Theorem proving using equational matings and rigid E-unification

  • Authors:

  • Jean Gallier;Paliath Narendran;Stan Raatz;Wayne Snyder

  • Affiliations:

  • -;-;-;-

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1992

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Abstract

In this paper, it is shown that the method of matings due toAndrews and Bibel can be extended to (first-order) languages withequality. A decidable version ofE-unification calledrigid E-unification is introduced,and it is shown that the method of equational matings remains completewhen used in conjunction with rigidE-unification. Checking that a familyof mated sets is an equational mating is equivalent to the followingrestricted kind ofE-unification.Problem Given E&ar;=Ei∣1≤i≤n a family of nfinite sets of equations and S=ui,vi∣1≤i≤n a set of n pairsof terms, is there a substitution q such that, treating each set qEi as a set of groundequations (i.e., holding the variables in qEi “rigid”), qui, and qvi are provably equal from qEi for i=1,...,n?Equivalently, is there a substitution q such that qui and qvi can be shown congruent from qEi by the congruence closure method fori=1,...,n?A substitution q solving the above problem is called arigid E&ar;-unifier of S, anda pair E&ar;,S such that S hassome rigid E&ar;-unifier is called an equationalpremating. It is show that deciding whether a pairE&ar;,S is an equational premating is an NP-completeproblem.