Some applications of the decidability of DPDA's equivalence

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2055 LNCS, Issue , 2001, Pages 114-132

  Sénizergues, Géraud ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTABILITY AND DECIDABILITY; EQUIVALENCE CLASSES; GRAPH THEORY; MICROCONTROLLERS; PROBLEM ORIENTED LANGUAGES; COMPUTER PROGRAMMING; COMPUTER PROGRAMMING LANGUAGES;

DETERMINISTIC PUSHDOWN AUTOMATA; EQUIVALENCE PROBLEM; INFINITE GRAPH; THEORETICAL COMPUTER SCIENCE;

COMPUTER SYSTEMS PROGRAMMING;

EID: 23044526000     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45132-3_7     Document Type: Conference Paper

References (75)

1. J. M. Autebert, L. Boasson, and G. Sénizergues. Groups and NTS languages. JCSS vol. 35, no2, pages 243-267, 1987.
2. S. Arnborg, B. Courcelle, A. Proskurowski, and D. Seese. An algebraic theory of graph reduction. J. ACM 40, pages 1134-1164, 1993.
3. M. Bauderon. Infinite hypergraph II, systems of recursive equations. TCS 103, pages 165-190, 1992.
4. J. Baeten, J. Bergstra, and J. Klop. Decidability of bisimulation equivalence for processes generating context-free languages. In Proceedings of PARLE 87, pages 94-111. LNCS 259, 1987.
5. A. Blumensath and E. Gräedel. Automatic structures. In Proceedings LICS, pages 105-118. IEEE Computer Society Press, 2000.
6. R. V. Book and F. Otto. String Rewriting Systems. Texts and monographs in Computer Science. Springer-Verlag, 1993.
7. P. Butzbach. Une famille de congruences de Thue pour lesquelles l'équivalence est décidable. In Proceedings 1rst ICALP, pages 3-12. LNCS, 1973.
8. D. Caucal. Graphes canoniques des graphes algébriques. RAIRO, Informatique Théorique et Applications, 24(4), pages 339-352, 1990.
9. D. Caucal. Bisimulation of context-free grammars and of pushdown automata. In Modal Logic and process algebra, pages 85-106. CSLI Lectures Notes, vol. 53, 1995.
10. S. Christensen, Y. Hirshfeld, and F. Moller. Bisimulation is decidable for basic parallel processes. LNCS 715, Springer, pages 143-157, 1993.
11. S. Christensen, H. Hüttel, and C. Stirling. Bisimulation equivalence is decidable for all context-free processes. Information and Computation 121, pages 143-148, 1995.
12. Y. Cochet. Sur l'algébricité des classes de certaines congruences définies sur le monoide libre. Thèse de l'université de Rennes, 1971.
13. B. Courcelle. A representation of trees by languages, I. Theoretical Computer Science 6, pages 255-279, 1978.
14. B. Courcelle. A representation of trees by languages, II. Theoretical Computer Science 7, pages 25-55, 1978.
15. B. Courcelle. Fundamental properties of infinite trees. Theoretical Computer Science 25, pages 95-169, 1983.
16. B. Courcelle. The monadic second-order logic of graphs ii: infinite graphs of bounded width. Math. Systems Theory 21, pages 187-221, 1989.
17. B. Courcelle. The monadic second-order logic of graphs iv: definability properties of equational graphs. Annals of Pure and Applied Logic 49, pages 193-255, 1990.
18. B. Courcelle. Recursive applicative program schemes. In Handbook of Theoretical Computer Science, edited by J. Van Leeuwen, pages 461-490. Elsevier, 1990.
19. A. Carbone and S. Semmes. A graphic apology for symmetry and implicitness. Preprint, 1999.
20. N. Dershowitz and J. P. Jouannaud. Rewrite systems. In Handbook of theoretical computer science, vol. B, Chapter 2, pages 243-320. Elsevier, 1991.
21. D. B. A. Epstein, J. W. Cannon, D. F. Holt, S. V. F. Levy, M. S. Paterson, and W. P. Thurston. Word processing in groups. Jones and Bartlett, 1992.
22. J. Engelfriet. Deciding the NTS-property of context-free grammars. In Important Results and Trends in Theoretical Computer Science, (Colloquium in honor of Aarto Salomaa), pages 124-130. Springer-Verlag, LNCS nr 812, 1994.
