Acceptance Conditions for ω-Languages

  • Alberto Dennunzio
  • Enrico Formenti
  • Julien Provillard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7410)

Abstract

This paper investigates acceptance conditions for finite automata recognizing ω-regular languages. Their expressive power and their position w.r.t. the Borel hierarchy is also studied. The full characterization for the conditions (ninf, ⊓ ), (ninf, ⊆ ) and (ninf, = ) is given. The final section provides a partial characterization of (fin, = ).

Keywords

finite automata acceptance conditions ω-regular languages 

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References

  1. 1.
    Büchi, J.R.: Symposium on decision problems: On a decision method in restricted second order arithmetic. In: Suppes, P., Nagel, E., Tarski, A. (eds.) Logic, Methodology and Philosophy of Science Proceeding of the 1960 International Congress. Studies in Logic and the Foundations of Mathematics, vol. 44, pp. 1–11. Elsevier (1960)Google Scholar
  2. 2.
    Hartmanis, J., Stearns, R.E.: Sets of numbers defined by finite automata. American Mathematical Monthly 74, 539–542 (1967)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Kupferman, O., Vardi, M.Y.: From Complementation to Certification. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 591–606. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Kurshan, R.P.: Computer aided verification of coodinating process. Princeton Univ. Press (1994)Google Scholar
  5. 5.
    Landweber, L.H.: Decision problems for omega-automata. Mathematical Systems Theory 3(4), 376–384 (1969)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Litovsky, I., Staiger, L.: Finite acceptance of infinite words. Theor. Comput. Sci. 174(1-2), 1–21 (1997)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Moriya, T., Yamasaki, H.: Accepting conditions for automata on ω-languages. Theor. Comput. Sci. 61, 137–147 (1988)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Muller, D.E.: Infinite sequences and finite machines. In: Proceedings of the 1963 Proceedings of the Fourth Annual Symposium on Switching Circuit Theory and Logical Design, SWCT 1963, pp. 3–16. IEEE Computer Society, Washington, DC (1963)CrossRefGoogle Scholar
  9. 9.
    Perrin, D., Pin, J.-E.: Infinite words, automata, semigroups, logic and games. Pure and Applied Mathematics, vol. 141. Elsevier (2004)Google Scholar
  10. 10.
    Staiger, L., Wagner, K.W.: Automatentheoretische und automatenfreie charakterisierungen topologischer klassen regulärer folgenmengen. Elektronische Informationsverarbeitung und Kybernetik 10(7), 379–392 (1974)MathSciNetMATHGoogle Scholar
  11. 11.
    Staiger, L.: ω-languages. In: Handbook of Formal Languages, vol. 3, pp. 339–387 (1997)Google Scholar
  12. 12.
    Thomas, W.: Automata on infinite objects. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, pp. 135–191. Elsevier (1990)Google Scholar
  13. 13.
    Vardi, M.Y.: The Büchi Complementation Saga. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 12–22. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Wagner, K.W.: On ω-regular sets. Information and Control 43(2), 123–177 (1979)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alberto Dennunzio
    • 2
  • Enrico Formenti
    • 1
  • Julien Provillard
    • 1
  1. 1.Laboratoire I3SUniversité Nice-Sophia AntipolisSophia AntipolisFrance
  2. 2.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano–BicoccaMilanoItaly

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