On Equality Up-to Constraints over Finite Trees, Context Unification and One-Step Rewriting

Author: Joachim Niehren and Manfred Pinkal and Peter Ruhrberg

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We introduce equality up-to constraints over finite trees and investigate their expressiveness. Equality up-to constraints subsume equality constraints, subtree constraints, and one-step rewriting constraints. We establish a close correspondence between equality up-to constraints over finite trees and context unification. Context unification subsumes string unification and is subsumed by linear second-order unification. We obtain the following three new results. The satisfiability problem of equality up-to constraints is equivalent to context unification, which is an open problem. The positive existential fragment of the theory of one-step rewriting is decidable. The $\exists^*\forall^*\exists^*$ fragment of the theory of context unification is undecidable.