191:
24:
for which membership of a word in the language can be determined by looking at the first and last symbol and each two-symbol substring of the word. Equivalently, it is a language recognised by a
624:
316:
944:
617:
831:
610:
555:
756:
846:
771:
585:
524:
489:
939:
924:
112:
996:
800:
29:
817:
742:
346:
914:
810:
547:
991:
986:
735:
887:
882:
968:
Any language in each category is generated by a grammar and by an automaton in the category in the same line.
898:
836:
761:
841:
789:
602:
416:
934:
909:
766:
727:
267:
919:
861:
805:
104:
654:
581:
551:
520:
485:
436:
903:
856:
823:
669:
591:
561:
530:
495:
428:
342:
866:
781:
748:
664:
637:
633:
595:
565:
534:
499:
25:
21:
877:
659:
641:
508:
432:
980:
962:
519:. Research Monograph. Vol. 65. With an appendix by William Henneman. MIT Press.
573:
513:
929:
851:
776:
335:
440:
345:
not containing the empty string is the image of a local language under a
892:
606:
961:
Each category of languages, except those marked by a , is a
186:{\displaystyle (RA^{*}\cap A^{*}S)\setminus A^{*}FA^{*}\ .}
546:. Translated from the French by Reuben Thomas. Cambridge:
270:
115:
512:
310:
185:
216:depends only on the prefix and suffix of length
618:
338:, but not complement, union or concatenation.
8:
940:Counter-free (with aperiodic finite monoid)
650:
625:
611:
603:
278:
269:
171:
158:
139:
126:
114:
417:"Families of locally testable languages"
401:
399:
397:
369:
367:
365:
363:
359:
151:
832:Linear context-free rewriting language
208:is one for which membership of a word
757:Linear context-free rewriting systems
7:
471:McNaughton & Papert (1971) p.18
453:McNaughton & Papert (1971) p.14
330:The family of local languages over
240:. A local language is 2-testable.
79:if and only if the first letter of
965:of the category directly above it.
14:
334:is closed under intersection and
578:Jewels of Formal Language Theory
299:
290:
148:
116:
30:deterministic finite automaton
1:
542:Sakarovitch, Jacques (2009).
433:10.1016/S0304-3975(98)00332-6
95:and no factor of length 2 in
421:Theoretical Computer Science
415:Caron, Pascal (2000-07-06).
347:strictly alphabetic morphism
311:{\displaystyle aa^{*},\ \ .}
544:Elements of automata theory
103:. This corresponds to the
1013:
847:Deterministic context-free
772:Deterministic context-free
548:Cambridge University Press
220:and the set of factors of
958:
920:Nondeterministic pushdown
648:
484:. Chapman and Hall/CRC.
480:Lawson, Mark V. (2004).
405:Sakarovitch (2009) p.228
28:, a particular kind of
997:Combinatorics on words
925:Deterministic pushdown
801:Recursively enumerable
312:
187:
580:. Pitman Publishing.
515:Counter-free Automata
313:
188:
87:, the last letter of
47:if there are subsets
35:Formally, a language
910:Tree stack automaton
507:McNaughton, Robert;
268:
113:
818:range concatenation
743:range concatenation
462:Lawson (2004) p.132
391:Lawson (2004) p.129
382:Lawson (2004) p.130
373:Salomaa (1981) p.97
249:Over the alphabet {
236:-testable for some
308:
196:More generally, a
183:
105:regular expression
16:In mathematics, a
974:
973:
953:
952:
915:Embedded pushdown
811:Context-sensitive
736:Context-sensitive
670:Abstract machines
655:Chomsky hierarchy
557:978-0-521-84425-3
304:
289:
179:
71:such that a word
43:is defined to be
39:over an alphabet
1004:
992:Formal languages
987:Semigroup theory
969:
966:
930:Visibly pushdown
904:Thread automaton
852:Visibly pushdown
820:
777:Visibly pushdown
745:
732:(no common name)
651:
638:formal languages
627:
620:
613:
604:
599:
569:
538:
518:
503:
472:
469:
463:
460:
454:
451:
445:
444:
412:
406:
403:
392:
389:
383:
380:
374:
371:
343:regular language
317:
315:
314:
309:
302:
287:
283:
282:
230:locally testable
228:; a language is
192:
190:
189:
184:
177:
176:
175:
163:
162:
144:
143:
131:
130:
1012:
1011:
1007:
1006:
1005:
1003:
1002:
1001:
977:
976:
975:
970:
967:
960:
954:
949:
871:
815:
794:
740:
721:
644:
642:formal grammars
634:Automata theory
631:
588:
572:
558:
541:
527:
509:Papert, Seymour
506:
492:
482:Finite automata
479:
476:
475:
470:
466:
461:
457:
452:
448:
414:
413:
409:
404:
395:
390:
386:
381:
377:
372:
361:
356:
327:
321:
274:
266:
265:
246:
167:
154:
135:
122:
111:
110:
26:local automaton
22:formal language
12:
11:
5:
1010:
1008:
1000:
999:
994:
989:
979:
978:
972:
971:
959:
956:
955:
951:
950:
948:
947:
945:Acyclic finite
942:
937:
932:
927:
922:
917:
912:
906:
901:
896:
895:Turing Machine
890:
888:Linear-bounded
885:
880:
878:Turing machine
874:
872:
870:
869:
864:
859:
854:
849:
844:
839:
837:Tree-adjoining
834:
829:
826:
821:
813:
808:
803:
797:
795:
793:
792:
787:
784:
779:
774:
769:
764:
762:Tree-adjoining
759:
754:
751:
746:
738:
733:
730:
724:
722:
720:
719:
716:
713:
710:
707:
704:
701:
698:
695:
692:
689:
686:
683:
680:
676:
673:
672:
667:
662:
657:
649:
646:
645:
632:
630:
629:
622:
615:
607:
601:
600:
586:
570:
556:
539:
525:
504:
490:
474:
473:
464:
455:
446:
427:(1): 361–376.
407:
393:
384:
375:
358:
357:
355:
352:
351:
350:
339:
326:
323:
319:
318:
307:
301:
298:
295:
292:
286:
281:
277:
273:
262:
261:
245:
242:
194:
193:
182:
174:
170:
166:
161:
157:
153:
150:
147:
142:
138:
134:
129:
125:
121:
118:
18:local language
13:
10:
9:
6:
4:
3:
2:
1009:
998:
995:
993:
990:
988:
985:
984:
982:
964:
963:proper subset
957:
946:
943:
941:
938:
936:
933:
931:
928:
926:
923:
921:
918:
916:
913:
911:
907:
905:
902:
900:
897:
894:
891:
889:
886:
884:
881:
879:
876:
875:
873:
868:
865:
863:
860:
858:
855:
853:
850:
848:
845:
843:
840:
838:
835:
833:
830:
827:
825:
822:
819:
814:
812:
809:
807:
804:
802:
799:
798:
796:
791:
790:Non-recursive
788:
785:
783:
780:
778:
775:
773:
770:
768:
765:
763:
760:
758:
755:
752:
750:
747:
744:
739:
737:
734:
731:
729:
726:
725:
723:
717:
714:
711:
708:
705:
702:
699:
696:
693:
690:
687:
684:
681:
678:
677:
675:
674:
671:
668:
666:
663:
661:
658:
656:
653:
652:
647:
643:
639:
635:
628:
623:
621:
616:
614:
609:
608:
605:
597:
593:
589:
587:0-273-08522-0
583:
579:
575:
574:Salomaa, Arto
571:
567:
563:
559:
553:
549:
545:
540:
536:
532:
528:
526:0-262-13076-9
522:
517:
516:
510:
505:
501:
497:
493:
491:1-58488-255-7
487:
483:
478:
477:
468:
465:
459:
456:
450:
447:
442:
438:
434:
430:
426:
422:
418:
411:
408:
402:
400:
398:
394:
388:
385:
379:
376:
370:
368:
366:
364:
360:
353:
348:
344:
340:
337:
333:
329:
328:
324:
322:
305:
296:
293:
284:
279:
275:
271:
264:
263:
259:
256:
252:
248:
247:
243:
241:
239:
235:
231:
227:
223:
219:
215:
211:
207:
203:
199:
180:
172:
168:
164:
159:
155:
145:
140:
136:
132:
127:
123:
119:
109:
108:
107:
106:
102:
98:
94:
90:
86:
82:
78:
74:
70:
66:
62:
59:and a subset
58:
54:
50:
46:
42:
38:
33:
31:
27:
23:
19:
899:Nested stack
842:Context-free
767:Context-free
728:Unrestricted
577:
543:
514:
481:
467:
458:
449:
424:
420:
410:
387:
378:
331:
320:
258:
254:
250:
237:
233:
229:
225:
221:
217:
213:
209:
205:
201:
197:
195:
100:
96:
92:
88:
84:
80:
76:
72:
68:
64:
60:
56:
52:
48:
44:
40:
36:
34:
17:
15:
908:restricted
336:Kleene star
981:Categories
596:0487.68064
566:1188.68177
535:0232.94024
500:1086.68074
354:References
325:Properties
224:of length
862:Star-free
816:Positive
806:Decidable
741:Positive
665:Languages
441:0304-3975
280:∗
232:if it is
204:language
173:∗
160:∗
152:∖
141:∗
133:∩
128:∗
660:Grammars
576:(1981).
511:(1971).
244:Examples
202:testable
883:Decider
857:Regular
824:Indexed
782:Regular
749:Indexed
935:Finite
867:Finite
712:Type-3
703:Type-2
685:Type-1
679:Type-0
594:
584:
564:
554:
533:
523:
498:
488:
439:
341:Every
303:
288:
178:
99:is in
91:is in
83:is in
75:is in
893:PTIME
45:local
20:is a
640:and
582:ISBN
552:ISBN
521:ISBN
486:ISBN
437:ISSN
51:and
592:Zbl
562:Zbl
531:Zbl
496:Zbl
429:doi
425:242
212:in
63:of
55:of
983::
636::
590:.
560:.
550:.
529:.
494:.
435:.
423:.
419:.
396:^
362:^
32:.
828:—
786:—
753:—
718:—
715:—
709:—
706:—
700:—
697:—
694:—
691:—
688:—
682:—
626:e
619:t
612:v
598:.
568:.
537:.
502:.
443:.
431::
349:.
332:A
306:.
300:]
297:b
294:a
291:[
285:,
276:a
272:a
260:}
257:,
255:b
253:,
251:a
238:k
234:k
226:k
222:w
218:k
214:L
210:w
206:L
200:-
198:k
181:.
169:A
165:F
156:A
149:)
146:S
137:A
124:A
120:R
117:(
101:F
97:w
93:S
89:w
85:R
81:w
77:L
73:w
69:A
67:×
65:A
61:F
57:A
53:S
49:R
41:A
37:L
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