Abstract
We present in this paper an application of the ACL2 system to reason about propositional satisfiability provers. For that purpose, we present a framework where we define a generic transformation based SAT-prover, and we show how this generic framework can be formalized in the ACL2 logic, making a formal proof of its termination, soundness and completeness. This generic framework can be instantiated to obtain a number of verified and executable SAT-provers in ACL2, and this can be done in an automatized way. Three case studies are considered: semantic tableaux, sequent and Davis-Putnam methods.
This work has been supported by project TIC2000-1368-C03-02 (Ministry of Science and Technology, Spain)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Aguilera, I.P. de Guzman, M. Ojeda-Aciego and A. Valverde. Reductions for non-clausal theorem proving. Theoretical Computer Science 266, pages 81–112. Elsevier, 2001.
M. Bezem. Completeness of resolution revisited. Theoretical Computer Science 74, no. 2, pages 227–237, 1990.
R. S. Boyer and J S. Moore. A Computational Logic. Academic Press, 1979.
J. Caldwell. Decidability Extracted: Synthesizing “Correct-by-Construction” Decision Procedures from Constuctive Proofs. PhD thesis, Cornell University, 1998
N. Dershowitz and Z. Manna. Proving Termination with Multiset Orderings. In Proceedings of the Sixth International Colloquium on Automata, Languages and Programming, LNCS 71, pages 188–202. Springer-Verlag, 1979.
M.C. Fitting. First-Order Logic and Automated Theorem Proving. Springer-Verlag, New York, 1990.
J.H. Gallier. Logic for Computer Science, Foundations of Automatic Theorem Proving. Harper and Row Publishers, 1986.
M. Kaufmann, P. Manolios, and J S. Moore. Computer-Aided Reasoning: An Approach. Kluwer Academic Publishers, 2000.
F.J. Martin-Mateos, J.A. Alonso, M.J. Hidalgo, and J.L. Ruiz-Reina. A Generic Instantiation Tool and a Case Study: A Generic Multiset Theory, 2002.
F.J. Martin-Mateos. Teoria computacional (en ACL2) sobre calculos proposicionales. PhD thesis, University of Seville, 2002.
J.L. Ruiz-Reina. Una teoria computacional acerca de la logica ecuacional. PhD thesis, University of Seville, 2001.
J.L. Ruiz-Reina, J.A. Alonso, M.J. Hidalgo, and F.J. Martin. Multiset Relations: a Tool for Proving Termination. In Second ACL2 Workshop, Technical Report TR-00-29, Computer Science Departament, University of Texas, 2000.
J.L. Ruiz-Reina, J.A. Alonso, M.J. Hidalgo, and F.J. Martin. Mechanical verification of a rule-based unification algorithm in the Boyer-Moore theorem prover. In Proceedings AGP’99, Joint Conference on Declarative Programming, L’Aquila (Italia), 1999.
R.M. Smullyan. First-Order Logic. Springer-Verlag: Heidelberg, Germany, 1968.
H. Zhang and M.E. Stickel. Implementing the Davis-Putnam method Journal of Automated Reasoning, 24(1–2):277–296, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Martín-Mateos, F.J., Alonso, J.A., Hidalgo, M.J., Ruiz-Reina, J.L. (2003). Verification in ACL2 of a Generic Framework to Synthesize SAT-Provers. In: Leuschel, M. (eds) Logic Based Program Synthesis and Transformation. LOPSTR 2002. Lecture Notes in Computer Science, vol 2664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45013-0_15
Download citation
DOI: https://doi.org/10.1007/3-540-45013-0_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40438-5
Online ISBN: 978-3-540-45013-9
eBook Packages: Springer Book Archive