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Combined Hierarchical Matching: the Regular Case

Authors Serdar Erbatur , Andrew M. Marshall , Christophe Ringeissen



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Author Details

Serdar Erbatur
  • University of Texas at Dallas, TX, USA
Andrew M. Marshall
  • University of Mary Washington, Fredericksburg, VA, USA
Christophe Ringeissen
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France

Acknowledgements

We would like to thank the reviewers for their comments that were very helpful to improve the readability of the paper.

Cite AsGet BibTex

Serdar Erbatur, Andrew M. Marshall, and Christophe Ringeissen. Combined Hierarchical Matching: the Regular Case. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 6:1-6:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.FSCD.2022.6

Abstract

Matching algorithms are often central sub-routines in many areas of automated reasoning. They are used in areas such as functional programming, rule-based programming, automated theorem proving, and the symbolic analysis of security protocols. Matching is related to unification but provides a somewhat simplified problem. Thus, in some cases, we can obtain a matching algorithm even if the unification problem is undecidable. In this paper we consider a hierarchical approach to constructing matching algorithms. The hierarchical method has been successful for developing unification algorithms for theories defined over a constructor sub-theory. We show how the approach can be extended to matching problems which allows for the development, in a modular way, of hierarchical matching algorithms. Here we focus on regular theories, where both sides of each equational axiom have the same set of variables. We show that the combination of two hierarchical matching algorithms leads to a hierarchical matching algorithm for the union of regular theories sharing only a common constructor sub-theory.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
  • Theory of computation → Automated reasoning
Keywords
  • Matching
  • combination problem
  • equational theories

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