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Journal of Automated Reasoning

, Volume 23, Issue 2, pp 107–136 | Cite as

Computational Complexity of Simultaneous Elementary Matching Problems

  • Miki Hermann
  • Phokion G. Kolaitis
Article

Abstract

The simultaneous elementary E-matching problem for an equational theory E is to decide whether there is an E-matcher for a given system of equations in which the only nonconstant function symbols occurring in the terms to be matched are the ones constrained by the equational axioms of E. We study the computational complexity of simultaneous elementary matching problems for the equational theories A of semigroups, AC of commutative semigroups, and ACU of commutative monoids. In each case, we delineate the boundary between NP-completeness and solvability in polynomial time by considering two parameters, the number of equations in the systems and the number of constant symbols in the signature. Moreover, we analyze further the intractable cases of simultaneous elementary AC-matching and ACU-matching by also taking into account the maximum number of occurrences of each variable. Using combinatorial optimization techniques, we show that if each variable is restricted to having at most two occurrences, then several cases of simultaneous elementary AC-matching and ACU-matching can be solved in polynomial time.

automated deduction equational matching associative-commutative matching Diophantine equations computational complexity NP-completeness #P-completeness 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Miki Hermann
    • 1
  • Phokion G. Kolaitis
    • 2
  1. 1.LORIA (CNRS)Vandœuvre-lès-NancyFrance
  2. 2.Computer Science DepartmentUniversity of CaliforniaSanta CruzU.S.A

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