InforLorV4, Main, Exploration, bibRecord, 002815

Automatic decidability and combinability

Identifieur interne : 002815 ( Main/Exploration ); précédent : 002814; suivant : 002816

Automatic decidability and combinability

Auteurs : Christopher Lynch [États-Unis] ; Silvio Ranise [Italie] ; Christophe Ringeissen [France] ; Duc-Khanh Tran [Namibie]

Source :

Information and computation : (Print) [ 0890-5401 ] ; 2011.

RBID : Pascal:11-0330330

Descripteurs français

Pascal (Inist)
- Informatique théorique, Automatique, Décidabilité, Vérification, Equation ordre 1, Disponibilité, Coopération, Théorie décision, Arithmétique Presburger, Structure donnée, Problème satisfiabilité, Question réponse, Saturation, Résolution problème, 68Q60, Satisfiabilité, Procédure décision, Raisonnement équationnel, 68P05, Satisfiability problem, 41A40, 68T20.

English descriptors

KwdEn :
- Automatic, Availability, Computer theory, Cooperation, Data structure, Decidability, Decision theory, First order equation, Presburger arithmetic, Problem solving, Question answering, Satisfiability problem, Saturation, Verification.

Abstract

Verification problems can often be encoded as first-order validity or satisfiability problems. The availability of efficient automated theorem provers is a crucial pre-requisite for automating various verification tasks as well as their cooperation with specialized decision procedures for selected theories, such as Presburger Arithmetic. In this paper, we investigate how automated provers based on a form of equational reasoning, called paramodulation, can be used in verification tools. More precisely, given a theory T axiomatizing some data structure, we devise a procedure to answer the following questions. Is the satisfiability problem of T decidable by paramodulation? Can a procedure based on paramodulation for T be efficiently combined with other specialized procedures by using the Nelson-Oppen schema? Finally, if paramodulation decides the satisfiability problem of two theories, does it decide satisfiability in their union? The procedure capable of answering all questions above is based on Schematic Saturation; an inference system capable of over-approximating the inferences of paramodulation when solving satisfiability problems in a given theory T. Clause schemas derived by Schematic Saturation describe all clauses derived by paramodulation so that the answers to the questions above are obtained by checking that only finitely many different clause schemas are derived or that certain clause schemas are not derived.

Url:

https://hal.inria.fr/inria-00586936

Affiliations:

Le document en format XML

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<front><div type="abstract" xml:lang="en">Verification problems can often be encoded as first-order validity or satisfiability problems. The availability of efficient automated theorem provers is a crucial pre-requisite for automating various verification tasks as well as their cooperation with specialized decision procedures for selected theories, such as Presburger Arithmetic. In this paper, we investigate how automated provers based on a form of equational reasoning, called paramodulation, can be used in verification tools. More precisely, given a theory T axiomatizing some data structure, we devise a procedure to answer the following questions. Is the satisfiability problem of T decidable by paramodulation? Can a procedure based on paramodulation for T be efficiently combined with other specialized procedures by using the Nelson-Oppen schema? Finally, if paramodulation decides the satisfiability problem of two theories, does it decide satisfiability in their union? The procedure capable of answering all questions above is based on Schematic Saturation; an inference system capable of over-approximating the inferences of paramodulation when solving satisfiability problems in a given theory T. Clause schemas derived by Schematic Saturation describe all clauses derived by paramodulation so that the answers to the questions above are obtained by checking that only finitely many different clause schemas are derived or that certain clause schemas are not derived.</div>
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Serveur d'exploration sur la recherche en informatique en Lorraine

Automatic decidability and combinability

Automatic decidability and combinability

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri

	Serveur d'exploration sur la recherche en informatique en Lorraine
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