473:
1623:
can be applied to a regular tree grammar to compute for each nonterminal the minimum weight of a derivable tree. Based on this information, it is straightforward to enumerate its language in increasing weight order. In particular, any nonterminal with infinite minimum weight produces the empty
1688:
2008:
1681:
1280:
Comon, Hubert; Dauchet, Max; Gilleron, Remi; LΓΆding, Christof; Jacquemard, Florent; Lugiez, Denis; Tison, Sophie; Tommasi, Marc (12 October 2007).
472:
1895:
1674:
1820:
1555:
Thatcher, J.W.; Wright, J.B. (1968). "Generalized Finite
Automata Theory with an Application to a Decision Problem of Second-Order Logic".
1910:
1835:
1328:
1478:
2003:
1988:
1864:
1210:
1881:
1806:
28:
1310:
1978:
1192:
1874:
1178:
2050:
1799:
1496:
Algorithms for
Regular Tree Grammar Network Search and Their Application to Mining Humanβviral Infection Patterns
1162:
1951:
1946:
1648:
Bogaert, B.; Tison, Sophie (1992). "Equality and
Disequality Constraints on Direct Subterms in Tree Automata".
2032:
Any language in each category is generated by a grammar and by an automaton in the category in the same line.
1620:
1962:
1900:
1825:
1602:
1369:
1260:
1239:
32:
1646:
Regular tree automata have been generalized to admit equality tests between sibling nodes in trees. See:
1905:
1853:
1666:
1436:
Gilleron, R.; Tison, S.; Tommasi, M. (1993). "Solving
Systems of Set Constraints using Tree Automata".
1998:
1973:
1830:
1791:
1466:
1374:
1265:
1607:
56:
44:
1983:
1925:
1869:
1572:
1456:
1387:
1334:
1185:
1157:
Rajeev Alur and
Parthasarathy Madhusudan related a subclass of regular binary tree languages to
1718:
1474:
1324:
1217:
1204:
1200:
1196:
1189:
865:, using the nonterminal set and the alphabet from above, but extending the production set by
1967:
1920:
1887:
1733:
1635:
1564:
1541:
1531:
1500:
1379:
1316:
952:
counterpart in
Standard ML, nor in any other functional language. It is a proper subset of
1930:
1845:
1812:
1728:
1701:
1697:
1144:
712:
708:
477:
225:
103:
52:
1470:
1941:
1723:
1705:
1595:
Algorithms on regular tree grammars are discussed from an efficiency-oriented view in:
1591:. Studies in Computer Science and Artificial Intelligence. Vol. 10. North-Holland.
1233:
1151:
40:
1536:
1519:
1312:
Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04
561:(.,.) } is our ranked alphabet, arities indicated by dummy arguments (i.e. the symbol
2044:
2026:
1639:
460:
17:
1576:
1616:
1406:
Emmelmann, Helmut (1991). "Code
Selection by Regularly Controlled Term Rewriting".
1338:
184:
48:
1391:
55:
can be seen as a special kind of regular tree grammar, describing a set of single-
1993:
1915:
1840:
1158:
751:
1599:
ACM Conference on
Functional Programming Languages and Computer Architecture
1383:
1354:
1320:
1303:
1656:
Allowing equality tests between deeper nodes leads to undecidability. See:
1150:
The regular tree languages are also the languages recognized by bottom-up
1281:
1597:
Aiken, A.; Murphy, B. (1991). "Implementing
Regular Tree Expressions".
1568:
1546:
1421:
Comon, Hubert (1990). "Equational
Formulas in Order-Sorted Algebras".
194:
according to their arities, where nonterminals are considered nullary.
1259:"Regular tree grammars as a formalism for scope underspecification".
711:; it is a tree of trees (main picture), whereas a derivation tree in
207:
implicitly defines a set of trees: any tree that can be derived from
1138:
Alternative characterizations and relation to other formal languages
1956:
1461:
484:
in linear (upper left table) and graphical (main picture) notation
471:
107:
1626:
Knuth, D.E. (1977). "A Generalization of Dijkstra's Algorithm".
