Skip to main content
SpringerLink
Log in

Logical Characterizations of PSPACE

  • Conference paper
  • First Online:
Computer Science Logic (CSL 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3210))

Included in the following conference series:

Abstract

We present two, quite different, logical characterizations of the computational complexity class PSPACE on unordered, finite relational structures. The first of these, the closure of second-order logic under the formation of partial fixed points is well-known in the folklore but does not seem to be in the literature. The second, the closure of first-order logic under taking partial fixed points and under an operator for nondeterministic choice, is novel. We also present syntactic normal forms for the two logics and compare the second with other choice-based fixed-point logics found in the literature.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Abiteboul, S., Simon, E., Vianu, V.: Non-deterministic languages to express deterministic transformations. In: Proceedings of 9th ACM Symposium on Principles of Database Systems, pp. 218–229. ACM Press, New York (1990)

    Google Scholar 

  2. Abiteboul, S., Vianu, V.: Fixpoint extensions of first-order and datalog-like languages. In: Proceedings of 4th IEEE Annual Symposium on Logic in Computer Science, pp. 71–79. IEEE Computer Society Press, Los Alamitos (1989)

    Google Scholar 

  3. Blass, A., Gurevich, Y.: The logic of choice. Journal of Symbolic Logic 65(3), 1264–1310 (2000)

    Article  MathSciNet  Google Scholar 

  4. Dawar, A.: A restricted second order logic for finite structures. Information and Computation 143(2), 154–174 (1998)

    Article  MathSciNet  Google Scholar 

  5. Dawar, A., Richerby, D.M.: Fixed-point logics with nondeterministic choice. Journal of Logic and Computation 13(4), 503–530 (2003)

    Article  MathSciNet  Google Scholar 

  6. Ebbinghaus, H.-D.: Extended logics: The general framework. In: Barwise, J., Feferman, S. (eds.) Model-Theoretic Logics, pp. 25–76. Springer, Heidelberg (1985)

    Google Scholar 

  7. Ebbinghaus, H.-D., Flum, J.: Finite Model Theory, 2nd edn. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  8. Fagin, R.: Generalized first-order spectra and polynomial-time recognizable sets. In: Karp, R. (ed.) Complexity of Computation. SIAM-AMS Proceedings, vol. 7, pp. 43–73. SIAM-AMS, Philadelphia (1974)

    Google Scholar 

  9. Fagin, R.: Monadic generalized spectra. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 21, 89–96 (1975)

    Article  MathSciNet  Google Scholar 

  10. Gire, F., Hoang, H.K.: An extension of fixpoint logic with a symmetrybased choice construct. Information and Computation 144(1), 40–65 (1998)

    Article  MathSciNet  Google Scholar 

  11. Hilbert, D., Bernays, P.: Grundlagen der Mathematik, vol. 2. Springer, Heidelberg (1939)

    MATH  Google Scholar 

  12. Harel, D., Peleg, D.: On static logics, dynamic logics, and complexity classes. Information and Control 60(1–3), 86–102 (1984)

    Article  MathSciNet  Google Scholar 

  13. Immerman, N.: Relational queries computable in polynomial time. Information and Control 68(1–3), 86–104 (1986)

    Article  MathSciNet  Google Scholar 

  14. Immerman, N.: Logics that capture complexity classes. SIAM Journal of Computing 16(4), 236–244 (1987)

    Article  Google Scholar 

  15. Immerman, N.: Nondeterministic space is closed under complementation. SIAM Journal of Computing 17(5), 935–938 (1988)

    Article  MathSciNet  Google Scholar 

  16. Kolaitis, P.G., Vardi, M.Y.: Infinitary logics and 0-1 laws. Information and Computation 98(2), 258–294 (1992)

    Article  MathSciNet  Google Scholar 

  17. Otto, M.: Epsilon-logic is more expressive than first-order logic over finite structures. Journal of Symbolic Logic 65(4), 1749–1757 (2000)

    Article  MathSciNet  Google Scholar 

  18. Savitch, W.J.: Relationships between nondeterministic and deterministic tape complexities. J. Computer and System Sciences 4(2), 177–192 (1970)

    Article  MathSciNet  Google Scholar 

  19. Stockmeyer, L.J.: The polynomial-time hierarchy. Theoretical Computer Science 3(1), 1–22 (1976)

    Article  MathSciNet  Google Scholar 

  20. Szelepcsényi, R.: The method of forced enumeration for nondeterministic automata. Acta Informatica 26(3), 279–284 (1988)

    Article  MathSciNet  Google Scholar 

  21. Trakhtenbrot, B.A.: Impossibility of an algorithm for the decision problem in finite classes. Doklady Akademii Nauk SSSR 70, 569–572 (1950), (In Russian; English translation: AMS Translations, Series 2, 23:1–5, 1963.)

    MATH  Google Scholar 

  22. Vardi, M.Y.: Complexity of relational query languages. In: Proceedings of 14th ACM Symposium on Theory of Computing, pp. 137–146. ACM Press, New York (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Cambridge Computer Laboratory, William Gates Building, J.J. Thomson Avenue, Cambridge, CB3 0FD, UK

    David Richerby

Authors
  1. David Richerby
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Wroclaw University, Poland

    Jerzy Marcinkowski

  2. Polish Academy of Sciences, Institute of Computer Science, Poland

    Andrzej Tarlecki

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Richerby, D. (2004). Logical Characterizations of PSPACE. In: Marcinkowski, J., Tarlecki, A. (eds) Computer Science Logic. CSL 2004. Lecture Notes in Computer Science, vol 3210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30124-0_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30124-0_29

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23024-3

  • Online ISBN: 978-3-540-30124-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation