메뉴 건너뛰기




Volumn 2, Issue 2, 2001, Pages 216-254

MSO Definable String Transductions and Two-Way Finite-State Transducers

Author keywords

B chi; Elgot; Hennie machine; interpretation; monadic secondorder logic; string transductions; Theory; Trakhtenbrot; two way finite state transducers

Indexed keywords


EID: 84886574830     PISSN: 15293785     EISSN: 1557945X     Source Type: Journal    
DOI: 10.1145/371316.371512     Document Type: Article
Times cited : (190)

References (66)
  • 2
    • 0014925304 scopus 로고
    • A characterization of two-way deterministic classes of languages
    • Aho, A. V. and Ullman, J. D. 1970. A characterization of two-way deterministic classes of languages. J. Comput. Syst. Sci. 4, 523-538.
    • (1970) J. Comput. Syst. Sci. , vol.4 , pp. 523-538
    • Aho, A.V.1    Ullman, J.D.2
  • 3
    • 33748629112 scopus 로고    scopus 로고
    • Two-way automata and length-preserving homomorphisms
    • Birget, J.-C. 1996. Two-way automata and length-preserving homomorphisms. Math. Syst. Theor. 29, 191-226.
    • (1996) Math. Syst. Theor. , vol.29 , pp. 191-226
    • Birget, J.-C.1
  • 4
    • 0034247087 scopus 로고    scopus 로고
    • A comparison of tree transductions defined by monadic second order logic and by attribute grammars
    • Bloem, R. and Engelfriet, J. 2000. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. J. Comput. Syst. Sci. 61, 1-50.
    • (2000) J. Comput. Syst. Sci. , vol.61 , pp. 1-50
    • Bloem, R.1    Engelfriet, J.2
  • 5
    • 70350098746 scopus 로고
    • Weak second-order arithmetic and finite automata
    • Büchi, J. R. 1960. Weak second-order arithmetic and finite automata. Z. Math. Logik Grundlagen Math. 6, 66-92.
    • (1960) Z. Math. Logik Grundlagen Math. , vol.6 , pp. 66-92
    • Büchi, J.R.1
  • 6
    • 0002921593 scopus 로고
    • On a decision method in restricted second order arithmetic
    • Büchi, J. R. 1962. On a decision method in restricted second order arithmetic. In Proc. Int. Congr.
    • (1962) Proc. Int. Congr.
    • Büchi, J.R.1
  • 8
  • 9
    • 84876638503 scopus 로고
    • Serial composition of 2-way finite-state transducers and simple programs on strings
    • A. Salomaa and M. Steinby, Eds. Lect. Notes Comput. Sci. Springer Verlag, Berlin
    • Chytil, M. P. and Jakl, V. 1977. Serial composition of 2-way finite-state transducers and simple programs on strings. In Automata, Languages and Programming, Fourth Colloquium, A. Salomaa and M. Steinby, Eds. Lect. Notes Comput. Sci., vol. 52. Springer Verlag, Berlin, 135-147.
    • (1977) Automata, Languages and Programming, Fourth Colloquium , vol.52 , pp. 135-147
    • Chytil, M.P.1    Jakl, V.2
  • 11
    • 0026123837 scopus 로고
    • The monadic second-order logic of graphs V: On closing the gap between definability and recognizability
    • Courcelle, B. 1991. The monadic second-order logic of graphs V: On closing the gap between definability and recognizability. Theor. Comput. Sci. 80, 153-202.
    • (1991) Theor. Comput. Sci. , vol.80 , pp. 153-202
    • Courcelle, B.1
  • 12
    • 0026885661 scopus 로고
    • The monadic second-order logic of graphs VII: Graphs as relational structures
    • Courcelle, B. 1992. The monadic second-order logic of graphs VII: Graphs as relational structures. Theor. Comput. Sci. 101, 1, 3-33.
    • (1992) Theor. Comput. Sci. , vol.101 , Issue.1 , pp. 3-33
    • Courcelle, B.1
  • 13
    • 0028420231 scopus 로고
    • Monadic second-order definable graph transductions: a survey
    • Courcelle, B. 1994. Monadic second-order definable graph transductions: a survey. Theor. Comput. Sci. 126, 53-75.
