Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Computer Science Logic

CSL 1991: Computer Science Logic pp 68–78Cite as

How to implement first order formulas in local memory machine models

  • Conference paper
  • First Online:

  • 135 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 626))

Abstract

The paper indicates how the validity of a fixed first order formula in any finite structure can be checked by realistic local memory parallel computers.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. Abolhassan, J. Keller, W. Paul: On physical realizations of the theoretical PRAM model, Technical Report # 21/90, Sonderforschungsbereich 124 — VLSI-Entwurfsmethoden und Parallelität, University of Saarbrücken.

    Google Scholar 

  2. , S. Akl: The design and analysis of parallel algorithms, Prentice Hall, Englewood Cliffs, New Jersey, 1989

    Google Scholar 

  3. B. Awerbuch, A. Israeli, Y. Shiloach: Efficient simulation of PRAM by ultracomputer, preprint, Technion-Israel Institute of Technology, 1983.

    Google Scholar 

  4. B. Awerbuch, Y. Shiloach: New connectivity and MSF algorithms for shuffle exchange network and PRAM, IEEE-Transactions on Computing C-36 (1987), pp. 1258–1263.

    Google Scholar 

  5. K. Batcher: Sorting networks and their applications, Proceedings of the AFIPS 1968, Atlanta City, New jersey, pp. 307–314.

    Google Scholar 

  6. Y. Chin, Y. Lam, I. Chen: Efficient parallel algorithms for some graph problems, Communication of the ACM 25 (1982), pp. 659–665.

    Google Scholar 

  7. S. Cook: A taxonomy of problems with fast parallel algorithms, Information and Control 64 (1985), pp. 2–22.

    Google Scholar 

  8. R. Cypher, G. Plaxton: Deterministic sorting in nearly logarithmic time on a hypercube and related computers, 2n d ACM-STOC (1990), pp. 193–203.

    Google Scholar 

  9. R. Fagin: Generalized first order spectra and polynomial time recognizable sets, in ”Complexity of Computations” (R. Karp ed.), SIAM-AMS-proceedings 7 (1974), pp.27–41.

    Google Scholar 

  10. S. Fortune, J. Wyllie: Parallelism in random access machines, 10th ACM-STOC (1978), pp. 114–118.

    Google Scholar 

  11. A. Gibbons, W. Rytter: Efficient Parallel Algorithms, Cambridge University Press, Cambridge, 1989.

    Google Scholar 

  12. N. Immerman: Languages which capture complexity classes, 15th ACM-STOC (1983) pp. 347–354.

    Google Scholar 

  13. N. Immerman: Expressibility and parallel complexity, SIAM-Journal on Computing 18 (1989), pp. 625–638.

    Google Scholar 

  14. N. Jones, A. Selman: Turing machines and spectra of first order formulas, Journal of Symbolic Logic 39 (1974), pp. 139–150.

    Google Scholar 

  15. R. Miller, Q. Stout: Graph and image processing algorithms for hypercube, Proceedings 1986 SIAM Conference on Hypercube Multiprocessors (1987), pp. 418–425.

    Google Scholar 

  16. A. Ranade: How to emulate shared memory, IEEE-FOCS 1987, pp.185–194.

    Google Scholar 

  17. D. Rödding, H. Schwichtenberg: Bemerkungen zum Spektralproblem, Zeitschrift für Mathematische Logik 18 (1972), pp. 1–12.

    Google Scholar 

  18. E. Upfal: An O(log N) deterministic packet routing scheme, 21st ACM-STOC (1989), pp. 241–250.

    Google Scholar 

Download references

Author information

Author notes

  1. Elias Dahlhaus

    Present address: Basser Department of Computer Science, University of Sydney, 2006, NSW, Australia

Authors and Affiliations

  1. Department of Computer Science, University of Bonn, Römerstrasse 164, D-5300, Bonn 1

    Elias Dahlhaus

Authors
  1. Elias Dahlhaus
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Egon Börger Gerhard Jäger Hans Kleine Büning Michael M. Richter

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dahlhaus, E. (1992). How to implement first order formulas in local memory machine models. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023758

Download citation

  • DOI: https://doi.org/10.1007/BFb0023758

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55789-0

  • Online ISBN: 978-3-540-47285-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation