InforLorV4, Main, Exploration, bibRecord, 000425

A Polite Non-Disjoint Combination Method: Theories with Bridging Functions Revisited

Identifieur interne : 000425 ( Main/Exploration ); précédent : 000424; suivant : 000426

A Polite Non-Disjoint Combination Method: Theories with Bridging Functions Revisited

Auteurs : Paula Chocron [France] ; Pascal Fontaine [France] ; Christophe Ringeissen [France]

Source :

RBID : Hal:hal-01157898

Abstract

The Nelson-Oppen combination method is ubiquitous in Satisfiability Modulo Theories solvers. However, one of its major drawbacks is to be restricted to disjoint unions of theories. We investigate the problem of extending this combination method to particular non-disjoint unions of theories connected via bridging functions. The motivation is, e.g., to solve verification problems expressed in a combination of data structures connected to arithmetic with bridging functions such as the length of lists and the size of trees. We present a sound and complete combination procedure à la Nelson-Oppen for the theory of absolutely free data structures, including lists and trees. This combination procedure is then refined for standard interpretations. The resulting theory has a nice politeness property, enabling combinations with arbitrary decidable theories of elements.

Url:

https://hal.inria.fr/hal-01157898

DOI: 10.1007/978-3-319-21401-6_29

Affiliations:

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Le document en format XML

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<country>France</country>
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<settlement type="city">Metz</settlement>
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<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">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>
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<front><div type="abstract" xml:lang="en">The Nelson-Oppen combination method is ubiquitous in Satisfiability  Modulo Theories solvers. However, one of its major drawbacks is to  be restricted to disjoint unions of theories.  We investigate the  problem of extending this combination method to particular  non-disjoint unions of theories connected via bridging functions.  The motivation is, e.g., to solve verification problems expressed in  a combination of data structures connected to arithmetic with  bridging functions such as the length of lists and the size of  trees.  We present a sound and complete combination procedure à la  Nelson-Oppen for the theory of absolutely free data structures,  including lists and trees.  This combination procedure is then  refined for standard interpretations.  The resulting theory has a  nice politeness property, enabling combinations with arbitrary  decidable theories of elements.</div>
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<tree><country name="France"><noRegion><name sortKey="Chocron, Paula" sort="Chocron, Paula" uniqKey="Chocron P" first="Paula" last="Chocron">Paula Chocron</name>
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<name sortKey="Fontaine, Pascal" sort="Fontaine, Pascal" uniqKey="Fontaine P" first="Pascal" last="Fontaine">Pascal Fontaine</name>
<name sortKey="Ringeissen, Christophe" sort="Ringeissen, Christophe" uniqKey="Ringeissen C" first="Christophe" last="Ringeissen">Christophe Ringeissen</name>
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A Polite Non-Disjoint Combination Method: Theories with Bridging Functions Revisited

A Polite Non-Disjoint Combination Method: Theories with Bridging Functions Revisited

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