Unification and Matching Modulo Leaf-Permutative Equational Presentations

Authors:
Thierry Boy De La Tour;Mnacho Echenim;Paliath Narendran
Affiliations:
CNRS/INPG - Laboratoire d'Informatique de Grenoble, France;CNRS/INPG - Laboratoire d'Informatique de Grenoble, France;Department of Computer Science, University at Albany -- SUNY, Albany, U. S. A. NY 12222
Venue:
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Year:
2008

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Abstract

Unification modulo variable-permuting equational presentations is known to be undecidable. We address here the problem of the existence of a unification algorithm for the class of linearvariable-permuting presentations, also known as leaf-permutativepresentations. We show that there is none, by exhibiting a leaf-permutative presentation whose unification problem is undecidable. We also exhibit one such presentation whose word and pattern matching problems are PSPACE-complete. The proof proceeds in three stages, by transforming length-preserving string-rewriting systems into atomic, then into bit-swappingstring-rewriting systems, and finally into leaf-permutative presentations.