Confluence of Prefix-Constrained Rewrite Systems

Authors Nirina Andrianarivelo, Pierre Réty

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Nirina Andrianarivelo
  • LIFO - Université d'Orléans, B.P. 6759, 45067 Orléans cedex 2, France
Pierre Réty
  • LIFO - Université d'Orléans, B.P. 6759, 45067 Orléans cedex 2, France

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Nirina Andrianarivelo and Pierre Réty. Confluence of Prefix-Constrained Rewrite Systems. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Prefix-constrained rewriting is a strict extension of context-sensitive rewriting. We study the confluence of prefix-constrained rewrite systems, which are composed of rules of the form L: l -> r where L is a regular string language that defines the allowed rewritable positions. The usual notion of Knuth-Bendix's critical pair needs to be extended using regular string languages, and the convergence of all critical pairs is not enough to ensure local confluence. Thanks to an additional restriction we get local confluence, and then confluence for terminating systems, which makes the word problem decidable. Moreover we present an extended Knuth-Bendix completion procedure, to transform a non-confluent prefix-constrained rewrite system into a confluent one.

Subject Classification

ACM Subject Classification
  • Theory of computation → Rewrite systems
  • prefix-constrained term rewriting
  • confluence
  • critical pair


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