Technical Reports (CIS)

Rigid E-Unification: NP-Completeness and Applications to Equational Matings

Jean H. Gallier, University of Pennsylvania
Paliath Narendran, University of Calgary
David Plaisted, University of North Carolina
Wayne Snyder, Boston University

Document Type Technical Report

University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-88-14.

Abstract

Rigid E-unification is a restricted kind of unification modulo equational theories, or E-unification, that arises naturally in extending Andrews's theorem proving method of matings to first-order languages with equality. This extension was first presented in Gallier, Raatz, and Snyder, where it was conjectured that rigid E-unification is decidable. In this paper, it is shown that rigid E-unification is NP-complete and that finite complete sets of rigid E-unifiers always exist. As a consequence, deciding whether a family of mated sets is an equational mating is an NP-complete problem. Some implications of this result regarding the complexity of theorem proving in first-order logic with equality are also discussed.

 

Date Posted: 25 September 2007