Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Languages, Automata, and Logic

  • Chapter
Handbook of Formal Languages

Abstract

The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.

E-Mail:wt@informatik.uni-kiel.de. Work supported by Deutsche Forschungsgemeinschaft (DFG Th 352/3-2) and ESPRIT BRA Working Group No. 6317 ASMICS 2 (“Algebraic and Syntactic Methods in Computer Science”)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Alur, D. Dill. A theory of timed automata, Theor. Comput. Sci. 126 (1994), 183–235.

    MathSciNet  MATH  Google Scholar 

  2. A. V. Aho, J. E. Hoperoft, J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass. 1974.

    MATH  Google Scholar 

  3. A. Arnold, D. Niwiński, Fixed point characterization of weak monadic logic definable sets of trees, in: Tree Automata and Languages (M. Nivat, A. Podelski, Eds.), Elsevier Science Publishers, Amsterdam 1992, pp. 159–188.

    Google Scholar 

  4. A. Arnold, Finite Transition Systems, Masson, Paris, and Prentice-Hall, Hemel Hempstead 1994.

    MATH  Google Scholar 

  5. A. Arnold, An initial semantics of the μ-calculus on trees and Rabin’s complementation theorem, Theor. Comput. Sci. 148 (1994), 121–132.

    Google Scholar 

  6. D. A. M. Barrington, K. J. Compton, H. Straubing, D. Thérien, Regular languages in NC 1,J. Comput. System Sci. 38 (1988), 478–499.

    Google Scholar 

  7. V. Bruyère, G. Hansel, C. Michaux, R. Villemaire, Logic and p-recognizable sets of integers, Bull. Belg. Math. Soc. Simon Stevin 1 (1994), 191–238.

    MathSciNet  MATH  Google Scholar 

  8. D. Basin, N. Klarlund, Hardware verification using monadic second-order logic, in: Computer Aided Verification (P. Wolper, Ed.), Lecture Notes in Computer Science 939, Springer-Verlag, Berlin 1995, pp. 31–41.

    Google Scholar 

  9. J. R. Büchi, L. H. Landweber, Solving sequential conditions by finite-state strategies, Trans. Amer. Math. Soc. 138 (1969), 295–311.

    MathSciNet  Google Scholar 

  10. D. Beauquier, D. Niwinski, Automata on infinite trees with counting constraints, Information and Computation 120 (1995), 117–125.

    MathSciNet  MATH  Google Scholar 

  11. D. Beauquier and J.-E. Pin, Factors of words, in: Automata, Languages, and Programming, Proc. 16th ICALP (G. Ausiello et al., Eds.), Lecture Notes in Computer Science 372, Springer-Verlag, Berlin 1989, pp. 63–79.

    Google Scholar 

  12. F. Blanchet-Sadri, Some logical characterizations of the dot-depth hierarchy and applications, J. Comput. System Sci. 51 (1995), 324–337.

    MathSciNet  MATH  Google Scholar 

  13. J. R. Büchi, Weak second-order arithmetic and finite automata, Z. Math. Logik Grundl. Math. 6 (1960), 66–92.

    MATH  Google Scholar 

  14. J. R. Büchi, On a decision method in restricted second-order arithmetic, in: Proc. 1960 Int. Congr. for Logic, Methodology and Philosophy of Science,Stanford Univ. Press, Stanford, 1962, pp. 1–11.

    Google Scholar 

  15. J. R. Büchi, Regular canonical systems, Arch. Math. Logik Grundlagenforschung 6 (1964), 91–111.

    MATH  Google Scholar 

  16. J. R. Büchi, Using determinacy to eliminate quantifiers, in: Fundamentals of Computation Theory (M. Karpinski, Ed.), Lecture Notes in Computer Science 56, Springer-Verlag, Berlin 1977, pp. 367–378.

    Google Scholar 

  17. J. R. Büchi, State-strategies for games in Fσδ ∩ Gδσ, J. Symb. Logic 48 (1983), 1171–1198.

    MATH  Google Scholar 

  18. O. Carton, Chain automata, in: Technology and Applications, Information Processing’94, Vol. I (B. Pherson, I. Simon, Eds.), IFIP, North-Holland, Amsterdam 1994, pp. 451–458.

