863:
614:
is similar in principle to composition, but allows for an arbitrary number of possibly non-binary constraints; the generated constraint is on an arbitrary subset of the variables of the original constraints. Given constraints
777:
659:
574:
469:
425:
361:
317:
273:
532:
711:
606:
507:
731:
679:
381:
222:
202:
182:
162:
142:
122:
102:
82:
62:
42:
904:
933:
848:
832:
813:
576:
that is satisfied by an evaluation if this evaluation can be extended to the other variables in such a way the original constraint
923:
897:
788:
363:
that is satisfied by every evaluation of the two non-shared variables for which there exists a value of the shared variable
890:
17:
736:
618:
870:
928:
430:
386:
322:
278:
234:
844:
828:
809:
537:
819:
684:
579:
480:
383:
such that the evaluation of these three variables satisfies the two original constraints
512:
874:
716:
664:
366:
227:
Some operations on constraints produce a new constraint that is a consequence of them.
207:
187:
167:
147:
127:
107:
87:
67:
47:
27:
917:
802:
477:
restricts the effects of a constraint to some of its variables. Given a constraint
24:
is a relationship between constraints and their consequences. A set of constraints
862:
319:
with a common variable. The composition of such two constraints is the constraint
733:
satisfies this constraint if it can be extended to the other variables so that
681:
of their variables, the extended composition of them is the constraint
124:
is a valuation of the variables in the scopes of the constraints in
878:
739:
719:
687:
667:
621:
582:
540:
515:
483:
433:
389:
369:
325:
281:
237:
210:
190:
170:
150:
130:
110:
90:
70:
50:
30:
771:
725:
705:
673:
653:
600:
568:
526:
501:
463:
419:
375:
355:
311:
267:
216:
196:
176:
156:
136:
116:
96:
76:
56:
36:
898:
840:Programming with constraints: An introduction
8:
905:
891:
763:
744:
738:
718:
686:
666:
645:
626:
620:
581:
539:
514:
482:
432:
388:
368:
324:
280:
236:
231:operates on a pair of binary constraints
209:
189:
169:
149:
129:
109:
89:
69:
49:
29:
838:Marriott, Kim; Peter J. Stuckey (1998).
7:
859:
857:
824:Principles of constraint programming
772:{\displaystyle C_{1},\ldots ,C_{m}}
654:{\displaystyle C_{1},\ldots ,C_{m}}
534:of its variables is the constraint
14:
861:
789:Constraint satisfaction problem
700:
688:
595:
583:
563:
541:
496:
484:
458:
449:
437:
434:
414:
405:
393:
390:
350:
341:
329:
326:
306:
297:
285:
282:
262:
253:
241:
238:
204:also satisfies the constraint
1:
826:. Cambridge University Press.
877:. You can help Knowledge by
509:its projection to a subset
950:
856:
934:Applied mathematics stubs
464:{\displaystyle ((y,z),S)}
420:{\displaystyle ((x,y),R)}
356:{\displaystyle ((x,z),Q)}
312:{\displaystyle ((y,z),S)}
268:{\displaystyle ((x,y),R)}
713:where an evaluation of
569:{\displaystyle (t',R')}
144:and all constraints in
18:constraint satisfaction
924:Constraint programming
873:-related article is a
801:Dechter, Rina (2003).
773:
727:
707:
675:
655:
602:
570:
528:
503:
465:
421:
377:
357:
313:
269:
229:Constraint composition
218:
198:
178:
158:
138:
118:
98:
84:is also a solution to
78:
58:
38:
804:Constraint processing
774:
728:
708:
706:{\displaystyle (A,R)}
676:
656:
603:
601:{\displaystyle (t,R)}
571:
529:
504:
502:{\displaystyle (t,R)}
475:Constraint projection
466:
422:
378:
358:
314:
270:
219:
199:
179:
159:
139:
119:
104:. In other words, if
99:
79:
64:if every solution to
59:
44:entails a constraint
39:
737:
717:
685:
665:
619:
612:Extended composition
580:
538:
513:
481:
431:
387:
367:
323:
279:
235:
208:
188:
168:
148:
128:
108:
88:
68:
48:
28:
22:constraint inference
871:applied mathematics
779:are all satisfied.
807:. Morgan Kaufmann.
