NP-Completeness Results for Deductive Problems on Stratified Terms

In [1] Avenhaus and Plaisted proposed the notion of stratified terms, in order to represent concisely the sets of consequences of clauses under leaf permutative theories. These theories contain variablepermuting equations, so that the consequences appear as simple “permuted” variants of each other. Deducing directly with stratified terms can reduce exponentially the search space, but we show that the problems involved (e.g. unifiability) are NP-complete. We use computational group theory to show membership in NP, while NP-hardness is obtained through an interesting problem in group theory.