    • (1994) Theor. Comput. Sci. , vol.126 , pp. 53-75
    • Courcelle, B.1
  • 14
    • 0000090439 scopus 로고    scopus 로고
    • The expression of graph properties and graph transformations in monadic second-order logic
    • Foundations, G. Rozenberg, Ed. World Scientific Publishing Co.
    • Courcelle, B. 1997. The expression of graph properties and graph transformations in monadic second-order logic. In Handbook of graph grammars and computing by graph transformation, vol. 1: Foundations, G. Rozenberg, Ed. World Scientific Publishing Co., 313-400.
    • (1997) Handbook of graph grammars and computing by graph transformation , vol.1 , pp. 313-400
    • Courcelle, B.1
  • 15
    • 0000413488 scopus 로고
    • A logical characterization of the sets of hypergraphs defined by hyperedge replacement grammars
    • Courcelle, B. and Engelfriet, J. 1995. A logical characterization of the sets of hypergraphs defined by hyperedge replacement grammars. Math. Syst. Theor. 28, 515-552.
    • (1995) Math. Syst. Theor. , vol.28 , pp. 515-552
    • Courcelle, B.1    Engelfriet, J.2
  • 16
    • 0000185443 scopus 로고
    • Tree acceptors and some of their applications
    • Doner, J. 1970. Tree acceptors and some of their applications. J. Comput. Syst. Sci. 4, 406-451.
    • (1970) J. Comput. Syst. Sci. , vol.4 , pp. 406-451
    • Doner, J.1
  • 17
    • 17444410972 scopus 로고
    • Logical definability of trace languages
    • V. Diekert and G. Rozenberg, Eds. World Scientific Appendix to Chapter 10.
    • Ebinger, W. 1995. Logical definability of trace languages. In The Book of Traces, V. Diekert and G. Rozenberg, Eds. World Scientific, 382-390. Appendix to Chapter 10.
    • (1995) The Book of Traces , pp. 382-390
    • Ebinger, W.1
  • 18
    • 84944056157 scopus 로고
    • Decision problems of finite automata design and related arithmetics
    • Elgot, C. C. 1961. Decision problems of finite automata design and related arithmetics. Trans. AMS 98, 21-52.
    • (1961) Trans. AMS , vol.98 , pp. 21-52
    • Elgot, C.C.1
  • 19
    • 34250393783 scopus 로고
    • Top-down tree transducers with regular look-ahead
    • Engelfriet, J. 1977. Top-down tree transducers with regular look-ahead. Math. Syst. Theor. 10, 289-303.
    • (1977) Math. Syst. Theor. , vol.10 , pp. 289-303
    • Engelfriet, J.1
  • 20
    • 0002290381 scopus 로고
    • Three hierarchies of transducers
    • Engelfriet, J. 1982. Three hierarchies of transducers. Math. Syst. Theor. 15, 95-125.
    • (1982) Math. Syst. Theor. , vol.15 , pp. 95-125
    • Engelfriet, J.1
  • 21
    • 84909938476 scopus 로고
    • A characterization of context-free NCE graph languages by monadic second-order logic on trees
    • H. Ehrig, H.-J. Kreowski, and G. Rozenberg, Eds. Lect. Notes Comput. Sci. Springer Verlag, Berlin
    • Engelfriet, J. 1991a. A characterization of context-free NCE graph languages by monadic second-order logic on trees. In Graph Grammars and Their Application to Computer Science, H. Ehrig, H.-J. Kreowski, and G. Rozenberg, Eds. Lect. Notes Comput. Sci., vol. 532. Springer Verlag, Berlin, 311-327.
    • (1991) Graph Grammars and Their Application to Computer Science , vol.532 , pp. 311-327
    • Engelfriet, J.1
  • 22
    • 0026254904 scopus 로고
    • Iterated stack automata and complexity classes
    • Engelfriet, J. 1991b. Iterated stack automata and complexity classes. Inf. Comput. 95, 21-75.
    • (1991) Inf. Comput. , vol.95 , pp. 21-75
    • Engelfriet, J.1
  • 23
    • 0001218274 scopus 로고    scopus 로고
    • Context-free graph grammars
    • G. Rozenberg and A. Salomaa, Eds Beyond Words. Springer Verlag, Berlin
    • Engelfriet, J. 1997. Context-free graph grammars. In Handbook of Formal Languages, G. Rozenberg and A. Salomaa, Eds. Vol. 3: Beyond Words. Springer Verlag, Berlin, 125-213.
    • (1997) Handbook of Formal Languages , vol.3 , pp. 125-213
    • Engelfriet, J.1
  • 24
    • 0026238993 scopus 로고
    • The string generating power of context-free hypergraph grammars
    • Engelfriet, J. and Heyker, L. M. 1991. The string generating power of context-free hypergraph grammars. J. Comput. Syst. Sci. 43, 328-360.
    • (1991) J. Comput. Syst. Sci. , vol.43 , pp. 328-360
    • Engelfriet, J.1    Heyker, L.M.2
  • 25
    • 84876913981 scopus 로고    scopus 로고
    • Two-way finite state transducers and monadic second-order logic
    • Wiedermann, P. van Emde Boas, and M. Nielsen, Eds. Lect. Notes Comput. Sci. Springer Verlag, Berlin
    • Engelfriet, J. and Hoogeboom, H. J. 1999. Two-way finite state transducers and monadic second-order logic. In 26-th International Colloquium on Automata, Languages and Programming, J. Wiedermann, P. van Emde Boas, and M. Nielsen, Eds. Lect. Notes Comput. Sci., vol. 1644. Springer Verlag, Berlin, 311-320.
    • (1999) 26-th International Colloquium on Automata, Languages and Programming , vol.1644 , pp. 311-320
    • Engelfriet, J.1    Hoogeboom, H.J.2
  • 26
    • 0001975506 scopus 로고    scopus 로고
    • Macro tree transducers, attribute grammars, and MSO definable tree translations
    • Engelfriet, J. and Maneth, S. 1999. Macro tree transducers, attribute grammars, and MSO definable tree translations. Inf. Comput. 154, 34-91.
    • (1999) Inf. Comput. , vol.154 , pp. 34-91
    • Engelfriet, J.1    Maneth, S.2
  • 27
    • 0031383397 scopus 로고    scopus 로고
    • Logical description of context-free graph languages
    • Engelfriet, J. and van Oostrom, V. 1997. Logical description of context-free graph languages. J. Comput. Syst. Sci. 55, 489-503.
    • (1997) J. Comput. Syst. Sci. , vol.55 , pp. 489-503
    • Engelfriet, J.1    van Oostrom, V.2
  • 29
    • 0009156675 scopus 로고
    • Hierarchy theorems for two-way finite state transducers
    • Greibach, S. A. 1978a. Hierarchy theorems for two-way finite state transducers. Acta Inf. 11, 89-101.
    • (1978) Acta Inf. , vol.11 , pp. 89-101
    • Greibach, S.A.1
  • 30
    • 0010563934 scopus 로고
    • One way finite visit automata
    • Greibach, S. A. 1978b. One way finite visit automata. Theor. Comput. Sci. 6, 175-221.
    • (1978) Theor. Comput. Sci. , vol.6 , pp. 175-221
    • Greibach, S.A.1
  • 31
    • 0347645060 scopus 로고
    • Visits, crosses, and reversals for nondeterministic off-line machines
    • Greibach, S. A. 1978c. Visits, crosses, and reversals for nondeterministic off-line machines. Inf. and Con. 36, 174-216.
    • (1978) Inf. and Con. , vol.36 , pp. 174-216
    • Greibach, S.A.1
  • 32
    • 0346964548 scopus 로고
    • The unsolvability of the equivalence problem for A-free nondeterministic generalized machines
    • Griffiths, T. V. 1968. The unsolvability of the equivalence problem for A-free nondeterministic generalized machines. J. ACM 15, 409-413.
