Abstract
Equational formulae are first-order formulae over an alphabet F of function symbols whose only predicate symbol is syntactic equality. Unification problems are an important special case of equational formulae, where no universal quantifiers and no negation occur. By the negation elimination problem we mean the problem of deciding whether a given equational formula is semantically equivalent to a unification problem. This decision problem has many interesting applications in machine learning, logic programming, functional programming, constrained rewriting, etc. In this work we present a new algorithm for the negation elimination problem of equational formulae with purely existential quantifier prefix. Moreover, we prove the coNP-completeness for equational formulae in DNF and the Π2p-hardness in case of CNF.
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