On equality up-to constraints over finite trees, context unification, and one-step rewriting

  • Joachim Niehren
  • Manfred Pinkal
  • Peter Ruhrberg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1249)


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 ∃*∀*∃* fragment of the theory of context unification is undecidable.


tree constraints subtree relation string unification context unification linear second-order unification one-step rewriting semantic processing of natural language 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Joachim Niehren
    • 1
  • Manfred Pinkal
    • 2
  • Peter Ruhrberg
    • 2
  1. 1.Programming Systems LabGermany
  2. 2.Department of Computational LinguisticsUniversität des SaarlandesSaarbrückenGermany

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