    Google Scholar 

  19. D. Caucal, On infinite transition graphs having a decidable monadic theory, in: Automata, Languages, and Programming, Proc. ICALP’96, (F. Meyer auf der Heide, B. Monien, Eds.), Lecture Notes in Computer Science, 1099, Springer-Verlag, Berlin 1996 pp. 194–205.

    Google Scholar 

  20. A. Church, Logic, arithmetic, and automata, Proc. Intern. Congr. Math. 1962, Almqvist and Wiksells, Uppsala 1963, pp. 21–35.

    Google Scholar 

  21. C. Choffrut, L. Guerra, Logical definability of some rational trace languages, Math. Syst. Theory 28 (1995), 397–420.

    MathSciNet  MATH  Google Scholar 

  22. E. Clarke, O. Grumberg, D. Long, Verification tools for finite-state concurrent systems, in: A Decade of Concurrency (J. W. de Bakker et al., Eds.), Lecture Notes in Computer Science 803, Springer-Verlag, Berlin 1994, pp. 124–175.

    Google Scholar 

  23. J. Cohen, D. Perrin and J. E. Pin, On the expressive power of temporal logic, J. Comput. System Sci. 46 (1993), 271–294.

    MathSciNet  MATH  Google Scholar 

  24. B. Courcelle, The monadic second-order logic of graphs I: recognizable sets of finite graphs Inform. and Comput. 85 (1990), 12–75.

    MathSciNet  MATH  Google Scholar 

  25. B. Courcelle, The monadic second-order theory of graphs V: on closing the gap between definability and recognizability, Theor. Comput. Sci. 80 (1991), 153–202.

    MathSciNet  MATH  Google Scholar 

  26. B. Courcelle, Monadic second-order definable graph transductions: a survey, Theor. Comput. Sci. 126 (1994), 53–75.

    MathSciNet  MATH  Google Scholar 

  27. B. Courcelle, The monadic second-order theory of graphs IX: Machines and their behaviours, Theor. Comput. Sci. 151 (1995), 125–162.

    MathSciNet  MATH  Google Scholar 

  28. B. Courcelle, The expression of graph properties and graph transformations in monadic second-order logic, in: Handbook of Graph Transformations, Vol. I: Foundations (G. Rozenberg, Ed.), World Scientific, Singapore 1996.

    Google Scholar 

  29. J. Doner, Tree acceptors and some of their applications, J. Comput. System Sci. 4 (1970), 406–451.

    MathSciNet  MATH  Google Scholar 

  30. V. Diekert, G. Rozenberg (Eds.), The Book of Traces, World Scientific, Singapore 1995.

    Google Scholar 

  31. M. Dauchet, S. Tison, The theory of ground rewrite systems is decidable, Proc. 5th IEEE Symp. on Logic in Computer Science,1990, pp. 242–248.

    Google Scholar 

  32. H. D. Ebbinghaus, J. Flum, Finite Model Theory,Springer-Verlag, New York 1995.

    MATH  Google Scholar 

  33. H. D. Ebbinghaus, J. Flum, W. Thomas, Mathematical Logic (2nd Ed.), Springer-Verlag, New York 1994.

    MATH  Google Scholar 

  34. J. Engelfriet, H. J. Hoogeboom, X-automata on w-words, Theor. Comput. Sci. 110 (1993), 1–51.

    MathSciNet  MATH  Google Scholar 

  35. E. A. Emerson, C. S. Jutla, The complexity of tree automata and logics of programs, in: Proc. 29th IEEE Symp. on Foundations of Computer Science, 1988, pp. 328–337.

    Google Scholar 

  36. E. A. Emerson, C. S. Jutla, Tree automata, Mu-calculus and determinacy, in: Proc. 32nd IEEE Symp. on Foundations of Computer Science (1991), 368–377.

    Google Scholar 

  37. E. A. Emerson, C. S. Jutla, A. P. Sistla, On model checking for fragments of p,-calculus, in: Computer Aided Verification (C. Courcoubetis, Ed.), Lecture Notes in Computer Science 697, Springer-Verlag, Berlin 1993, pp. 385–396.

    Google Scholar 

  38. C. C. Elgot, Decision problems of finite automata design and related arithmetics, Trans. Amer. Math. Soc. 98, (1961), 21–52.

    MathSciNet  Google Scholar 

  39. E. A. Emerson, Temporal and modal logic, in: Handbook of Theoretical Computer Science, Vol. B (J. v. Leeuwen, Ed.), Elsevier Science Publishers, Amsterdam 1990, pp. 995–1072.

