Combining Satisfiability Procedures for Unions of Theories with a Shared Counting Operator
Identifieur interne : 002F08 ( Main/Exploration ); précédent : 002F07; suivant : 002F09Combining Satisfiability Procedures for Unions of Theories with a Shared Counting Operator
Auteurs : Enrica Nicolini [France] ; Christophe Ringeissen [France] ; Michael Rusinowitch [France]Source :
- Fundamenta Informaticae [ 0169-2968 ] ; 2010.
English descriptors
- mix :
Abstract
We present some decidability results for the universal fragment of theories modeling data structures and endowed with arithmetic constraints. More precisely, all the theories taken into account extend a theory that constrains the function symbol for the successor. A general decision procedure is obtained, by devising an appropriate calculus based on superposition. Moreover, we derive a decidability result for the combination of the considered theories for data structures and some fragments of arithmetic by applying a general combination schema for theories sharing a common subtheory. The effectiveness of the resulting algorithm is ensured by using the proposed calculus and a careful adaptation of standard methods for reasoning about arithmetic, such as Gauss elimination, Fourier-Motzkin elimination and Groebner bases computation.
Url:
DOI: 10.3233/FI-2010-362
Affiliations:
- France
- Franche-Comté, Grand Est, Lorraine (région)
- Belfort, Besançon, Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Bourgogne Franche-Comté, Université de Franche-Comté, Université de Lorraine, Université de technologie de Belfort-Montbéliard
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Le document en format XML
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<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
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<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
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</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université Nancy 2</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
<placeName><settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
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<orgName type="university">Institut national polytechnique de Lorraine</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
<placeName><settlement type="city" wicri:auto="siege">Besançon</settlement>
<region type="region" nuts="2">Franche-Comté</region>
</placeName>
<orgName type="university">Université de Franche-Comté</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName>
<placeName><settlement type="city" wicri:auto="siege">Belfort</settlement>
<region type="region" nuts="2">Franche-Comté</region>
</placeName>
<orgName type="university">Université de technologie de Belfort-Montbéliard</orgName>
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</author>
</analytic>
<idno type="DOI">10.3233/FI-2010-362</idno>
<series><title level="j">Fundamenta Informaticae</title>
<idno type="ISSN">0169-2968</idno>
<imprint><date type="datePub">2010</date>
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<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Combination</term>
<term>Equational Reasoning</term>
<term>Integer Offsets</term>
<term>Satisfiability Procedure</term>
<term>Union of Non-Disjoint Theories</term>
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<front><div type="abstract" xml:lang="en">We present some decidability results for the universal fragment of theories modeling data structures and endowed with arithmetic constraints. More precisely, all the theories taken into account extend a theory that constrains the function symbol for the successor. A general decision procedure is obtained, by devising an appropriate calculus based on superposition. Moreover, we derive a decidability result for the combination of the considered theories for data structures and some fragments of arithmetic by applying a general combination schema for theories sharing a common subtheory. The effectiveness of the resulting algorithm is ensured by using the proposed calculus and a careful adaptation of standard methods for reasoning about arithmetic, such as Gauss elimination, Fourier-Motzkin elimination and Groebner bases computation.</div>
</front>
</TEI>
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<li>Grand Est</li>
<li>Lorraine (région)</li>
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<li>Nancy</li>
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<orgName><li>Institut national polytechnique de Lorraine</li>
<li>Université Nancy 2</li>
<li>Université de Bourgogne Franche-Comté</li>
<li>Université de Franche-Comté</li>
<li>Université de Lorraine</li>
<li>Université de technologie de Belfort-Montbéliard</li>
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<tree><country name="France"><region name="Grand Est"><name sortKey="Nicolini, Enrica" sort="Nicolini, Enrica" uniqKey="Nicolini E" first="Enrica" last="Nicolini">Enrica Nicolini</name>
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<name sortKey="Ringeissen, Christophe" sort="Ringeissen, Christophe" uniqKey="Ringeissen C" first="Christophe" last="Ringeissen">Christophe Ringeissen</name>
<name sortKey="Rusinowitch, Michael" sort="Rusinowitch, Michael" uniqKey="Rusinowitch M" first="Michael" last="Rusinowitch">Michael Rusinowitch</name>
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