1438:
10th Annual Symposium on Theoretical Aspects of Computer Science
1220:
about a finite algebra (which is always a regular tree language)
933:) is the set of all finite lists of boolean values that contain
441:
denotes the set of all trees composed from symbols of Ξ£, while β
1670:
1660:
Automates d'Arbres avec Tests d'ΓgalitΓ©s entre Cousins Germains
1451:
Burghardt, Jochen (2002). "Axiomatization of Finite Algebras".
457:
A language generated by some regular tree grammar is called a
1104:
are also regular tree languages, and it is decidable whether
2025:
Each category of languages, except those marked by a , is a
750:
corresponds to the algebraic data type declarations (in the
725:
is the set of all finite lists of boolean values, that is,
1514:
Regular tree grammars were already described in 1968 by:
187:, i.e. the set of all trees composed from symbols in
1455:. LNAI. Vol. 2479. Springer. pp. 222β234.
1060:
both are regular tree languages, then the tree sets
820:) corresponds to a Standard-ML value of type BList.
106:(i.e., an alphabet whose symbols have an associated
1652:. LNCS. Vol. 577. Springer. pp. 161β172.
1440:. LNCS. Vol. 665. Springer. pp. 505β514.
1410:. Workshops in Computing. Springer. pp. 3β29.
1174:Applications of regular tree grammars include:
1143:Regular tree grammars are a generalization of
1682:
1408:Code Generation - Concepts, Tools, Techniques
372:means a tree with exactly one hole in it; if
8:
1154:and nondeterministic top-down tree automata.
974:), too, as the following derivation shows:
2004:Counter-free (with aperiodic finite monoid)
1282:"Tree Automata Techniques and Applications"
1236:β a generalization of regular tree grammars
963:). The above example term happens to be in
872:, consisting of the following productions:
136:is a finite set of productions of the form
1714:
1689:
1675:
1667:
1587:Nivat, Maurice; Podelski, Andreas (1992).
1606:
1545:
1535:
1460:
1373:
1264:
715:is a tree of strings (upper left table).
1615:Given a mapping from trees to weights,
1251:
639:An example derivation from the grammar
588:consists of the following productions:
380:denotes the result of filling the tree
1896:Linear context-free rewriting language
1821:Linear context-free rewriting systems
1520:"The Minimalization of Tree Automata"
1216:The set of all truths expressible in
7:
1585:A book devoted to tree grammars is:
448:denotes successive applications of β
223:. This set of trees is known as the
1453:Advances in Artificial Intelligence
1355:"Adding nesting structure to words"
2029:of the category directly above it.
1621:Dijkstra's shortest-path algorithm
707:The image shows the corresponding
120:is the starting nonterminal, with
25:
1353:Alur, R.; Madhusudan, P. (2009).
1302:Alur, R.; Madhusudan, P. (2004).
578:is our starting nonterminal, and
99:is a finite set of nonterminals,
718:The tree language generated by
391:The tree language generated by
233:. More formally, the relation β
1628:Information Processing Letters
1:
1537:10.1016/s0019-9958(68)90917-0
538:} is our set of nonterminals,
1640:10.1016/0020-0190(77)90002-3
1304:"Visibly pushdown languages"
29:theoretical computer science
1589:Tree Automata and Languages
1557:Mathematical Systems Theory
1494:Ziv-Ukelson, Smoly (2016).
1181:in compiler code generation
2067:
1911:Deterministic context-free
1836:Deterministic context-free
1163:visibly pushdown languages
2022:
1984:Nondeterministic pushdown
1712:
823:For another example, let
318:), if there is a context
250:) is defined as follows:
756:
276:derived in a single step
71:is defined by the tuple
43:that describes a set of
1524:Information and Control
1518:Brainerd, W.S. (1968).
1384:10.1145/1516512.1516518
1321:10.1145/1007352.1007390
1213:about mathematical sets
937:at least once. The set
754:programming language):
67:A regular tree grammar
1989:Deterministic pushdown
1865:Recursively enumerable
1240:Tree-adjoining grammar
485:
33:formal language theory
1619:'s generalization of
1179:Instruction selection
1145:regular word grammars
475:
18:Regular tree language
1974:Tree stack automaton
1658:Tommasi, M. (1991).
1601:. pp. 427β447.
1315:. pp. 202β211.
183:) is the associated
53:regular word grammar
37:regular tree grammar
1882:range concatenation
1807:range concatenation
1471:2014arXiv1403.7347B
1042:Language properties
736:) happens to equal
376:is such a context,
211:using the rule set
199:Derivation of trees
1569:10.1007/BF01691346
1498:. J. of Comp. Bio.
1362:Journal of the ACM
1343:Sect.4, Theorem 5,
1186:decision procedure
486:
2038:
2037:
2017:
2016:
1979:Embedded pushdown
1875:Context-sensitive
1800:Context-sensitive
1734:Abstract machines
1719:Chomsky hierarchy
1218:first-order logic
1195:of formulas over
1190:first-order logic
384:into the hole of
322:and a production
16:(Redirected from
2058:
2051:Formal languages
2033:
2030:
1994:Visibly pushdown
1968:Thread automaton
1916:Visibly pushdown
1884:
1841:Visibly pushdown
1809:
1796:(no common name)
1715:
1702:formal languages
1691:
1684:
1677:
1668:
1663:
1653:
1643:
1612:
1610:
1592:
1580:
1551:
1549:
1539:
1502:
1499:
1491:
1485:
1484:
1464:
1448:
1442:
1441:
1433:
1427:
1426:
1418:
1412:
1411:
1403:
1397:
1395:
1377:
1359:
1350:
1344:
1342:
1308:
1299:
1293:
1292:
1290:
1288:
1277:
1271:
1270:
1268:
1256:
1203:(β) as the only
1119:
1089:
864:
809:Every member of
805:
802:
799:
796:
793:
790:
787:
784:
781:
778:
775:
772:
769:
766:
763:
760:
430:
395:is the language
336:
298:
273:
193:
171:
153:
129:
110:) disjoint from
21:
2066:
2065:
2061:
2060:
2059:
2057:
2056:
2055:
2041:
2040:
2039:
2034:
2031:
2024:
2018:
2013:
1935:
1879:
1858:
1804:
1785:
1708:
1706:formal grammars
1698:Automata theory
1695:
1657:
1650:Proc. 9th STACS
1647:
1625:
1624:language. See:
1596:
1586:
1554:
1517:
1511:
1509:Further reading
1506:
1505:
1493:
1492:
1488:
1481:
1450:
1449:
1445:
1435:
1434:
1430:
1420:
1419:
1415:
1405:
1404:
1400:
1375:10.1.1.145.9971
1357:
1352:
1351:
1347:
1331:
1306:
1301:
1300:
1296:
1286:
1284:
1279:
1278:
1274:
1266:10.1.1.164.5484
1258:
1257:
1253:
1248:
1230:
1172:
1140:
1133:
1126:
1118:
1111:
1105:
1103:
1096:
1088:
1081:
1074:
1067:
1061:
1059:
1052:
1044:
997:
982:
973:
962:
947:
932:
917:
902:
881:
871:
862:
855:
848:
841:
837:
830:
824:
819:
807:
806:
803:
800:
797:
794:
791:
788:
785:
782:
779:
776:
773:
770:
767:
764:
761:
758:
749:
742:
735:
724:
709:derivation tree
645:
587:
573:
544:
529:
519:
512:
505:
501:
494:
483:
478:derivation tree
470:
453:
447:
440:
425:
414:
396:
359:
346:
323:
317:
311:
305:
292:
285:
279:
267:
260:
254:
245:
238:
215:is said to be
201:
188:
178:
165:
155:
145:
121:
104:ranked alphabet
65:
23:
22:
15:
12:
11:
5:
2064:
2062:
2054:
2053:
2043:
2042:
2036:
2035:
2023:
2020:
2019:
2015:
2014:
2012:
2011:
2009:Acyclic finite
2006:
2001:
1996:
1991:
1986:
1981:
1976:
1970:
1965:
1960:
1959:Turing Machine
1954:
1952:Linear-bounded
1949:
1944:
1942:Turing machine
1938:
1936:
1934:
1933:
1928:
1923:
1918:
1913:
1908:
1903:
1901:Tree-adjoining
1898:
1893:
1890:
1885:
1877:
1872:
1867:
1861:
1859:
1857:
1856:
1851:
1848:
1843:
1838:
1833:
1828:
1826:Tree-adjoining
1823:
1818:
1815:
1810:
1802:
1797:
1794:
1788:
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1783:
1780:
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1679:
1671:
1665:
1664:
1654:
1644:
1613:
1608:10.1.1.39.3766
1593:
1583:
1582:
1581:
1552:
1530:(5): 484β491.
1510:
1507:
1504:
1503:
1486:
1479:
1443:
1428:
1413:
1398:
1345:
1330:978-1581138528
1329:
1294:
1272:
1250:
1249:
1247:
1244:
1243:
1242:
1237:
1234:Set constraint
1229:
1226:
1225:
1224:
1221:
1214:
1207:
1201:set membership
1182:
1171:
1168:
1167:
1166:
1155:
1148:
1139:
1136:
1131:
1124:
1120:, and whether
1116:
1109:
1101:
1094:
1086:
1079:
1072:
1065:
1057:
1050:
1043:
1040:
995:
980:
971:
960:
945:
930:
920:
919:
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900:
895:
879:
869:
860:
853:
846:
839:
835:
828:
817:
757:
747:
743:. The grammar
740:
733:
722:
643:
637:
636:
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634:
616:
607:
598:
585:
579:
571:
566:
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366:
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315:
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265:
258:
243:
234:
200:
197:
196:
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176:
163:
131:
115:
100:
64:
61:
45:directed trees
41:formal grammar
24:
14:
13:
10:
9:
6:
4:
3:
2:
2063:
2052:
2049:
2048:
2046:
2028:
2027:proper subset
2021:
2010:
2007:
2005:
2002:
2000:
1997:
1995:
1992:
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1883:
1878:
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1868:
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1860:
1855:
1854:Non-recursive
1852:
1849:
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1480:3-540-44185-9
1476:
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1255:
1252:
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1232:
1231:
1227:
1223:Graph-search
1222:
1219:
1215:
1212:
1208:
1206:
1202:
1198:
1194:
1191:
1187:
1183:
1180:
1177:
1176:
1175:
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1156:
1153:
1152:tree automata
1149:
1146:
1142:
1141:
1137:
1135:
1130:
1123:
1115:
1108:
1100:
1093:
1085:
1078:
1071:
1064:
1056:
1049:
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1029:
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1021:
1017:
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1009:
1005:
1001:
994:
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986:
979:
975:
970:
966:
959:
955:
951:
944:
940:
936:
929:
925:
922:The language
914:
910:
906:
899:
896:
893:
889:
885:
878:
875:
874:
873:
868:
859:
852:
845:
834:
827:
821:
816:
812:
755:
753:
746:
739:
732:
728:
721:
716:
714:
713:word grammars
710:
705:
703:
699:
695:
691:
687:
683:
679:
675:
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663:
659:
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611:
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584:
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565:has arity 2),
564:
560:
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548:
540:
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533:
526:
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521:
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509:
498:
491:
479:
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467:
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461:tree language
455:
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62:
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58:
54:
50:
46:
42:
38:
34:
30:
19:
1963:Nested stack
1906:Context-free
1831:Context-free
1792:Unrestricted
1659:
1649:
1631:
1627:
1617:Donald Knuth
1598:
1588:
1563:(1): 57β81.
1560:
1556:
1527:
1523:
1495:
1489:
1452:
1446:
1437:
1431:
1422:
1416:
1407:
1401:
1365:
1361:
1348:
1311:
1297:
1285:. Retrieved
1275:
1254:
1173:
1170:Applications
1159:nested words
1128:
1121:
1113:
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