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Regular expression order-sorted unification and matching.

Temur Kutsia1, Mircea Marin2

  • 1RISC, Johannes Kepler University Linz, Austria.

Journal of Symbolic Computation
|November 3, 2015
PubMed
Summary
This summary is machine-generated.

We introduce regular expression order-sorted (REOS) unification, a decidable and infinitary unification type. This new method generalizes existing unification problems and enhances sequence unification with regular constraints.

Keywords:
MatchingOrdered-sortsRegular expressionsUnification

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Area of Science:

  • Theoretical Computer Science
  • Automata Theory
  • Formal Languages

Background:

  • Order-sorted unification is a fundamental concept in automated reasoning and logic programming.
  • Existing unification methods often lack expressiveness for complex constraints.
  • Regular tree automata and sequence unification have been studied independently.

Purpose of the Study:

  • To extend order-sorted unification by incorporating regular expression sorts.
  • To establish the decidability and type of this new unification problem.
  • To generalize and unify existing unification and matching problems.

Main Methods:

  • Introducing regular expression sorts for variables and function symbols.
  • Establishing a connection between REOS unification and finite bottom-up unranked tree automata.
  • Developing a sort weakening algorithm for constructing unifiers.
  • Designing a complete algorithm for REOS matching.

Main Results:

  • Regular expression order-sorted (REOS) unification is proven to be infinitary and decidable.
  • REOS unification generalizes order-sorted unification, sequence unification, and word unification with regular constraints.
  • The decidability of REOS unification implies decidability for sequence unification with regular hedge language constraints.
  • REOS matching is shown to be NP-complete, and the counting problem is #P-complete.

Conclusions:

  • REOS unification offers a more expressive and powerful framework for symbolic computation.
  • The decidability results have significant implications for automated reasoning and constraint solving.
  • The generalization of existing problems provides a unified perspective on unification research.