On the complexity of equational problems in CNF

AbstractEquational problems (i.e. first-order formulae with quantifier prefix ∃∗∀∗, whose only predicate symbol is syntactic equality) are an important tool in many areas of automated deduction, e.g. restricting the set of ground instances of a clause via equational constraints allows the definition of stronger redundancy criteria and hence, in general, of more efficient theorem provers. Moreover, the inference rules themselves can be restricted via constraints. In automated model building, equational problems play an important role both in the definition of an appropriate model representation and in the evaluation of clauses in such models. Also, many problems in the area of logic programming can be reduced to equational problem solving. Finally, equational problems over a finite domain correspond to the evaluation of certain queries over relational databases.The goal of this work is a complexity analysis of the satisfiability problem of equational problems. The main results will be a proof of the NP-completeness (and, in particular, the NP-membership) of equational problems in CNF over an infinite domain and of the Σ2p-completeness in the case of CNF over a finite domain