    Google Scholar 

  40. E. A. Emerson, Automated temporal reasoning about reactive systems, in: Logics for Concurrency: Structure versus Automata (F. Moller, G. Birtwistle, Eds.), Lecture Notes in Computer Science 1043, Springer-Verlag, Berlin 1996, pp. 41–101.

    Google Scholar 

  41. W. Ebinger, A. Muscholl, Logical definability on infinite traces, Theor. Comput. Sci. 154 (1996), 67–84.

    MathSciNet  MATH  Google Scholar 

  42. C. C. Elgot, M. O. Rabin, Decidability and undefinability of second (first) order theory of (generalized) successor, J. Symbolic Logic 31 (1966), 169–181.

    MATH  Google Scholar 

  43. A. Ehrenfeucht, G. Rozenberg, T-structures, T-functions, and texts, Theor. Comput. Sci. 116 (1993), 227–290.

    MathSciNet  MATH  Google Scholar 

  44. K. Etessami, Th. Wilke, An Until hierarchy for temporal logic, in: Proc. 11th IEEE Symp. on Logic in Computer Science, 1996, pp. 108–117.

    Google Scholar 

  45. R. Fagin, Generalized first-order spectra and polynomial-time recognizable sets, in: Complexity of Computation (R. M. Karp, Ed.), SIAM-A MS Proceedings 7 (1974), pp. 43–73.

    Google Scholar 

  46. C. Frougny, J. Sakarovitch, Synchronized rational relations of finite and infinite words, Theor. Comput. Sci. 108 (1993), 45–82.

    MathSciNet  MATH  Google Scholar 

  47. R. Fagin, L. J. Stockmeyer, MY. Vardi, On monadic NP vs monadic co-NP, Information and Computation 120 (1995), 78–92.

    MathSciNet  MATH  Google Scholar 

  48. D. Gabbay, I. Hodkinson, M. Reynolds, Temporal Logic, Vol. 1, Clarendon Press, Oxford 1994.

    Google Scholar 

  49. Y. Gurevich, L. Harrington, Trees, automata, and games, in: Proc. 14th ACM Symp. on the Theory of Computing,1982, pp. 60–65.

    Google Scholar 

  50. D. Giammarresi, A. Restivo, S. Seibert, W. Thomas, Monadic second-order logic over rectangular pictures and recognizability by tiling systems, Information and Computation 125 (1996), 32–45.

    MathSciNet  MATH  Google Scholar 

  51. F. Gécseg, M. Steinby, Tree Automata, Akadémiai Kiodó, Budapest 1984.

    MATH  Google Scholar 

  52. T. A. Henzinger, The theory of hybrid automata, in: Proc. 11th IEEE Symp. on Logic in Computer Science, 1996, 278–292.

    Google Scholar 

  53. W. Hanf, Model-theoretic methods in the study of elementary logic, in: The Theory of Models (J. Addison, L. Henkin, P. Suppes, Eds.), North-Holland, Amsterdam 1965, pp. 132–145.

    Google Scholar 

  54. H. J. Hoogeboom, P. ten Pas, MSO-definable text languages, in: Mathematical Foundations of Computer Science 1994 (I. Prívara et al., Eds.), Lecture Notes in Computer Science 841, Springer-Verlag, Berlin 1994, pp. 413–422.

    Google Scholar 

  55. H. J. Hoogeboom, G. Rozenberg, Infinitary languages: basic theory and applications to concurrent systems, in: Current Trends in Concurrency (J. de Bakker et al., Eds.), Lecture Notes in Computer Science 224, Springer-Verlag, Berlin 1986, pp. 266–342.

    Google Scholar 

  56. N Immerman, Languages that capture complexity classes, SIAM J. Comput. 16 (1987), 761–778.

    MathSciNet  Google Scholar 

  57. D. Janin, I. Walukiewicz, Automata for the modal p-calculus and related results, in: Math. Found. of Comput. Sci. 1995 (J. Wiedermann, P. Hájek, Eds.), Lecture Notes in Computer Science 969, Springer-Verlag, Berlin 1995, pp. 552–562.

    Google Scholar 

  58. J. A. Kamp, Tense logic and the theory of linear order, Ph. D. Thesis, Univ. of California, Los Angeles, 1968.

    Google Scholar 

  59. O. Kupferman, O. Grumberg, Branching-time temporal logic and tree automata, Information and Computation 125 (1996), 62–69.

