Advertisement

Automatic Synthesis of Decision Procedures: A Case Study of Ground and Linear Arithmetic

  • Predrag Janičić
  • Alan Bundy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4573)

Abstract

We address the problem of automatic synthesis of decision procedures. Our synthesis mechanism consists of several stages and sub-mechanisms and is well-suited to the proof-planning paradigm. The system (adeptus), that we present in this paper, synthesised a decision procedure for ground arithmetic completely automatically and it used some specific method generators in generating a decision procedure for linear arithmetic, in only a few seconds of cpu time. We believe that this approach can lead to automated assistance in constructing decision procedures and to more reliable implementations of decision procedures.

Keywords

Decision Procedure Output Class Disjunctive Normal Form Language Construct Automatic Synthesis 
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.
    Armando, A., Ranise, S., Rusinowitch, M.: Uniform Derivation of Decision Procedures by Superposition. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Boyer, R.S., Moore, J.S.: Integrating Decision Procedures into Heuristic Theorem Provers: A Case Study of Linear Arithmetic. Machine Intelligence 11 (1988)Google Scholar
  3. 3.
    Bundy, A.: The Use of Explicit Plans to Guide Inductive Proofs. In: Lusk, R., Overbeek, R. (eds.) 9th Conference on Automated Deduction (1988)Google Scholar
  4. 4.
    Bundy, A.: The Use of Proof Plans for Normalization. In: Boyer, R.S. (ed.) Essays in Honor of Woody Bledsoe (1991)Google Scholar
  5. 5.
    Hodes, L.: Solving Problems by Formula Manipulation in Logic and Linear Inequalities. In: ProcIJCAI-71 (1971)Google Scholar
  6. 6.
    Jamnik, M., Kerber, M., Pollet, M., Benzmuller, C.: Automatic Learning of Proof Methods in Proof Planning. CSRP-02-5, University of Birmingham (2002)Google Scholar
  7. 7.
    Janičić, P., Bundy, A.: A General Setting for the Flexible Combining and Augmenting Decision Procedures. Journal of Automated Reasoning 28(3) (2002)Google Scholar
  8. 8.
    Knuth, D.E., Bendix, P.B.: Simple word problems in universal algebra. In: Leech, J. (ed.) Computational problems in abstract algebra, Pergamon Press, New York (1970)Google Scholar
  9. 9.
    Lassez, J.-L., Maher, M.: On Fourier’s algorithm for linear arithmetic constraints. Journal of Automated Reasoning 9, 373–379 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Socher-Ambosius, R.: Boolean algebra admits no convergent rewriting system. In: Book, R.V. (ed.) Rewriting Techniques and Applications. LNCS, vol. 488, Springer, Heidelberg (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Predrag Janičić
    • 1
  • Alan Bundy
    • 2
  1. 1.Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 BelgradeSerbia
  2. 2.School of Informatics, University of Edinburgh, Appleton Tower, Crichton St, Edinburgh EH8 9LEUK

Personalised recommendations