    • (1968) J. ACM 15 , pp. 409-413
    • Griffiths, T.V.1
  • 33
    • 33744937808 scopus 로고
    • The equivalence problem for deterministic two-way sequential transducers is decidable
    • Gurari, E. M. 1982. The equivalence problem for deterministic two-way sequential transducers is decidable. SIAM J. Comput. 11, 3, 448-452.
    • (1982) SIAM J. Comput. , vol.11 , Issue.3 , pp. 448-452
    • Gurari, E.M.1
  • 34
    • 0000841450 scopus 로고
    • One-tape, off-line turing machine computations
    • Hennie, F. C. 1965. One-tape, off-line turing machine computations. Inf. and Con. 8, 553-578.
    • (1965) Inf. and Con. , vol.8 , pp. 553-578
    • Hennie, F.C.1
  • 35
    • 0004240663 scopus 로고
    • Encyclopedia of Mathematics and its Applications Cambridge University Press.
    • Hodges, W. 1993. Model Theory. Encyclopedia of Mathematics and its Applications, vol. 42. Cambridge University Press.
    • (1993) Model Theory. , vol.42
    • Hodges, W.1
  • 36
    • 0031533854 scopus 로고    scopus 로고
    • Monadic second-order definable text languages
    • Hoogeboom, H. J. and Ten Pas, P. 1997. Monadic second-order definable text languages. ACM Trans. Comput. Syst. 30, 335-354.
    • (1997) ACM Trans. Comput. Syst. , vol.30 , pp. 335-354
    • Hoogeboom, H.J.1    Ten Pas, P.2
  • 38
    • 85025423140 scopus 로고
    • Also in: IEEE Conference Record of 8th Annual Symposium on Switching and Automata Theory
    • Austin, Texas
    • Also in: IEEE Conference Record of 8th Annual Symposium on Switching and Automata Theory, Austin, Texas, 1967, pages 140-147.
    • (1967) , pp. 140-147
  • 41
    • 0016472549 scopus 로고
    • Two-way a-transducers and AFL
    • Kiel, D. 1975. Two-way a-transducers and AFL. J. Comput. Syst. Sci. 10, 88-109.
    • (1975) J. Comput. Syst. Sci. , vol.10 , pp. 88-109
    • Kiel, D.1
  • 42
    • 0003067817 scopus 로고
    • Representation of events in nerve nets and finite automata
    • Annals of Mathematics Studies Princeton University Press, Princeton, N.J.
    • Kleene, S. C. 1956. Representation of events in nerve nets and finite automata. In Automata Studies. Annals of Mathematics Studies, vol. 34. Princeton University Press, Princeton, N.J., 3-42.
    • (1956) Automata Studies. , vol.34 , pp. 3-42
    • Kleene, S.C.1
  • 44
    • 78649882717 scopus 로고    scopus 로고
    • Recognizability equals monadic second-order definability for sets of graphs of bounded tree-width
    • Lect. Notes Comput. Sci. Springer Verlag, Berlin
    • Lapoire, D. 1998. Recognizability equals monadic second-order definability for sets of graphs of bounded tree-width. in 15th Annual Symposium on Theoretical Aspects of Computer Science. Lect. Notes Comput. Sci., vol. 1373. Springer Verlag, Berlin, 618-628.
    • (1998) 15th Annual Symposium on Theoretical Aspects of Computer Science , vol.1373 , pp. 618-628
    • Lapoire, D.1
  • 45
    • 84957051392 scopus 로고    scopus 로고
    • The descriptive complexity approach to LOGCFL
    • C. Meinel and S. Tison, Eds. Lect. Notes Comput. Sci. Springer Verlag, Berlin Full version: Electronic Colloquium on Computational Complexity, Report TR98-059
    • Lautemann, C., McKenzie, P., Schwentick, T., and Vollmer, H. 1999. The descriptive complexity approach to LOGCFL. In 16th Symposium on Theoretical Aspects of Computer Science, C. Meinel and S. Tison, Eds. Lect. Notes Comput. Sci., vol. 1563. Springer Verlag, Berlin, 444-454. Full version: Electronic Colloquium on Computational Complexity, Report TR98-059.