    MathSciNet  MATH  Google Scholar 

  60. N. Klarlund, Progress measures, immediate determinacy, and a subset construction for tree automata, Ann. Pure Appl. Logic 69 (1994), 243–168.

    MathSciNet  Google Scholar 

  61. N. Klarlund, M. Mukund, M. Sohoni, Determinizing Büchi asynchronous automata, in: Foundations of Software Technology and Theoretical Computer Science (P. S. Thiagarajan, Ed.), Lecture Notes in Computer Science 1026, Springer-Verlag, Berlin 1995, pp. 456–470.

    Google Scholar 

  62. S. C. Krishnan, A. Puri, R. K. Brayton, Structural complexity of ω-automata, in: STACS’95 (E. W. Mayr, C. Puech, Eds.), Lecture Notes in Computer Science 900, Springer-Verlag 1995, pp. 143–156.

    Google Scholar 

  63. T. Kamimura, G. Slutzki, Parallel and two-way automata on directed ordered acyclic graphs, Inform. Contr. 49 (1981), 10–51.

    MathSciNet  MATH  Google Scholar 

  64. R. P. Kurshan, Computer-Aided Verification of Coordinating Processes, Princeton University Press, Princeton, N. J. 1994.

    Google Scholar 

  65. R. Ladner, Application of model theoretic games to discrete linear orders and finite automata, Information and Control 33 (1977), 281–303.

    MathSciNet  MATH  Google Scholar 

  66. L. H. Landweber, Decision problems for ω-automata, Math. Systems Theory 3 (1969), 376–384.

    MathSciNet  MATH  Google Scholar 

  67. O. Lichtenstein, A. Pnueli, L. Zuck, The glory of the past, in: Logics of Programs (R. Parikh et al., Eds.), Lecture Notes in Computer Science 193, Springer-Verlag, Berlin 1985, pp. 196–218.

    Google Scholar 

  68. C. Lautemann, Th. Schwentick, D. Thérien, Logics for context-free languages, in: Computer Science Logic (L. Pacholski, J. Tiuryn, Eds.), Lecture Notes in Computer Science 933, Springer-Verlag, Berlin 1995, pp. 205–216.

    Google Scholar 

  69. K. McMillan, Symbolic Model Checking,Kluwer, Dordrecht 1993.

    MATH  Google Scholar 

  70. R. McNaughton, Testing and generating infinite sequences by a finite automaton, Inform. Contr. 9 (1966), 521–530.

    MathSciNet  MATH  Google Scholar 

  71. R. McNaughton, Infinite games played on finite graphs, Ann. Pure Appl. Logic 65 (1993), 149–184.

    MathSciNet  MATH  Google Scholar 

  72. R. McNaughton and S. Papert, Counter-Free Automata, MIT Press, Cambridge, Mass. 1971.

    MATH  Google Scholar 

  73. M. Michel, Complementation is more difficult with automata on infinite words, manuscript, CNET, Paris, 1988.

    Google Scholar 

  74. R. Milner, Operational and algebraic semantics of concurrent processes, in: Handbook of Theoretical Computer Science (J. v. Leeuwen, Ed.), Elsevier Science Publ., Amsterdam 1990, pp. 1201–1242.

    Google Scholar 

  75. Y. N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam 1980.

    MATH  Google Scholar 

  76. Z. Manna, A. Pnueli, The Temporal Logic of Reactive and Concurrent Programs, Springer-Verlag, Berlin, Heidelberg, New York 1992.

    Google Scholar 

  77. D. E. Muller, P. E. Schupp, The theory of ends, pushdown automata, and second-order logic, Theor. Comput. Sci. 37 (1985), 51–75.

    MathSciNet  MATH  Google Scholar 

  78. D. E. Muller, P. E. Schupp, Alternating automata on infinite trees, Theor.Comput. Sci. 54 (1987), 267–276.

    MathSciNet  MATH  Google Scholar 

  79. D. E. Muller, P. E. Schupp, Simulating alternating tree automata by non-deterministic automata: new results and new proofs of the theorems of Rabin, McNaughton and Safra, Theor. Comput. Sci. 141 (1995), 69–107.

    MathSciNet  MATH  Google Scholar 

  80. A. W. Mostowski, Regular expressions for infinite trees and a standard form of automata, in: A. Skowron (ed.), Computation Theory, Lecture Notes in Computer Science 208, Springer-Verlag, Berlin 1984, pp. 157–168.

