Dauchet, Max

Heuillard, Thierry

Lescanne, Pierre

Tison, Sophie

The aim of this paper is to propose a simple algorithm to decide the confluence of ground term rewriting systems. This algorithm is derived from decidability results presented in (1). Here a simple view of the problem and its solution is proposed. Let us recall that a ground term rewriting system is a term rewriting system where each rule is a pair of ground terms, i.e., a pair of terms without variables. Recall the confluence is not decidable for general term rewriting systems, but this paper proves it is for ground term rewriting systems following a conjecture made by Huet and Oppen (3) in their survey. We also sketch a simple algorithm for checking this property. This algorithm is based on tree automata and tree transducers. Here, we regard them as rewriting systems and specialists in automata theory would translate that easily in their language. In the second part of this paper, a new class of tree transducers is introduced : ground tree transducers, GTT in short. In the third part, stability of GTT relation w.r.t inverse, composition, iteration and precongruence closure of union is proved. In the fourth part, each ground term rewriting system is associated with a GTT and the confluence of ground term rewriting system is reduced to the inclusion of GTT relations. Part 5 solves the decision problem by encoding GTT into rational tree languages

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HAL Id: inria-00075878https://hal.inria.fr/inria-00075878Submitted on 24 May 2006HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Decidability of the confluence of ground term rewritingsystemsPierre Lescanne, Thierry Heuillard, Max Dauchet, Sophie TisonTo cite this version:Pierre Lescanne, Thierry Heuillard, Max Dauchet, Sophie Tison. Decidability of the confluence ofground term rewriting systems. [Research Report] RR-0675, INRIA. 1987. ￿inria-00075878￿

Decidability of the Confluence of Ground Term Rewriting Systems.

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