Equivalence and Inclusion Problem for Strongly Unambiguous Büchi Automata

  • Nicolas Bousquet
  • Christof Löding
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6031)

Abstract

We consider the inclusion and equivalence problem for unambiguous Büchi automata. We show that for a strong version of unambiguity introduced by Carton and Michel these two problems are solvable in polynomial time. We generalize this to Büchi automata with a fixed finite degree of ambiguity in the strong sense. We also discuss the problems that arise when considering the decision problems for the standard notion of ambiguity for Büchi automata.

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References

  1. 1.
    Aho, A., Hopcroft, J., Ullman, J.: The Design and Analysis of Computer Algorithms. Addison-Wesley, New York (1974)MATHGoogle Scholar
  2. 2.
    Arnold, A.: Rational ω-languages are non-ambiguous. Theoretical Computer Science 26, 221–223 (1983)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)MATHGoogle Scholar
  4. 4.
    Büchi, J.R.: On a decision method in restricted second order arithmetic. In: International Congress on Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford University Press, Stanford (1962)Google Scholar
  5. 5.
    Calbrix, H., Nivat, M., Podelski, A.: Ultimately periodic words of rational ω-languages. In: Main, M.G., Melton, A.C., Mislove, M.W., Schmidt, D., Brookes, S.D. (eds.) MFPS 1993. LNCS, vol. 802, pp. 554–566. Springer, Heidelberg (1994)Google Scholar
  6. 6.
    Carayol, A., Löding, C.: MSO on the infinite binary tree: Choice and order. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 161–176. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Carton, O., Michel, M.: Unambiguous Büchi automata. Theor. Comput. Sci. 297(1-3), 37–81 (2003)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Löding, C., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications, http://tata.gforge.inria.fr/ (last release: October 12, 2007)
  9. 9.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)MATHGoogle Scholar
  10. 10.
    Landweber, L.H.: Decision problems for ω-automata. Mathematical Systems Theory 3, 376–384 (1969)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    McNaughton, R.: Testing and generating infinite sequences by a finite automaton. Information and Control 9(5), 521–530 (1966)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Niwiński, D., Walukiewicz, I.: Ambiguity problem for automata on infinite trees (unpublished note)Google Scholar
  13. 13.
    Seidl, H.: Deciding equivalence of finite tree automata. SIAM J. Comput. 19(3), 424–437 (1990)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Stearns, R.E., Hunt III, H.B.: On the equivalence and containment problems for unambiguous regular expressions, regular grammars and finite automata. SIAM Journal on Computing 14(3), 598–611 (1985)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Stockmeyer, L.J.: The Complexity of Decision Problems in Automata Theory and Logic. PhD thesis, Dept. of Electrical Engineering, MIT, Boston, Mass. (1974)Google Scholar
  16. 16.
    Thomas, W.: Languages, automata, and logic. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Language Theory, vol. III, pp. 389–455. Springer, Heidelberg (1997)Google Scholar
  17. 17.
    Valiant, L.G.: Relative complexity of checking and evaluating. Inf. Process. Lett. 5(1), 20–23 (1976)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Nicolas Bousquet
    • 1
  • Christof Löding
    • 2
  1. 1.ENS ChachanFrance
  2. 2.Informatik 7RWTH AachenAachenGermany

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