    Google Scholar 

  81. A. W. Mostowski, Games with forbidden positions, Preprint No. 78, Uniwersytet Gdanski, Instytyt Matematyki, 1991.

    Google Scholar 

  82. A. W. Mostowski, Hierarchies of weak automata and weak monadic formulas, Theor. Comput. Sci. 83 (1991), 323–335.

    MathSciNet  MATH  Google Scholar 

  83. D. E. Muller, Infinite sequences and finite machines, in: Proc. 4th IEEE Symp. on Switching Circuit Theory and Logical Design,1963, pp. 3–16.

    Google Scholar 

  84. A. Muchnik, Games on infinite trees and automata with dead-ends. A new proof for the decidability of the monadic second-order theory of two successors, Bull. of the EATCS 48 (1992), 220–267 (Russian version in Semiotics and Information 24 (1984)).

    Google Scholar 

  85. C. Michaux, R. Villemaire, Presburger arithmetic and recognizability of natural numbers by automata: new proofs of Cobham’s and Semenov’s theorems, Ann. Pure Appl. Logic 77 (1996), 251–277.

    MathSciNet  MATH  Google Scholar 

  86. D. Niwinski, Fixed points vs infinite generation, in: Proc. 3rd IEEE Symp. on Logic in Computer Science, 1988, pp. 402–409.

    Google Scholar 

  87. D. Niwinski, Fixed points characterization of infinite behaviour of finite state systems, Theor. Comput. Sci. (to appear).

    Google Scholar 

  88. D. Perrin, Finite Automata, in: Handbook of Theoretical Computer Science,Vol. B (J. van Leuwen, ed.), Elsevier Science Publishers, Amsterdam 1990, pp. 1–57.

    Google Scholar 

  89. J.-E. Pin, Varieties of Formal Languages, Plenum, New-York, 1986.

    MATH  Google Scholar 

  90. D. Perrin and J.-E. Pin, First-order logic and star-free sets, J. Comput. System Sci. 32 (1986), 393–406.

    MathSciNet  MATH  Google Scholar 

  91. A. Potthoff, First-order logic on finite trees, in: TAPSOFT ’85 (P. D. Mosses et al., Eds.), Lecture Notes in Computer Science, Springer-Verlag, Berlin 1995, pp. 125–139.

    Google Scholar 

  92. A. Potthoff, S. Seibert, W. Thomas, Nondeterminism versus determinism of finite automata over directed acyclic graphs, Bull. Belg. Math. Soc. Simon Stevin 1 (1994), 285–298.

    MathSciNet  MATH  Google Scholar 

  93. A. Potthoff, W. Thomas, Regular tree languages without unary symbols are star-free, in: Fundamentals of of Computation Theory (Z. Esik, Ed.), Lecture Notes in Computer Science 710, Springer-Verlag, Berlin 1993, pp. 396–405.

    Google Scholar 

  94. M. O. Rabin, Decidability of second-order theories and automata on infinite trees, Trans. Amer. Math. Soc. 141 (1969), 1–35.

    MathSciNet  MATH  Google Scholar 

  95. M. O. Rabin, Weakly definable relations and special automata, in: Mathematical Logic and Foundations of Set Theory (Y. Bar-Hillel, Ed.), North-Holland, Amsterdam 1970, pp. 1–23.

    Google Scholar 

  96. M. O. Rabin, Automata on infinite objects and Church’s Problem, Amer. Math. Soc., Providence, RI, 1972.

    Google Scholar 

  97. S. Safra, On the complexity of ω-automata, in: Proc. 29th IEEE Symp. On Foundations of Computer Science, 1988, pp. 319–327.

    Google Scholar 

  98. S. Safra, Exponential determinization for ω-automata with strong-fairness acceptance condition, in: Proc. 24th ACM Symp. on the Theory of Computing, 1992, pp. 275–282.

    Google Scholar 

  99. A. P. Sistla, E. M. Clarke, The complexity of propositional linear time logics, J. Assoc. Comput. Mach. 32 (1985), 733–749.

    MathSciNet  MATH  Google Scholar 

  100. M. P. Schützenberger, On finite monoids having only trivial subgroups, Information and Control 8 (1965), 190–194.

    MathSciNet  MATH  Google Scholar 

  101. D. Seese, Interpretability and tree automata: a simple way to solve algorithmic problems on graphs closely related to trees, in: Tree Automata and Languages (M. Nivat, A. Podelski, Eds.), Elsevier Science Publishers, 1992, pp. 83–114.

