Computational Complexity of Simultaneous Elementary Matching Problems - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Automated Reasoning Année : 1999

Computational Complexity of Simultaneous Elementary Matching Problems

Résumé

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 non-constant 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 taking also 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.
Fichier non déposé

Dates et versions

inria-00098986 , version 1 (26-09-2006)

Identifiants

  • HAL Id : inria-00098986 , version 1

Citer

Miki Hermann, Phokion G. Kolaitis. Computational Complexity of Simultaneous Elementary Matching Problems. Journal of Automated Reasoning, 1999, 23 (2), pp.107-136. ⟨inria-00098986⟩
65 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More