    • (1999) 16th Symposium on Theoretical Aspects of Computer Science , vol.1563 , pp. 444-454
    • Lautemann, C.1    McKenzie, P.2    Schwentick, T.3    Vollmer, H.4
  • 46
    • 51249194645 scopus 로고
    • A logical calculus of the ideas imminent in nervous activity
    • McCulloch, W. S. and Pitts, W. 1943. A logical calculus of the ideas imminent in nervous activity. Bull. Math. Bioph. 5, 115-133.
    • (1943) Bull. Math. Bioph. , vol.5 , pp. 115-133
    • McCulloch, W.S.1    Pitts, W.2
  • 48
    • 0004113933 scopus 로고
    • Finite automata and the representation of events
    • WADD TR-57-624, Wright Patterson AFB, Ohio.
    • Myhill, J. 1957. Finite automata and the representation of events. Tech. Rep. WADD TR-57-624, Wright Patterson AFB, Ohio.
    • (1957) Tech. Rep.
    • Myhill, J.1
  • 49
    • 84968499135 scopus 로고
    • Linear automata transformation
    • Nerode, A. 1958. Linear automata transformation. Proc. AMS 9, 541-544.
    • (1958) Proc. AMS , vol.9 , pp. 541-544
    • Nerode, A.1
  • 50
    • 0020117822 scopus 로고
    • The equivalence problem for LL- and LR-regular grammars
    • Nijholt, A. 1982. The equivalence problem for LL- and LR-regular grammars. J. Comput. Syst. Sci. 24, 149-161.
    • (1982) J. Comput. Syst. Sci. , vol.24 , pp. 149-161
    • Nijholt, A.1
  • 51
    • 0000262403 scopus 로고    scopus 로고
    • Regularity of splicing languages
    • Pixton, D. 1996. Regularity of splicing languages. Discr. Appl. Math. 69, 101-124.
    • (1996) Discr. Appl. Math. , vol.69 , pp. 101-124
    • Pixton, D.1
  • 52
    • 51249162610 scopus 로고
    • Real-time computation
    • Rabin, M. O. 1963. Real-time computation. Isr. J. Math 1, 203-211.
    • (1963) Isr. J. Math , vol.1 , pp. 203-211
    • Rabin, M.O.1
  • 53
    • 84968501436 scopus 로고
    • Decidability of second-order theories and automata on infinite trees
    • Rabin, M. O. 1969. Decidability of second-order theories and automata on infinite trees. Trans. AMS 141, 1-35.
    • (1969) Trans. AMS , vol.141 , pp. 1-35
    • Rabin, M.O.1
  • 54
    • 33847763935 scopus 로고
    • Decidable theories
    • J. Barwise, Ed. Studies in Logic and the Foundations of Mathematics North-Holland
    • Rabin, M. O. 1977. Decidable theories. In Handbook of Mathematical Logic, J. Barwise, Ed. Studies in Logic and the Foundations of Mathematics, vol. 30. North-Holland, 595-629.
    • (1977) Handbook of Mathematical Logic , vol.30 , pp. 595-629
    • Rabin, M.O.1
  • 55
    • 0000973916 scopus 로고
    • Finite automata and their decision problems
    • Rabin, M. O. and Scott, D. 1959. Finite automata and their decision problems. IBM J. Res. Dev. 3, 114-125.
    • (1959) IBM J. Res. Dev. , vol.3 , pp. 114-125
    • Rabin, M.O.1    Scott, D.2
  • 56
    • 12844265780 scopus 로고
    • Also in: E. F. Moore, Ed. Addison-Wesley, Reading, MA
    • Also in: E. F. Moore, Ed., Sequential Machines: Selected Papers. Addison-Wesley, Reading, MA, 1964, pages 63-91.
    • (1964) Sequential Machines: Selected Papers. , pp. 63-91
  • 57
    • 0016495792 scopus 로고
    • Bounded-crossing transducers
    • Rajlich, V. 1975. Bounded-crossing transducers. Inf. and Con. 27, 329-335.
