Handling Left-Quadratic Rules When Completing Tree Automata

Authors:
Y. Boichut;R. Courbis;P. -C. Héam;O. Kouchnarenko
Affiliations:
INRIA/PAREO, 615 rue du Jardin Botanique BP-101 F-54602 Villers-Lès Nancy Cedex;INRIA/CASSIS and LIFC / University of Franche-Comté 16 route de Gray F-25030 Besançon Cedex;INRIA/CASSIS and LIFC / University of Franche-Comté 16 route de Gray F-25030 Besançon Cedex;INRIA/CASSIS and LIFC / University of Franche-Comté 16 route de Gray F-25030 Besançon Cedex
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2008

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Abstract

This paper addresses the following general problem of tree regular model-checking: decide whether R^*(L)@?L"p=@A where R^* is the reflexive and transitive closure of a successor relation induced by a term rewriting system R, and L and L"p are both regular tree languages. We develop an automatic approximation-based technique to handle this - undecidable in general - problem in the case when term rewriting system rules are left-quadratic. The most common practical case is handled this way.