23. E. P. Friedman. Equivalence problems for deterministic context-free languages and monadic recursion schemes. Journal of Computer and System Sciences 14, pages 344-359, 1977.
24. J. H. Gallier. Dpda's in 'atomic normal form' and applications to equivalence problems. Theoretical Computer Science 14, pages 155-186, 1981.
25. S. Ginsburg and S. Greibach. Deterministic context-free languages. Information and Control, pages 620-648, 1966.
26. P. Grosset-Grange. Décidabilité de la confluence partielle d'un système semi-Thuéien rationnel. M émoire de DEA de l'université de Bordeaux 1, pages 1-21, 1993.
27. J. Groote and H. Hüttel. Undecidable equivalences for basic process algebra. Information and Computation 115, pages 354-371, 1994.
28. S. J. Garland and D. C. Luckham. Program schemes, recursion schemes, and formal languages. Journal of Computer and System Sciences 7, pages 119-160, 1973.
29. I. Guessarian. Algebraic Semantics. Lecture Notes in Computer Science, vol. 99, 1981.
30. Y. Hirshfeld, M. Jerrum, and F. Moller. A polynomial algorithm for deciding equivalence of normed context-free processes. In Proceedings of FOCS'94, pages 623-631. IEEE, 1994.
31. H. Hüttel and C. Stirling. Actions speak louder than words: Proving bisimilarity for context-free processes. In LICS'91, pages 376-385. IEEE, 1991.
32. G. Huet. Confluent reductions: abstract properties and applications to term rewriting systems. JACM vol. 27 no 4, pages 797-821, 1980.
33. I. I. Ianov. The logical schemes of algorithms. Problems of Cybernetics (USSR) 1, pages 82-140, 1960.
34. P. Jancar. Bisimulation is decidable for one-counter processes. In Proceedings ICALP 97, pages 549-559. Springer Verlag, 1997.
35. D. M. Kaplan. Regular expressions and the equivalence of programs. Journal of Computer and Systems Sciences 3, pages 361-386, 1969.
36. B. Khoussainov and A. Nerode. Automatic presentations of structures. In Logic and Computational Complexity, Indianapolis, 94, pages 367-392. L. N. C. S nr 960, 1995.
37. D. C. Luckham, D. M. Park, and M. S. Paterson. On formalised computer programs. Journal of Computer and Systems Sciences 4, pages 220-249, 1970.
38. O. Ly. Automatic graphs and D0L-sequences of finite graphs. Preprint, submitted to JCSS, pages 1-33, 2000.
39. O. Ly. Automatic graphs and graph D0L-systems. In Proceedings MFCS'2000, pages 539-548. Springer, LNCS No 1893, 2000.
40. Y. V. Matiyasevich. Personal communication. 1995.
41. R. Milner. Equivalences on program schemes. Journal of Computer and Systems Sciences 4, pages 205-219, 1970.
42. R. Milner. Communication and Concurrency. Prentice Hall, 1989.
43. K. Madlener, P. Narendran, and F. Otto. A specialized completion procedure for monadic string-rewriting systems presenting groups. In Proceedings 18th ICALP, pages 279-290. Springer, LNCS No 510, 1991.
44. K. Madlener, P. Narendran, F. Otto, and L. Zhang. On weakly confluent monadic string-rewriting systems. T. C. S. 113, pages 119-165, 1993.
45. C. Morvan. Rational graphs. In Proceedings STACS'2000. LNCS, 2000.
46. P. Narendran. It is decidable whether a monadic Thue system is canonical over a regular set. Math. Systems Theory 23, pages 245-254, 1990.
47. M. Nivat. On some families of languages related to the Dyck language. 2nd Annual Symposium on Theory of Computing, 1970.
48. M. Nivat. On the interpretation of recursive polyadic program schemes. Symposia Mathematica, vol. 15, Academic press, New-York, 1975.
49. F. Otto. On deciding the confluence of a finite string-rewriting system on a given congruence class. JCSS 35, pages 285-310, 1987.
50. F. Otto. Completing a finite special string-rewriting system on the congruence class of the empty word. Applicable Algebra in Engeneering Comm. Comput. 2, pages 257-274, 1992.
