Advertisement

Paths to high-performance automated theorem proving

  • Ralph Butler
  • Ewing Lusk
  • William McCune
  • Ross Overbeek
Logic Programming Oriented Deduction Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)

Abstract

We present four components of a strategy for the implementation of high-performance automated theorem proving systems. These are 1) clause compilation, 2) multiprocessing, 3) database indexing, and 4) clause-set "compaction". We describe each of these techniques and show how they can be integrated into a coherent system with significantly higher performance than traditional systems. The strategy described has been implemented, and we present results showing the effects of these techniques on Sam's Lemma, a relatively difficult theorem-proving problem.

Keywords

Theorem Prove Argonne National Laboratory Automate Theorem Prove Unit Clause Automate Deduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Gabriel, T. Lindholm, E. Lusk, and R. A. Overbeek, “A tutorial on the Warren abstract machine,” Technical Report ANL-84-84, Argonne National Laboratory, Argonne, Illinois (October, 1984).Google Scholar
  2. 2.
    J. Gabriel, T. Lindholm, E. L. Lusk, and R. A. Overbeek, “Logic Programming on the HEP,” in Parallel MIMD Computation: The HEP Supercomputer and its Applications, ed. J. S. Kowalik, The MIT Press (1985).Google Scholar
  3. 3.
    Steven Gregory, Design, application and implementation of a parallel logic programming language, Doctoral Thesis, Imperial College of Science and Technology, London, September 1985.Google Scholar
  4. 4.
    E. Lusk, William McCune, and R. Overbeek, “Logic machine architecture: kernel functions,” pp. 70–84 in Proceedings of the Sixth Conference on Automated Deduction, Springer-Verlag Lecture Notes in Computer Science, Vol. 138, ed. D. W. Loveland, Springer-Verlag, New York (1982).Google Scholar
  5. 5.
    E. Lusk, William McCune, and R. Overbeek, “Logic machine architecture: inference mechanisms,” pp. 85–108 in Proceedings of the Sixth Conference on Automated Deduction, Springer-Verlag Lecture Notes in Computer Science, Vol. 138, ed. D. W. Loveland, Springer-Verlag, New York (1982).Google Scholar
  6. 6.
    Ewing L. Lusk and Ross A. Overbeek, “Implementation of Monitors with Macros: A Programming Aid for the HEP and Other Parallel Processors,” Technical Report ANL-83-97, Argonne National Laboratory, Argonne, Illinois (December 1983).Google Scholar
  7. 7.
    Ewing L. Lusk and Ross A. Overbeek, “A Portable Environment for Research in Automated Reasoning,” pp. 43–52 in Proceedings of the 7th International Conference on Automated Deduction, Springer-Verlag Lecture Notes in Computer Science, Vol. 170, ed. R. E. Shostak, Springer-Verlag, New York (1984).Google Scholar
  8. 8.
    E. L. Lusk, R. L. Stevens, and R. A. Overbeek, “A tutorial on the use of monitors in C: writing portable code for multiprocessors,” ANL-85-2, Argonne National Laboratory (January 1985).Google Scholar
  9. 9.
    J. McCharen, R. Overbeek, and L. Wos, “Problems and experiments for and with automated theoremproving programs,” IEEE Transactions on Computers C-25(8), pp. 773–782 (1976).Google Scholar
  10. 10.
    R. Overbeek, “An implementation of hyper-resolution,” Computers and Mathematics with Applications 1, pp. 201–214 (1975).CrossRefGoogle Scholar
  11. 11.
    D. H. D. Warren, “Implementing Prolog — compiling predicate logic programs,” DAI Research Reports 39 and 40, University of Edinburgh (May 1977).Google Scholar
  12. 12.
    D. H. D. Warren, “An Abstract Prolog Instruction Set,” SRI Technical Note 309, SRI International (October 1983).Google Scholar
  13. 13.
    D. H. D. Warren, “Applied logic — its use and implementation as a programming tool,” SRI International Technical Note 290 (June 1983). University of Edinburgh Ph.D. thesis, 1977Google Scholar
  14. 14.
    M. J. Wise and D. M. W. Powers, “Indexing Prolog Clauses via Superimposed Code Words and Field Encoded Words,” Proceedings of the 1984 International Symposium on Logic Programming, Atlantic City, pp. 203–211 (February, 1984).Google Scholar
  15. 15.
    L. Wos, S. Winker, and E. Lusk, “An automated reasoning system,” Proceedings of the AFIPS National Computer Conference, pp. 697–702Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Ralph Butler
    • 1
  • Ewing Lusk
    • 1
  • William McCune
    • 1
  • Ross Overbeek
    • 1
  1. 1.Mathematics and Computer Science DivisionArgonne National LaboratoryArgonne

Personalised recommendations