Finite model search for equational theories (FMSET)

  • Belaid Benhamou
  • Laurent Henocque
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1476)


Finite model and counter model generation is a potential alternative in automated theorem proving. In this paper, we introduce a system called FMSET which generates finite structures representing models of equational theories. FMSET performs a satisfiability test over a set of special first order clauses called ≓simple clauses≓. Several experiments over a variety of problems have been pursued. FMSET uses symmetries to prune the search space from isomorphic branches with very competitive performances in the domain.


Computer Algebra Systems and Automated Theorem Provers 


Finite model equational theories symmetry 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Slaney M. Fujita and F. Bennett. Automatic generation of some results in finite algebra. In proceedings of the 13th Internationnal Joint Conference on Artificial Intelligence, Chambery, France, pages 52–57, 1993.Google Scholar
  2. 2.
    W. McCune. A Davis Putnam program and its application to finite fist order model search: quasi-group existence problems. Technical Report ANL/MCS-TM-1994, Argonne National Laboratory, 1994.Google Scholar
  3. 3.
    J. Slaney. Finder: Finite domain enumerator, version 3.0 notes and guide. Technical report, Austrian National University, 1993.Google Scholar
  4. 4.
    H. Zhang and M. Stickel. Implementing the Davis and Putnam algorithm by tries. Technical report, University of IOWA, 1994.Google Scholar
  5. 5.
    J. Zhang. Problems on the generation of finite models. in proceedings of CADE-12, Nancy, France, pages 753–757, 1994.Google Scholar
  6. 6.
    J. Zhang. Constructing finite algebras with FALCON. Journal of automated reasoning, 17, pages 1–22, 1996.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Belaid Benhamou
    • 1
  • Laurent Henocque
    • 1
  1. 1.Laboratoire d’Informatique de MarseilleCentre de Mathématiques et d’InformatiqueMarseille cedex 13France

Personalised recommendations