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The Wadge Hierarchy of Deterministic Tree Languages

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Automata, Languages and Programming (ICALP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4052))

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Abstract

We provide a complete description of the Wadge hierarchy for deterministically recognizable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to another. This extends Wagner’s results on the hierarchy of ω-regular languages to the case of trees.

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References

  1. Duparc, J.: A hierarchy of deterministic context-free ω-languages. Theoret. Comput. Sci. 290, 1253–1300 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Finkel, O.: Wadge Hierarchy of Omega Context Free Languages. Theoret. Comput. Sci. 269, 283–315 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kechris, A.S.: Classical Descriptive Set Theory. Graduate Texts in Mathematics 156 (1995)

    Google Scholar 

  4. Kupferman, O., Safra, S., Vardi, M.: Relating Word and Tree Automata. 11th IEEE Symp. on Logic in Comput. Sci, 322–332 (1996)

    Google Scholar 

  5. Murlak, F.: On deciding topological classes of deterministic tree languages. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 428–441. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. F. Murlak. The Wadge hierarchy of deterministic tree languages. Draft version, http://www.mimuw.edu.pl/~fmurlak/papers/conred.pdf

  7. Niwiński, D., Walukiewicz, I.: Relating hierarchies of word and tree automata. In: Meinel, C., Morvan, M. (eds.) STACS 1998. LNCS, vol. 1373, pp. 320–331. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  8. Niwiński, D., Walukiewicz, I.: A gap property of deterministic tree languages. Theoret. Comput. Sci. 303, 215–231 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Niwiński, D., Walukiewicz, I.: Deciding nondeterministic hierarchy of deterministic tree automata. In: Proc. WoLLiC 2004. Electronic Notes in Theoret. Comp. Sci, pp. 195–208 (2005)

    Google Scholar 

  10. Perrin, D., Pin, J.-E.: Infinite Words. Automata, Semigroups, Logic and Games. In: Pure and Applied Mathematics, vol. 141, Elsevier, Amsterdam (2004)

    Google Scholar 

  11. Selivanov, V.: Wadge Degrees of ω-languages of deterministic Turing machines. Theoret. Informatics Appl. 37, 67–83 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Skurczyński, J.: The Borel hierarchy is infinite in the class of regular sets of trees. Theoret. Comput. Sci. 112, 413–418 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  13. Urbański, T.F.: On deciding if deterministic Rabin language is in Büchi class. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 663–674. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  14. Wagner, K.: Eine topologische Charakterisierung einiger Klassen regulärer Folgenmengen. J. Inf. Process. Cybern. EIK 13, 473–487 (1977)

    MATH  Google Scholar 

  15. Wagner, K.: On ω-regular sets. Inform. and Control 43, 123–177 (1979)

    Article  MATH  MathSciNet  Google Scholar 

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Murlak, F. (2006). The Wadge Hierarchy of Deterministic Tree Languages. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787006_35

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  • DOI: https://doi.org/10.1007/11787006_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35907-4

  • Online ISBN: 978-3-540-35908-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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