51. F. Otto. The problem of deciding confluence on a given congruence class is tractable for finite special string-rewriting systems. Math. Systems Theory 25, pages 241-251, 1992.
52. F. Otto and L. Zhang. Decision problems for finite special string-rewriting systems that are confluent on some congruence class. Acta Informatica 28, pages 477-510, 1991.
53. D. Park. Concurrency and automata on infinite sequences. LNCS 104, pages 167-183, 1981.
54. M. S. Paterson. Equivalence problems in a model of computation. Ph. D. Thesis, University of Cambridge, England, 1967.
55. L. Pelecq. Isomorphismes et automorphismes des graphes context-free, équationnels et automatiques. Thèse de doctorat, Université Bordeaux I, Juin 1997.
56. B. K. Rosen. Program equivalence and context-free grammars. Journal of Computer and System Sciences 11, pages 358-374, 1975.
57. J. Rutledge. On Ianov's program schemata. Journal of the Association for Computing Machinery, pages 1-9, 1964.
58. J. Sakarovitch. Syntaxe des langages de Chomsky, essai sur le déterminisme. Thèse de doctorat d'état de l'université Paris VII, pages 1-175, 1979.
59. G. Sénizergues. The equivalence and inclusion problems for NTS languages. J. Comput. System Sci. 31(3), pages 303-331, 1985.
60. G. Sénizergues. Some decision problems about controlled rewriting systems. TCS 71, pages 281-346, 1990.
61. G. Sénizergues. Definability in weak monadic second-order logic of some infinite graphs. In Dagstuhl seminar on Automata theory: Infinite computations. Wadern, Germany, volume 28, pages 16-16, 1992.
62. G. Sénizergues. Formal languages and word-rewriting. In Term Rewriting, Advanced Course, pages 75-94. Springer, LNCS 909, edited by H. Comon and J. P. Jouannaud, 1994.
63. G. Sénizergues. L (A) = L (B) ? In Proceedings INFINITY 97, pages 1-26. Electronic Notes in Theoretical Computer Science 9, URL: http://www.elsevier.nl/locate/entcs/volume9.html, 1997.
64. G. Sénizergues. L (A) = L (B) ? Technical report, LaBRI, Université Bordeaux I, report nr1161-97, 1997. Pages 1-71.
65. G. Sénizergues. The Equivalence Problem for Deterministic Pushdown Automata is Decidable. In Proceedings ICALP 97, pages 671-681. Springer, LNCS 1256, 1997.
66. G. Sénizergues. Decidability of bisimulation equivalence for equational graphs of finite out-degree. In Rajeev Motwani, editor, Proceedings FOCS'98, pages 120-129. IEEE Computer Society Press, 1998.
67. G. Sénizergues. A polynomial algorithm testing partial confluence of basic semi-Thue systems. Theoretical Computer Science 192, pages 55-75, 1998.
68. G. Sénizergues. Complete Formal Systems for Equivalence Problems. Theoretical Computer Science, 231:309-334, 2000.
69. G. Sénizergues. The bisimulation problem for equational graphs of finite out-degree. submitted to SIAM Journal on Computing; can be accessed at URL: http://arXiv.org/abs/cs/0008018, pages 1-98, 2000.
70. G. Sénizergues. L (A) = L (B) ? decidability results from complete formal systems. Theoretical Computer Science, 251:1-166, 2001.
71. M. Solomon. Type definitions with parameters. In Conference Record of the Fifth Annual ACM Symposium on Principles of Programming Languages, pages 31-38, Tucson, Arizona, 1978. ACM SIGACT-SIGPLAN. Extended abstract.
72. C. Stirling. Decidability of bisimulation equivalence for normed pushdown processes. In Proceedings CONCUR 96, pages 217-232. Springer-Verlag, LNCS 1119, 1996.
73. C. Stirling. Decidability of dpda's equivalence. Technical report, Edinburgh ECS-LFCS-99-411, 1999. Pages 1-25, accepted for publication in TCS.
74. L. Zhang. Weak confluence is tractable for finite string-rewriting systems. preprint, pages 1-10, 1991.
75. L. Zhang. The pre-NTS property is undecidable for context-free grammars. IPL44, pages 181-184, 1992.