On superposition-based satisfiability procedures and their combination
Identifieur interne : 006609 ( Main/Merge ); précédent : 006608; suivant : 006610On superposition-based satisfiability procedures and their combination
Auteurs : Hélène Kirchner [France] ; Silvio Ranise [France] ; Christophe Ringeissen [France] ; DUC KHANH TRAN [France]Source :
- Lecture notes in computer science [ 0302-9743 ] ; 2005.
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- Pascal (Inist)
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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.
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wicri:level="1"><inist:fA14 i1="01"><s1>LORIA & INRIA-Lorraine</s1><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>LORIA & INRIA-Lorraine</wicri:noRegion><wicri:noRegion>LORIA & INRIA-Lorraine</wicri:noRegion></affiliation></author><author><name sortKey="Ranise, Silvio" sort="Ranise, Silvio" uniqKey="Ranise S" first="Silvio" last="Ranise">Silvio Ranise</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>LORIA & INRIA-Lorraine</s1><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>LORIA & INRIA-Lorraine</wicri:noRegion><wicri:noRegion>LORIA & INRIA-Lorraine</wicri:noRegion></affiliation></author><author><name sortKey="Ringeissen, Christophe" sort="Ringeissen, Christophe" uniqKey="Ringeissen C" first="Christophe" last="Ringeissen">Christophe Ringeissen</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>LORIA & INRIA-Lorraine</s1><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>LORIA & INRIA-Lorraine</wicri:noRegion><wicri:noRegion>LORIA & INRIA-Lorraine</wicri:noRegion></affiliation></author><author><name sortKey="Duc Khanh Tran" sort="Duc Khanh Tran" uniqKey="Duc Khanh Tran" last="Duc Khanh Tran">DUC KHANH TRAN</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>LORIA & INRIA-Lorraine</s1><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>LORIA & INRIA-Lorraine</wicri:noRegion><wicri:noRegion>LORIA & INRIA-Lorraine</wicri:noRegion></affiliation></author></analytic><series><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno><imprint><date when="2005">2005</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Aerospace</term><term>Arithmetics</term><term>Certification</term><term>Decidability</term><term>Disjunction</term><term>List processing</term><term>Non convex analysis</term><term>Satisfiability</term><term>Superposition</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Décidabilité</term><term>Traitement liste</term><term>Superposition</term><term>Satisfiabilité</term><term>Disjonction</term><term>Certification</term><term>Aérospatiale</term><term>Arithmétique</term><term>Analyse non convexe</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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></front></TEI><affiliations><list><country><li>France</li></country></list><tree><country name="France"><noRegion><name sortKey="Kirchner, Helene" sort="Kirchner, Helene" uniqKey="Kirchner H" first="Hélène" last="Kirchner">Hélène Kirchner</name></noRegion><name sortKey="Duc Khanh Tran" sort="Duc Khanh Tran" uniqKey="Duc Khanh Tran" last="Duc Khanh Tran">DUC KHANH TRAN</name><name sortKey="Ranise, Silvio" sort="Ranise, Silvio" uniqKey="Ranise S" first="Silvio" last="Ranise">Silvio Ranise</name><name sortKey="Ringeissen, Christophe" sort="Ringeissen, Christophe" uniqKey="Ringeissen C" first="Christophe" last="Ringeissen">Christophe Ringeissen</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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