    • (1975) Inf. and Con. , vol.27 , pp. 329-335
    • Rajlich, V.1
  • 58
    • 0013305695 scopus 로고
    • Interpretability and tree automata: a simple way to solve algorithmic problems on graphs closely related to trees
    • M. Nivat and A. Podelski, Eds. Elsevier Science Publishers, Amsterdam
    • Seese, D. 1992. Interpretability and tree automata: a simple way to solve algorithmic problems on graphs closely related to trees. In Tree Automata and Languages, M. Nivat and A. Podelski, Eds. Elsevier Science Publishers, Amsterdam, 83-114.
    • (1992) Tree Automata and Languages , pp. 83-114
    • Seese, D.1
  • 59
    • 0000065573 scopus 로고
    • The reduction of two-way automata to one-way automata
    • Shepherdson, J. C. 1959. The reduction of two-way automata to one-way automata. IBM J. Res. Dev. 3, 198-200.
    • (1959) IBM J. Res. Dev. , vol.3 , pp. 198-200
    • Shepherdson, J.C.1
  • 60
    • 85025392281 scopus 로고
    • Also in: E. F. Moore, Ed. Addison-Wesley, Reading, MA
    • Also in: E. F. Moore, Ed., Sequential Machines: Selected Papers. Addison-Wesley, Reading, MA, 1964, pages 92-97.
    • (1964) Sequential Machines: Selected Papers. , pp. 92-97
  • 61
    • 0002614970 scopus 로고
    • Generalized finite automata theory with an application to a decision problem of second-order logic
    • Thatcher, J. W. and Wright, J. B. 1968. Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Syst. Theor. 2, 57-82.
    • (1968) Math. Syst. Theor. , vol.2 , pp. 57-82
    • Thatcher, J.W.1    Wright, J.B.2
  • 62
    • 3142673201 scopus 로고    scopus 로고
    • Ehrenfeucht games, the composition method, and the monadic theory of ordinal words
    • J. Mycielski, G. Rozenberg, and A. Salomaa, Eds. Lect. Notes Comput. Sci. Springer Verlag, Berlin
    • Thomas, W. 1997a. Ehrenfeucht games, the composition method, and the monadic theory of ordinal words. In Structures in Logic and Computer Science-A Selection of Essays in Honor of A. Ehrenfeucht, J. Mycielski, G. Rozenberg, and A. Salomaa, Eds. Lect. Notes Comput. Sci., vol. 1261. Springer Verlag, Berlin, 118-143.
    • (1997) Structures in Logic and Computer Science-A Selection of Essays in Honor of A. Ehrenfeucht , vol.1261 , pp. 118-143
    • Thomas, W.1
  • 63
    • 0001568609 scopus 로고    scopus 로고
    • Languages, automata, and logic
    • G. Rozenberg and A. Salomaa, Eds. Beyond Words. Springer Verlag, Berlin
    • Thomas, W. 1997b. Languages, automata, and logic. In Handbook of Formal Languages, G. Rozenberg and A. Salomaa, Eds. Vol. 3: Beyond Words. Springer Verlag, Berlin, 389-455.
    • (1997) Handbook of Formal Languages , vol.3 , pp. 389-455
    • Thomas, W.1
  • 64
    • 0039016140 scopus 로고
    • Finite automata and the logic of one-place predicates
    • (in Russian)
    • Trakhtenbrot, B. A. 1962. Finite automata and the logic of one-place predicates. Siberian Mathematical Journal 3, 103-131 (in Russian).
    • (1962) Siberian Mathematical Journal , vol.3 , pp. 103-131
    • Trakhtenbrot, B.A.1
  • 65
    • 85025405244 scopus 로고
    • American Mathematical Society Translations, Series
    • English translation
    • English translation: American Mathematical Society Translations, Series 2, 59 (1966), 23-55.
    • (1966) , vol.2 , Issue.59 , pp. 23-55
  • 66
    • 0002700117 scopus 로고    scopus 로고
    • Regular languages
    • G. Rozenberg and A. Salomaa, Eds. Word, Language, Grammar. Springer Verlag, Berlin
    • Yu, S. 1997. Regular languages. In Handbook of Formal Languages, G. Rozenberg and A. Salomaa, Eds. Vol. 1: Word, Language, Grammar. Springer Verlag, Berlin, 41-110.
    • (1997) Handbook of Formal Languages , vol.1 , pp. 41-110
    • Yu, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.