Pushdown automata on infinite trees and omega-Kleene closure of context-free tree sets

  • A. Saoudi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 379)


Infinite Sequence Regular Language Finite Automaton Tree Automaton Computation Tree Logic 
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  1. [1]
    A. Arnold and M. Nivat, Formal computations of nondeterministic program schemes, Math. Syst. Theory 13(1980)219–236.Google Scholar
  2. [2]
    J.R. Büchi, On a decision method in restricted second order arithmetic, Proc. Cong. Logic Method and Philos. of Sci. 1960, Univ. Press, Stanford California.Google Scholar
  3. [3]
    R. S. Cohen and A. Y. Gold, Theory of ω-languages II: A study of various models of ω-types generation and recognition, J. Comput. Syst. Sci. 15(1977)185–208.Google Scholar
  4. [4]
    R. S. Cohen and A. Y. Gold, ω-computations of deterministic pushdown machines, J. Comput. Syst. Sci. 16(1978)275–300.Google Scholar
  5. [5]
    S. Eilenberg, Automata, Languages, and Machines, Academic Press(1974).Google Scholar
  6. [6]
    J. H. Gallier and K. Schimpf, Tree pushdown automata, J. Comput. Syst. Sci. 30(1985)25–40.Google Scholar
  7. [7]
    F. Gécseg and M. Steinby, Tree automata, Akademiai Kiado, Budapest (1984).Google Scholar
  8. [8]
    I. Guessarian, Pushdown tree automata, Math. Syst. Theory 16(1983) 237–264.Google Scholar
  9. [9]
    I. Guessarian, Algebraic semantics, Lect. Notes Comp. Sci. no. 99, Springer-Verlag, Berlin (1981).Google Scholar
  10. [10]
    T. Hafer and W. Thomas, Computation tree logic CTL* and path quantifiers in the theory of the binary tree, Proc. 14th ICALP, (T. Ottmann, ed.), LNCS no. 267, Springer-Verlag, Berlin(1987)269–279.Google Scholar
  11. [11]
    T. Hayashi and S. Miyano, Finite tree automata on infinite trees, Bull. Inform. Cybern. 21(1985)71–82.Google Scholar
  12. [12]
    K. Kobayashi, M. Takahashi and H. Yamasaki, Logical formulas and four subclasses of ω-regular languages, in Automata on infinite words, (M. Nivat and D. Perrin eds.), LNCS no. 192, Springer Verlag, Berlin(1984).Google Scholar
  13. [13]
    L. H. Landweber, Decision problem for ω-automata, Math. Syst. Theory 3(1969)376–384.Google Scholar
  14. [14]
    M. Linna, On ω-sets associated with context-free languages, Inf. and Control 31(1976)272–293.Google Scholar
  15. [15]
    D. E. Muller, Infinite sequences and finite machines, Proc. 4th IEEE on Switching Circuit Theory and Logical Design(1963)3–16.Google Scholar
  16. [16]
    D. Muller, A. Saoudi and P. Schupp, Alternating automata, the weak monadic theory and its complexity,13th Inter. Colloquium Automata, Languages and Programming, (L. Kott, ed.), L.N.C.S no. 226, Springer-Verlag, Berlin(1986)275–283.Google Scholar
  17. [17]
    T. Moriya, Topological characterisations of infinite tree languages, Theoret. Comput. Sci. 52(1987)165–171.Google Scholar
  18. [18]
    R. Mc Naughton, Testing and generating infinite sequences by a finite automata, Inform. and Control 9(1966)521–530.Google Scholar
  19. [19]
    M. Nivat et A. Saoudi, Automata on infinite trees and rational infinite tree sets, Rapport L.I.T.P no. 87–59, Univ. Paris VII, Submitted to J. Comput. Syst. Sci.Google Scholar
  20. [20]
    M. Nivat and A. Saoudi, Automata on infinite objects and their applications to logic programming, Univ. Paris VII, report no. 87–60(1987), to appear in Inf. and Computation.Google Scholar
  21. [21]
    D. Perrin, Recent results on automata and infinite words, Proc. Math. Found. of Comput. Sci. (M. P. Chytil and V. Koubek, eds.), LNCS no. 176(1984)134–148.Google Scholar
  22. [22]
    M. O. Rabin, Decidability of second order theories and automata on infinite trees, Trans. Amer. Math. Soc. 141(1969)1–35.Google Scholar
  23. [23]
    M. O. Rabin, Weakly definable relations and special automata, Math. Logic and Foundation of set theory, Y.Bar Hillel, Edit. Amsterdam North Holland (1970)1–23.Google Scholar
  24. [24]
    G. Rozenberg, Selective substitution grammars, Part I, Elektron. Inform. Kybernet. 13(1977)455–463.Google Scholar
  25. [25]
    A. Saoudi, Variétés d'automates descendants d'arbres infinis, Theoret. Comput. Sci. 43(1986)1–21.Google Scholar
  26. [26]
    A. Saoudi, Generalized automata on infinite trees and Muller-Mc Naughton's theorem, Univ. Paris VII, report no. 88-06(1988)Google Scholar
  27. [27]
    M. Takahashi, The greatest fixed points and rational omega-tree languages, Theoret. Comput. Sci. 44(1986)259–274.Google Scholar
  28. [28]
    J. W. Thatcher and J.B. Wright, Generalized finite automata theory with applications to a decision problem of second order logic, Math. Syst. Theory 2(1968)57–81.Google Scholar
  29. [29]
    W. Thomas, A Combinatorial approach to the theory of ω-automata, Inform. and Control 48(1981)261–283.Google Scholar
  30. [30]
    W. Thomas, A Hierarchy of sets of infinite trees, G.I Conference, L.N.C.S no. 145, (A. B. Cremers, H. P. Kriegel, eds.), Springer-Verlag, Berlin (1982)335–342.Google Scholar
  31. [31]
    W. Thomas, On chain logic, path logic, and first order logic over infinite trees, Proc. 2nd Symp. on Logic in Computer Sci. (1987)245–256.Google Scholar
  32. [32]
    K. Wagner and L. Staiger, Automatatheoretische und Automatenfreie Characterisierugen Topologischer Klasses Regular Folgmmengen, EIK 10(1974)379–392.Google Scholar
  33. [33]
    P. Wolper and M. Vardi, Reasoning about Fair Concurrent programs, Proc. 18th Symp. on Theory of Computing, Berkeley(1986).Google Scholar
  34. [34]
    A. W. Mostowski, Determinancy of Sinking Automata on Infinite trees and Inequalities between various Rabin's Pair Indices, Inform. Proc. Letters, vol. 15, no. 4(1982) 159–163.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • A. Saoudi
    • 1
  1. 1.Université Paris VII L.I.T.P.Paris

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