InforLorV4, Main, Exploration, bibRecordById, Pascal:05-0479611

On Superposition-Based Satisfiability Procedures and Their Combination

Identifieur interne : 006223 ( Main/Exploration ); précédent : 006222; suivant : 006224

On Superposition-Based Satisfiability Procedures and Their Combination

Auteurs : Hélène Kirchner ; Silvio Ranise ; Christophe Ringeissen ; Duc Khanh Tran

Source :

Lecture Notes in Computer Science [ 0302-9743 ]

RBID : ISTEX:7A1E52999C1FAB925076D1745362A7FA87ADF41B

Descripteurs français

Pascal (Inist)
- Analyse non convexe, Arithmétique, Aérospatiale, Certification, Disjonction, Décidabilité, Satisfiabilité, Superposition, Traitement liste.

English descriptors

KwdEn :
- Aerospace, Arithmetics, Certification, Decidability, Disjunction, List processing, Non convex analysis, Satisfiability, Superposition.

Abstract

Abstract: We study how to efficiently combine satisfiability procedures built by using a superposition calculus with satisfiability procedures for theories, for which the superposition calculus may not apply (e.g., for various decidable fragments of Arithmetic). Our starting point is the Nelson-Oppen combination method, where satisfiability procedures cooperate by exchanging entailed (disjunction of) equalities between variables. We show that the superposition calculus deduces sufficiently many such equalities for convex theories (e.g., the theory of equality and the theory of lists) and disjunction of equalities for non-convex theories (e.g., the theory of arrays) to guarantee the completeness of the combination method. Experimental results on proof obligations extracted from the certification of auto-generated aerospace software confirm the efficiency of the approach. Finally, we show how to make satisfiability procedures built by superposition both incremental and resettable by using a hierarchic variant of the Nelson-Oppen method.

Url:

https://api.istex.fr/ark:/67375/HCB-F4KMZM70-Z/fulltext.pdf

DOI: 10.1007/11560647_39

Affiliations:

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<front><div type="abstract" xml:lang="en">Abstract: We study how to efficiently combine satisfiability procedures built by using a superposition calculus with satisfiability procedures for theories, for which the superposition calculus may not apply (e.g., for various decidable fragments of Arithmetic). Our starting point is the Nelson-Oppen combination method, where satisfiability procedures cooperate by exchanging entailed (disjunction of) equalities between variables. We show that the superposition calculus deduces sufficiently many such equalities for convex theories (e.g., the theory of equality and the theory of lists) and disjunction of equalities for non-convex theories (e.g., the theory of arrays) to guarantee the completeness of the combination method. Experimental results on proof obligations extracted from the certification of auto-generated aerospace software confirm the efficiency of the approach. Finally, we show how to make satisfiability procedures built by superposition both incremental and resettable by using a hierarchic variant of the Nelson-Oppen method.</div>
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On Superposition-Based Satisfiability Procedures and Their Combination

On Superposition-Based Satisfiability Procedures and Their Combination

Source :

Descripteurs français

English descriptors

Abstract

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Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

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