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Latin American Symposium on Theoretical Informatics

LATIN 2000: LATIN 2000: Theoretical Informatics pp 407–416Cite as

Unambiguous Büchi Automata

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1776))

Abstract

In this paper, we introduce a special class of Büchi automata called unambiguous. In these automata, any infinite word labels exactly one path going infinitely often through final states. The word is accepted by the automaton if this path starts at an initial state. The main result of the paper is that any rational set of infinite words is recognized by such an automaton. We also provide two characterizations of these automata. We finally show that they are well suitable for boolean operations.

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References

  1. Arnold, A.: Rational omega-languages are non-ambiguous. Theoretical Computer Science 26(1-2), 221–223 (1983)

    Article  MathSciNet  Google Scholar 

  2. Beauquier, D., Perrin, D.: Codeterministic automata on infinite words. Information Processing Letters 20, 95–98 (1985)

    Article  MathSciNet  Google Scholar 

  3. Richard Büchi, J.: On a decision method in the restricted second-order arithmetic. In: Proc. Int. Congress Logic, Methodology and Philosophy of science, Berkeley, pp. 1–11 (1960); Stanford University Press (1962)

    Google Scholar 

  4. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Mostowski, A.W.: Determinancy of sinking automata on infinite trees and inequalities between various Rabin’s pair indices. Inform. Proc. Letters 15(4), 159–163 (1982)

    Article  MathSciNet  Google Scholar 

  8. Mostowski, A.W.: Regular expressions for infinite trees and a standard form for automata. In: Skowron, A. (ed.) SCT 1984. LNCS, vol. 208, pp. 157–168. Springer, Heidelberg (1984)

    Chapter  Google Scholar 

  9. Muller, D.: Infinite sequences and finite machines. In: Proc. of Fourth Annual IEEE Symp. (eds.): Switching Theory and Logical Design, pp. 3–16 (1963)

    Google Scholar 

  10. Perrin, D.: Finite automata. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, ch. 1, vol. B. Elsevier, Amsterdam (1990)

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  12. Sistla, A.P., Vardi, M.Y., Wolper, P.: The complementation problem for Büchi automata and applications to temporal logic. Theoret. Comput. Sci. 49, 217–237 (1987)

    Article  MathSciNet  Google Scholar 

  13. Thomas, W.: Automata on infinite objects. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, ch. 4, vol. B. Elsevier, Amsterdam (1990)

    Google Scholar 

  14. Moshe, Y.: An automata-theoretic approach to linear temporal logic. In: Moller, F., Birtwistle, G. (eds.) Logics for Concurrency. LNCS, vol. 1043, pp. 238–266. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut Gaspard Monge, 5, boulevard Descartes, F-77454, Marne-la-Vallée cedex 2, France

    Olivier Carton

  2. CNET, 38, rue du Général Leclerc, F-92131, Issy-les-Moulineaux, France

    Max Michel

Authors
  1. Olivier Carton
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  2. Max Michel
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Editor information

Editors and Affiliations

  1. ETH Zurich, Institute of Computational Science, CH-8092 Zurich and, Swiss Institute of Bioinformatics, Switzerland

    Gaston H. Gonnet

  2. Pedeciba Informática, Casilla de Correo 16120, Distrito 6, Montevideo, Uruguay

    Alfredo Viola

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© 2000 Springer-Verlag Berlin Heidelberg

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Carton, O., Michel, M. (2000). Unambiguous Büchi Automata. In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_40

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  • DOI: https://doi.org/10.1007/10719839_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67306-4

  • Online ISBN: 978-3-540-46415-0

  • eBook Packages: Springer Book Archive

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