Automatic Decidability and Combinability
Identifieur interne : 006A67 ( Hal/Corpus ); précédent : 006A66; suivant : 006A68Automatic Decidability and Combinability
Auteurs : Christopher Lynch ; Silvio Ranise ; Christophe Ringeissen ; Duc-Khanh TranSource :
- Information and Computation [ 0890-5401 ] ; 2011.
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:
DOI: 10.1016/j.ic.2011.03.005
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Hal:inria-00586936Le document en format XML
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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></front></TEI><hal api="V3"><titleStmt><title xml:lang="it">Automatic Decidability and Combinability</title><author role="aut"><persName><forename type="first">Christopher</forename><surname>Lynch</surname></persName><email></email><idno type="halauthor">101117</idno><affiliation ref="#struct-188674"></affiliation></author><author role="aut"><persName><forename type="first">Silvio</forename><surname>Ranise</surname></persName><email></email><idno type="halauthor">63593</idno><affiliation ref="#struct-82358"></affiliation></author><author role="aut"><persName><forename type="first">Christophe</forename><surname>Ringeissen</surname></persName><email>Christophe.Ringeissen@loria.fr</email><idno type="idhal">christophe-ringeissen</idno><idno type="halauthor">65182</idno><affiliation ref="#struct-2366"></affiliation></author><author role="aut"><persName><forename type="first">Duc-Khanh</forename><surname>Tran</surname></persName><email>khanhtd@soict.hut.edu.vn</email><idno type="halauthor">601376</idno><affiliation ref="#struct-153282"></affiliation></author><editor role="depositor"><persName><forename>Christophe</forename><surname>Ringeissen</surname></persName><email>Christophe.Ringeissen@loria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2011-04-18 18:48:35</date><date type="whenModified">2016-05-19 01:12:05</date><date type="whenReleased">2011-04-18 18:48:35</date><date type="whenProduced">2011</date></edition><respStmt><resp>contributor</resp><name key="103757"><persName><forename>Christophe</forename><surname>Ringeissen</surname></persName><email>Christophe.Ringeissen@loria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00586936</idno><idno type="halUri">https://hal.inria.fr/inria-00586936</idno><idno type="halBibtex">lynch:inria-00586936</idno><idno type="halRefHtml">Information and Computation, Elsevier, 2011, 209 (7), pp.1026-1047. <10.1016/j.ic.2011.03.005></idno><idno type="halRef">Information and Computation, Elsevier, 2011, 209 (7), pp.1026-1047. <10.1016/j.ic.2011.03.005></idno></publicationStmt><seriesStmt><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="UNIV-FCOMTE">Université de Franche-Comté</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="LORIA-FM" p="LORIA">Méthodes formelles</idno><idno type="stamp" n="INRIA2">INRIA 2</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="UNIV-BM">Université de Technologie de Belfort-Montbeliard</idno><idno type="stamp" n="ENSMM">Ecole Nationale Supérieure de Mécanique et des Microtechniques</idno><idno type="stamp" n="FEMTO-ST" p="UNIV-FCOMTE">Franche-Comté Electronique, Mécanique, Thermique et Optique - Sciences et Technologies</idno><idno type="stamp" n="UNIV-BM-THESE">Université de Technologie de Belfort-Montbeliard</idno></seriesStmt><notesStmt><note type="audience" n="2">International</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="it">Automatic Decidability and Combinability</title><author role="aut"><persName><forename type="first">Christopher</forename><surname>Lynch</surname></persName><idno type="halAuthorId">101117</idno><affiliation ref="#struct-188674"></affiliation></author><author role="aut"><persName><forename type="first">Silvio</forename><surname>Ranise</surname></persName><idno type="halAuthorId">63593</idno><affiliation ref="#struct-82358"></affiliation></author><author role="aut"><persName><forename type="first">Christophe</forename><surname>Ringeissen</surname></persName><email>Christophe.Ringeissen@loria.fr</email><idno type="idHal">christophe-ringeissen</idno><idno type="halAuthorId">65182</idno><affiliation ref="#struct-2366"></affiliation></author><author role="aut"><persName><forename type="first">Duc-Khanh</forename><surname>Tran</surname></persName><email>khanhtd@soict.hut.edu.vn</email><idno type="halAuthorId">601376</idno><affiliation ref="#struct-153282"></affiliation></author></analytic><monogr><idno type="halJournalId" status="VALID">14180</idno><idno type="issn">0890-5401</idno><idno type="eissn">1090-2651</idno><title level="j">Information and Computation</title><imprint><publisher>Elsevier</publisher><biblScope unit="volume">209</biblScope><biblScope unit="issue">7</biblScope><biblScope unit="pp">1026-1047</biblScope><date type="datePub">2011</date></imprint></monogr><idno type="doi">10.1016/j.ic.2011.03.005</idno></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><classCode scheme="halDomain" n="info.info-lo">Computer Science [cs]/Logic in Computer Science [cs.LO]</classCode><classCode scheme="halTypology" n="ART">Journal articles</classCode></textClass><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.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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