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Axiomatization of Finite Algebras

  • Jochen Burghardt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2479)

Abstract

We show that the set of all formulas in n variables valid in a finite class A of finite algebras is always a regular tree language, and compute a finite axiom set for A. We give a rational reconstruction of Barzdins’ liquid flow algorithm [BB91]. We show a sufficient condition for the existence of a class A of prototype algebras for a given theory Θ. Such a set allows us to prove Θ⊨φ simply by testing whether ϕ holds in A.

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References

  1. [AM91]
    A. Aiken and B. Murphy. Implementing regular tree expressions. In ACM Conference on Functional Programming Languages and Computer Architecture, pages 427–447, August 1991.Google Scholar
  2. [BB91]
    J.M. Barzdin and G.J. Barzdin. Rapid construction of algebraic axioms from samples. Theoretical Computer Science, 90:199–208, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [BH96]
    Jochen Burghardt and Birgit Heinz. Implementing anti-unification modulo equational theory. Arbeitspapier 1006, GMD, Jun 1996.Google Scholar
  4. [Bur02]
    Jochen Burghardt. Axiomatization of finite algebras. Arbeitspapier, GMD, 2002. forthcoming.Google Scholar
  5. [CDG+99]
    H. Comon, M. Dauchet, R. Gilleron, F. Jacquemard, D. Lugiez, S. Tison, and M. Tommasi. Tree Automata Techniques and Applications. WWW, Available from http://www.grappa.univ-lille3.fr/tata, Oct 1999.
  6. [DJ90]
    N. Dershowitz and J.-P. Jouannaud. Rewrite Systems, volume B of Handbook of Theoretical Computer Science, pages 243–320. Elsevier, 1990.Google Scholar
  7. [Gra94]
    Peter Graf. Substitution tree indexing. Technical Report MPI-I-94-251, Max-Planck-Institut für Informatik, Saarbrücken, Oct 1994.Google Scholar
  8. [McA92]
    David McAllester. Grammar rewriting. In Proc. CADE-11, volume 607 of LNAI. Springer, 1992.Google Scholar
  9. [MT92]
    K. Meinke and J.V. Tucker. Universal Algebra, volume 1 of Handbook of Logic in Computer Science. Clarendon, Oxford, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jochen Burghardt
    • 1
  1. 1.GMD FIRSTBerlin

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