Polynomial Equivalence of the Problems “Predicate Formulas Isomorphism and Graph Isomorphism”

Abstract

The problem of isomorphism checking of two elementary conjunctions of predicate formulas is considered in this work. Such a problem appears while solving some Artificial Intelligence problems, admitting formalization by means of predicate calculus language. The exact definition of the concept of isomorphism of such formulas is given in this paper. However, isomorphic elementary conjunctions of predicate formulas are formulas that, with some substitution of variables instead of their arguments, coincide with the accuracy of the order of writing literals. Problems are described that, when solved, mean the necessity of testing formulas for isomorphism arises. Polynomial equivalence of this problem with the Graph Isomorphism (GI) problem is proved.