    Google Scholar 

  102. D. Seese, Linear time computable problems and first-order descriptions, Math. Struct. in Comp. Sci. 1996.

    Google Scholar 

  103. S. Seibert, Quantifier hierarchies over word relations, in: Computer Science Logic (E. Börger et al. Eds.), Lecture Notes in Computer Science 626, Springer-Verlag, Berlin 1992, 329–338.

    Google Scholar 

  104. A. L. Semenov, Decidability of monadic theories, in: Proc. MFCS ’84 (M. P. Chytil, V, Koubek, Eds.), Lecture Notes in Computer Science 176, Springer-Verlag, Berlin 1984, pp. 162–175.

    Google Scholar 

  105. I. Simon, Piecewise testable events, Proc. 2nd GI Conf., Lecture Notes in Computer Science 33, Springer-Verlag, Berlin 1975, pp. 214–222.

    Google Scholar 

  106. J. Stupp, The lattice model is recursive in the original model, manuscript, The Hebrew Univ., Jerusalem 1975.

    Google Scholar 

  107. R. S. Streett, Propositional dynamic logic of looping and converse, Inform. Contr. 54 (1982), 121–141.

    MathSciNet  MATH  Google Scholar 

  108. L. Staiger, Research in the theory of ω-languages, J. Inf. Process. Cybern. EIK 23 (1987), 415–439.

    MathSciNet  MATH  Google Scholar 

  109. H. Straubing, Finite Automata, Formal Logic, and Circuit Complexity, Birkhäuser, Boston, 1994.

    MATH  Google Scholar 

  110. C. Stirling, Modal and temporal logics for processes, in: Logics for Con-currency: Structure versus Automata (F. Moller, G. Birtwistle, Eds.), Lecture Notes in Computer Science 1043, Springer-Verlag, Berlin 1996, pp. 149–237.

    Google Scholar 

  111. H. Straubing, D. Thérien and W. Thomas, Regular Languages Defined with Generalized Quantifiers, in: Information and Computation 118 (1995), 289–301.

    Google Scholar 

  112. L. Staiger, K. Wagner, Automatentheoretische und automatenfreie Charakterisierungen topologischer Klassen regulärer Folgenmengen, Elektron. Informationsverarbeitung u. Kybernetik EIK 10 (1974), 379–392.

    MathSciNet  MATH  Google Scholar 

  113. B. A. Trakhtenbrot, Y. M. Barzdin, Finite Automata, North-Holland, Amsterdam 1973.

    MATH  Google Scholar 

  114. W. Thomas, A combinatorial approach to the theory of ω-automata, Information and Control 48 (1981), 261–283.

    MathSciNet  MATH  Google Scholar 

  115. W. Thomas, Classifying regular events in symbolic logic, J. Comput. Syst. Sci. 25 (1982), 360–375.

    MATH  Google Scholar 

  116. W. Thomas, A hierarchy of sets of infinite trees, in: Theoretical Computer Science (A. B. Cremers, H. P. Kriegel, Eds.), Lecture Notes in Computer Science 145, Springer-Verlag, Berlin 1982, pp. 335–342.

    Google Scholar 

  117. W. Thomas, An application of the Ehrenfeucht—Fraïssé game in formal language theory, Bull. Soc. Math. France, Mem. 16 (1984), 11–21.

    MATH  Google Scholar 

  118. W. Thomas, Logical aspects in the study of tree languages, in: Ninth Coll. on Trees in Algebra and Programming (B. Courcelle, Ed.), Cambridge Univ. Press 1984, pp. 31–49.

    Google Scholar 

  119. W. Thomas, A concatenation game and the dot-depth hierarchy, in: Computation Theory and Logic (E. Börger, Ed.), Lecture Notes in Computer Science 270, Springer-Verlag, Berlin 1987, pp. 415–426.

    Google Scholar 

  120. W. Thomas, Automata on infinite objects, in: Handbook of Theoretical Computer Science, Vol. B (J. v. Leeuwen, Ed.), Elsevier Science Publishers, Amsterdam 1990, pp. 135–191.