769:
723:
703:
671:
651:
598:
566:
527:{\displaystyle t'}
524:
499:
461:
417:
373:
353:
309:
265:
214:
194:
174:
154:
134:
114:
94:
74:
54:
34:
886:
885:
726:{\displaystyle A}
674:{\displaystyle A}
376:{\displaystyle y}
217:{\displaystyle C}
197:{\displaystyle V}
177:{\displaystyle V}
164:are satisfied by
157:{\displaystyle D}
137:{\displaystyle D}
117:{\displaystyle V}
97:{\displaystyle C}
77:{\displaystyle D}
57:{\displaystyle C}
37:{\displaystyle D}
941:
907:
900:
893:
865:
858:
843:
827:
808:
778:
776:
775:
770:
768:
767:
749:
748:
732:
730:
729:
724:
712:
710:
709:
704:
680:
678:
677:
672:
660:
658:
657:
652:
650:
649:
631:
630:
607:
605:
604:
599:
575:
573:
572:
567:
562:
551:
533:
531:
530:
525:
523:
508:
506:
505:
500:
470:
468:
467:
462:
426:
424:
423:
418:
382:
380:
379:
374:
362:
360:
359:
354:
318:
316:
315:
310:
274:
272:
271:
266:
223:
221:
220:
215:
203:
201:
200:
195:
183:
181:
180:
175:
163:
161:
160:
155:
143:
141:
140:
135:
123:
121:
120:
115:
103:
101:
100:
95:
83:
81:
80:
75:
63:
61:
60:
55:
43:
41:
40:
35:
949:
948:
944:
943:
942:
940:
939:
938:
914:
913:
912:
911:
854:
837:
818:
800:
797:
785:
759:
740:
735:
734:
715:
714:
683:
682:
663:
662:
641:
622:
617:
616:
578:
577:
555:
544:
536:
535:
516:
511:
510:
479:
478:
429:
428:
385:
384:
365:
364:
321:
320:
277:
276:
233:
232:
206:
205:
186:
185:
166:
165:
146:
145:
126:
125:
106:
105:
86:
85:
66:
65:
46:
45:
26:
25:
12:
11:
5:
947:
945:
937:
936:
931:
926:
916:
915:
910:
909:
902:
895:
887:
884:
883:
866:
852:
851:
835:
820:Apt, Krzysztof
816:
796:
793:
792:
791:
784:
781:
766:
762:
758:
755:
752:
747:
743:
722:
702:
699:
696:
693:
690:
670:
648:
644:
640:
637:
634:
629:
625:
608:is satisfied.
597:
594:
591:
588:
585:
565:
561:
558:
554:
550:
547:
543:
522:
519:
498:
495:
492:
489:
486:
460:
457:
454:
451:
448:
445:
442:
439:
436:
416:
413:
410:
407:
404:
401:
398:
395:
392:
372:
352:
349:
346:
343:
340:
337:
334:
331:
328:
308:
305:
302:
299:
296:
293:
290:
287:
284:
264:
261:
258:
255:
252:
249:
246:
243:
240:
213:
193:
173:
153:
133:
113:
93:
73:
53:
33:
13:
10:
9:
6:
4:
3:
2:
946:
935:
932:
930:
927:
925:
922:
921:
919:
908:
903:
901:
896:
894:
889:
888:
882:
880:
876:
872:
867:
864:
860:
855:
850:
849:0-262-13341-5
846:
841:
836:
834:
833:0-521-82583-0
830:
825:
821:
817:
815:
814:1-55860-890-7
811:
806:
805:
799:
798:
794:
790:
787:
786:
782:
780:
764:
760:
756:
753:
750:
745:
741:
720:
697:
694:
691:
668:
646:
642:
638:
635:
632:
627:
623:
613:
609:
592:
589:
586:
559:
556:
552:
548:
545:
520:
517:
493:
490:
487:
476:
472:
455:
452:
446:
443:
440:
411:
408:
402:
399:
396:
370:
347:
344:
338:
335:
332:
303:
300:
294:
291:
288:
259:
256:
250:
247:
244:
230:
225:
211:
191:
171:
151:
131:
111:
91:
71:
51:
31:
23:
19:
879:expanding it
868:
853:
842:. MIT Press.
839:
823:
803:
611:
610:
474:
473:
228:
226:
21:
15:
661:and a list
918:Categories
795:References
929:Inference
754:…
636:…
822:(2003).
783:See also
560:′
549:′
521:′
184:, then
847:
831:
812:
869:This
875:stub
845:ISBN
829:ISBN
810:ISBN
427:and
275:and
16:In
920::
471:.
224:.
20:,
906:e
899:t
892:v
881:.
765:m
761:C
757:,
751:,
746:1
742:C
721:A
701:)
698:R
695:,
692:A
689:(
669:A
647:m
643:C
639:,
633:,
628:1
624:C
596:)
593:R
590:,
587:t
584:(
564:)
557:R
553:,
546:t
542:(
518:t
497:)
494:R
491:,
488:t
485:(
459:)
456:S
453:,
450:)
447:z
444:,
441:y
438:(
435:(
415:)
412:R
409:,
406:)
403:y
400:,
397:x
394:(
391:(
371:y
351:)
348:Q
345:,
342:)
339:z
336:,
333:x
330:(
327:(
307:)
304:S
301:,
298:)
295:z
292:,
289:y
286:(
283:(
263:)
260:R
257:,
254:)
251:y
248:,
245:x
242:(
239:(
212:C
192:V
172:V
152:D
132:D
112:V
92:C
72:D
52:C
32:D
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
