Matching Modulo Associativity and Idempotency Is NP—Complete

Abstract

Abstract. We show that AI-matching (AI denotes the theory of an associative and idempotent function symbol), which is solving matching word equations in free idempotent semigroups, is NP-complete. Note: full version of the paper appears as [8].

The complexity of the equivalence and equation solvability problems over nilpotent rings and groups

“…For recent results and detailed references see e.g. [1], [12], [13], [14], [17], [18], [21]. Although the literature is fairly extensive for monoids, the equivalence and equation solvability problems even for the simplest case, the case of nite groups, proved to be a far more challenging topic than for nite rings.…”

The complexity of the equivalence and equation solvability problems over meta-Abelian groups

“…[8,9,10]) or for nite semigroups and monoids (e.g. [2,6,20,21,22,23,24,29,31,33]). Just to mention some of the most recent results: following up on [2], Klíma nished the characterization for the transformation monoids [24], or Gorazd and Krzaczkowski characterized the complexity of these problems for all two-element general algebras [9,10].…”

Matching Modulo Associativity and Idempotency is NP-Complete

“…We show that AI-matching (AI denotes the theory of an associative and idempotent function symbol), which is solving matching word equations in free idempotent semigroups, is NP-complete. Note: this is a full version of the paper [9] and a revision of [8]. …”