| 747:1 743:P 716:2 712:P 689:1 685:P 662:2 658:P 654:+ 649:1 645:P 618:A 596:1 592:P 571:A 549:1 545:P 537:f 534:e 531:d 525:= 520:A 493:1 489:P 468:a 446:1 442:P 438:. 435:a 409:0 376:a 366:1 362:P 354:| 347:] 344:a 340:/ 336:b 333:[ 328:1 324:P 316:| 307:2 303:P 298:| 292:1 288:P 280:| 271:2 267:P 263:+ 258:1 254:P 246:| 239:A 232:| 223:1 219:P 215:. 212:a 205:| 198:0 192:P 133:( 120:) 114:( 109:) 105:( 95:· 88:· 81:· 74:· 47:. 20:)

Index

Calculus of Communicating Systems

verification
improve this article
adding citations to reliable sources
"Calculus of communicating systems"
news
newspapers
books
scholar
JSTOR
Learn how and when to remove this message
process calculus
Robin Milner
deadlock
livelock
labelled transition system
bisimilarity
BNF grammar
Communicating sequential processes
Tony Hoare
Algebra of Communicating Processes
Jan Bergstra
Jan Willem Klop
Universal algebra
pi-calculus
Robin Milner
PEPA
Jane Hillston
Vincent Danos

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

↑