    Google Scholar 

  121. W. Thomas, On logics, tilings, and automata, in: Automata, Languages, and Programming (J. Leach et al., Eds.), Lecture Notes in Computer Science 510, Springer-Verlag, Berlin 1991, pp. 441–453.

    Google Scholar 

  122. W. Thomas, On the synthesis of strategies in infinite games, in: STACS’95 (E. W. Mayr, C. Puech, Eds.), Lecture Notes in Computer Science 900, Springer-Verlag, Berlin 1995, pp. 1–13.

    Google Scholar 

  123. W. Thomas, H. Lescow, Logical specifications of infinite computations, in: A Decade of Concurrency (J. W. de Bakker et al., Eds.), Lecture Notes in Computer Science 803, Springer-Verlag, Berlin 1994, pp. 583–621.

    Google Scholar 

  124. J. W. Thatcher, J. B. Wright, Generalized finite automata with an application to a decision problem of second order logic, Math. Syst. Theory 2 (1968), 57–82.

    MathSciNet  Google Scholar 

  125. D. Thérien, Th. Wilke, Temporal logic and an effective characterization of the until hierarchy, in: Proc. 37th IEEE Symp. on Foundations of Computer Science, 1996, 264–273.

    Google Scholar 

  126. M. Y. Vardi, An automata-theoretic approach to linear temporal logic, in: Logics for Concurrency: Structure versus Automata (F. Moller, G. Birtwistle, Eds.), Lecture Notes in Computer Science 1043, Springer-Verlag, Berlin 1996, pp. 238–266.

    Google Scholar 

  127. M. Y. Vardi, P. Wolper, Reasoning about infinite computations, Information and Computation 115 (1994), 1–37.

    MathSciNet  MATH  Google Scholar 

  128. K. W. Wagner, On ω-regular sets, Inform. Contr. 43 (1979), 123–177.

    MATH  Google Scholar 

  129. I. Walukiewicz, Monadic second order logic on tree-like structures, in: STACS’96 (C. Puech, R. Reischuk, Eds.), Lecture Notes in Computer Science 1046, Springer-Verlag, Berlin 1996, pp. 401–414.

    Google Scholar 

  130. Th. Wilke, Locally threshold testable languages of infinite words, in: STACS ’83 (P. Enjalbert, A. Finkel, K. W. Wagner, Eds.), Lecture Notes in Computer Science 665, Springer-Verlag, Berlin 1993, pp. 607–616.

    Google Scholar 

  131. Th. Wilke, Specifying timed state sequences in powerful decidable logics and timed automata, in: Formal Techniques in Real Time and Fault Tolerant Systems (H. Langmaack et al., Eds.), Lecture Notes in Computer Science 863, Springer-Verlag, Berlin 1994, pp. 694–715.

    Google Scholar 

  132. Th. Wilke, H. Yoo, Computing the Wadge degree, the Lifschitz degree, and the Rabin index of a regular language of infinite words in polynomial time, in: TAPSOFT’95 (P. D. Mosses et al., Eds.), Lecture Notes in Computer Science 915, Springer-Verlag, Berlin 1995, 288–302.

    Google Scholar 

  133. A. Yakhnis, V. Yakhnis, Extension of Gurevich-Harrington’s restricted determinacy theorem: A criterion for the winning player and an explicit class of winning strategies, Ann. Pure Appl. Logic 48 (1990), 277–279.

    MathSciNet  MATH  Google Scholar 

  134. S. Zeitman, Unforgettable forgetful determinacy, J. Logic Computation 4 (1994), 273–283.

    MathSciNet  MATH  Google Scholar 

  135. W. Zielonka, Notes on finite asynchronous automata, RAIRO Inform. Théor. Appl. 21 (1987), 99–135.

    MathSciNet  MATH  Google Scholar 

  136. W. Zielonka, Infinite games on finitely coloured graphs with applications to automata on infinite trees, Rep. 1091–95, LaBRI, Univ. de Bordeaux, to appear in Theor. Comput. Sci..

    Google Scholar 

Download references

Authors
  1. Wolfgang Thomas
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Leiden University, P.O. Box 9512, NL-2300 RA, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Turku Centre for Computer Science Data City, FIN-20520, Turku, Finland

    Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Thomas, W. (1997). Languages, Automata, and Logic. In: Rozenberg, G., Salomaa, A. (eds) Handbook of Formal Languages. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59126-6_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59126-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63859-6

  • Online ISBN: 978-3-642-59126-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation