Skip to main content
SpringerLink
Log in

Two-Way Alternating Automata and Finite Models

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2380))

Included in the following conference series:

Abstract

A graph extension of two-way alternating automata on trees is considered. The following problem: “does a given automaton accept any finite graph?” is proven EXPTIME complete. Using this result, the decidability of the finite model problem for the modal μ-calculus with backward modalities is shown.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Mikolaj Bojańczyk. The finite graph problem for two-way alternating automata. In FOSSACS 2001, volume 2030 of LNCS, pages 88–103, 2001.

    Google Scholar 

  2. A. Saoudi D. E. Muller and P. E. Shupp. Weak alternating automata give a simple explanation why most temporal and dynamic logics are decidable in exponential time. In Proceedings 3rd IEEE Symposium on Logic in Computer Science, pages 422–427, 1988.

    Google Scholar 

  3. E. A. Emerson and C. Jutla. Tree automata, mu-calculus and determinacy. In Proc. 32th IEEE Symposium on Foundations of Computer Science, pages 368–377, 1991.

    Google Scholar 

  4. E. Grädel. On the restraining power of guards. Journal of Symbolic Logic, 1999.

    Google Scholar 

  5. E. Grädel and I. Walukiewicz. Guarded fixed point logic. In Proceedings 14th IEEE Symp. on Logic in Computer Science, pages 45–54, 1999.

    Google Scholar 

  6. Y. Gurevich and L. Harrington. Automata, trees and games. In Proc. 14th. Ann. ACM Symp. on the Theory of Computing, pages 60–65, 1982.

    Google Scholar 

  7. J. van Benthem H. Andreka and I. Nemeti. Modal logics and bounded fragments of predicate logic. Journal of Philosophical Logic, pages 217–274, 1998.

    Google Scholar 

  8. I. Hodkinson. Loosely guarded fragment has finite model property. J. Symbolic Logic, to appear.

    Google Scholar 

  9. D. Kozen. Results on the propositional μ-calculus. Theoretical Computer Science, 27:333–354, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. Ladner M. Fischer. Propositional dynamic logic of regular programs. Journal of Computer and System Sciences, 18:194–211, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Mostowski. Games with forbidden positions. Technical report, University of Gdańsk, 1991.

    Google Scholar 

  12. D.E. Muller and P.E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54:267–276, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. O. Rabin. Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc., 141, 1969.

    Google Scholar 

  14. G. Slutzki. Alternating tree automata. Theoretical Computer Science, 41:305–318, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  15. Wolfgang Thomas. Languages, automata, and logic. In Handbook of Formal Language Theory, III, pages 389–455. Springer, 1997.

    Google Scholar 

  16. M. Vardi. Reasoning about the past with two-way automata. In vol. 1443 LNCS, pages 628–641, 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wydzial MIM, Uniwersytet Warszawski, Banacha 2, Warszawa, Polska

    Mikolaj Bojarńczyk

Authors
  1. Mikolaj Bojarńczyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zentrum, ETH Zürich, 8092, Zürich, Switzerland

    Peter Widmayer  & Stephan Eidenbenz  & 

  2. Department of Languages and Sciences of the Computation E.T.S. de Ingeniería Informática, University of Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Francisco Triguero , Rafael Morales  & Ricardo Conejo ,  & 

  3. School of Cognitive and Computing Sciences, University of Sussex, Falmer, Brighton, BN1 9QN, UK

    Matthew Hennessy

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bojarńczyk, M. (2002). Two-Way Alternating Automata and Finite Models. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_71

Download citation

  • DOI: https://doi.org/10.1007/3-540-45465-9_71

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43864-9

  • Online ISBN: 978-3-540-45465-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation