Equation Satisfiability and Program Satisfiability for Finite Monoids

  • David Mix Barrington
  • Pierre McKenzie
  • Cris Moore
  • Pascal Tesson
  • Denis Thérien
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1893)


We study the computational complexity of solving equations and of determining the satisfiability of programs over a fixed finite monoid. We partially answer an open problem of [4] by exhibiting quasi-polynomial time algorithms for a subclass of solvable non-nilpotent groups and relate this question to a natural circuit complexity conjecture. In the special case when M is aperiodic, we show that PROGRAM SATISFIABILITY is in P when the monoid belongs to the variety DA and is NP-complete otherwise. In contrast, we give an example of an aperiodic outside DA for which EQUATION SATISFIABILITY is computable in polynomial time and discuss the relative complexity of the two problems. We also study the closure properties of classes for which these problems belong to P and the extent to which these fail to form algebraic varieties.


Polynomial Time Nilpotent Group Homomorphic Image Solvable Group Wreath Product 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • David Mix Barrington
    • 1
  • Pierre McKenzie
    • 2
  • Cris Moore
    • 3
  • Pascal Tesson
    • 4
  • Denis Thérien
    • 4
  1. 1.Dept. of Computer ScienceUniversity of MassachussetsUSA
  2. 2.Dept. d’Informatique et de Recherche OpérationnelleUniversité de MontréalMontréalCanada
  3. 3.Dept. of Computer ScienceUniversity of New MexicoUSA
  4. 4.School of Computer ScienceMcGill UniversityUSA

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