Bounding Resource Consumption with Gödel-Dummett Logics
Identifieur interne : 000C10 ( Istex/Curation ); précédent : 000C09; suivant : 000C11Bounding Resource Consumption with Gödel-Dummett Logics
Auteurs : Dominique Larchey-Wendling [France]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: Gödel-Dummett logic LC and its finite approximations LC n are the intermediate logics complete w.r.t. linearly ordered Kripke models. In this paper, we use LC n logics as a tool to bound resource consumption in some process calculi. We introduce a non-deterministic process calculus where the consumption of a particular resource denoted ∙ is explicit and provide an operational semantics which measures the consumption of this resource. We present a linear transformation of a process P into a formula f of LC n . We show that the consumption of the resource by P can be bounded by the positive integer n if and only if the formula f admits a counter-model in LC n . Combining this result with our previous results on proof and counter-model construction for LC n , we conclude that bounding resource consumption is (linearly) equivalent to searching counter-models in LC n .
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DOI: 10.1007/11591191_47
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Bounding Resource Consumption with Gödel-Dummett Logics</title><author><name sortKey="Larchey Wendling, Dominique" sort="Larchey Wendling, Dominique" uniqKey="Larchey Wendling D" first="Dominique" last="Larchey-Wendling">Dominique Larchey-Wendling</name><affiliation wicri:level="1"><mods:affiliation>LORIA – CNRS, Campus scientifique, BP 239, 54 506, Vandœuvre-lès-Nancy, France</mods:affiliation><country xml:lang="fr">France</country><wicri:regionArea>LORIA – CNRS, Campus scientifique, BP 239, 54 506, Vandœuvre-lès-Nancy</wicri:regionArea></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:338E39AB1A7A8A52495EA386B460F671BC127079</idno><date when="2005" year="2005">2005</date><idno type="doi">10.1007/11591191_47</idno><idno type="url">https://api.istex.fr/ark:/67375/HCB-V6KX3MDB-P/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">000C17</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000C17</idno><idno type="wicri:Area/Istex/Curation">000C10</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Bounding Resource Consumption with Gödel-Dummett Logics</title><author><name sortKey="Larchey Wendling, Dominique" sort="Larchey Wendling, Dominique" uniqKey="Larchey Wendling D" first="Dominique" last="Larchey-Wendling">Dominique Larchey-Wendling</name><affiliation wicri:level="1"><mods:affiliation>LORIA – CNRS, Campus scientifique, BP 239, 54 506, Vandœuvre-lès-Nancy, France</mods:affiliation><country xml:lang="fr">France</country><wicri:regionArea>LORIA – CNRS, Campus scientifique, BP 239, 54 506, Vandœuvre-lès-Nancy</wicri:regionArea></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Gödel-Dummett logic LC and its finite approximations LC n are the intermediate logics complete w.r.t. linearly ordered Kripke models. In this paper, we use LC n logics as a tool to bound resource consumption in some process calculi. We introduce a non-deterministic process calculus where the consumption of a particular resource denoted ∙ is explicit and provide an operational semantics which measures the consumption of this resource. We present a linear transformation of a process P into a formula f of LC n . We show that the consumption of the resource by P can be bounded by the positive integer n if and only if the formula f admits a counter-model in LC n . Combining this result with our previous results on proof and counter-model construction for LC n , we conclude that bounding resource consumption is (linearly) equivalent to searching counter-models in LC n .</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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