Ground Reducibility is EXPTIME-complete

Hubert Comon Florent Jacquemard 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We prove that ground reducibility is EXPTIME-complete in the general case. EXPTIME-hardness is proved by encoding the emptiness problem for the intersection of recognizable tree languages. It is more difficult to show that ground reducibility belongs to DEXPTIME. We associate first a tree automaton with disequality constraints to a rewrite system and a term. This automaton is deterministic and accepts a non-empty tree language iff the given term is not ground reducible by the system. The number of states of the automaton is exponential in the size of the term and the system, and the size of its constraints is polynomial in the size of the term and the system. Then we prove some new pumping lemmas, using a total ordering on the computations of the automaton. Thanks to these lemmas, we can show that emptiness for a tree automaton with disequality constraints can be decided in a time which is polynomial in the number of states and exponential in the size of the constraints. Altogether, we get a simply exponential time deterministic algorithm for ground reducibility decision.
Type de document :
Rapport
[Research Report] RR-3800, INRIA. 1999, pp.26
Liste complète des métadonnées

https://hal.inria.fr/inria-00072859
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 11:07:06
Dernière modification le : jeudi 11 janvier 2018 - 06:19:58
Document(s) archivé(s) le : dimanche 4 avril 2010 - 21:29:12

Fichiers

Identifiants

  • HAL Id : inria-00072859, version 1

Collections

Citation

Hubert Comon, Florent Jacquemard. Ground Reducibility is EXPTIME-complete. [Research Report] RR-3800, INRIA. 1999, pp.26. 〈inria-00072859〉

Partager

Métriques

Consultations de la notice

135

Téléchargements de fichiers

132