Clones of pivotally decomposable functions.
Identifieur interne : 001488 ( Hal/Curation ); précédent : 001487; suivant : 001489Clones of pivotally decomposable functions.
Auteurs : Miguel Couceiro [France] ; Bruno Teheux [Luxembourg (pays)]Source :
Abstract
This paper is a contribution to the understanding of the relation between pivotal decompositions of operations on a set A and clones on the same set. In this preliminary study we establish sufficient conditions on a pivotal operation Π so that the corresponding class of Π-decomposable functions constitutes a clone, and discuss the normal form representations that such pivotal operations induce. As a bi-product, we establish thatclones of Π-decomposable functions are determined by the unary sections of their members. We also outline several open questions, providing directions for further research
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In this preliminary study we establish sufficient conditions on a pivotal operation Π so that the corresponding class of Π-decomposable functions constitutes a clone, and discuss the normal form representations that such pivotal operations induce. As a bi-product, we establish thatclones of Π-decomposable functions are determined by the unary sections of their members. We also outline several open questions, providing directions for further research</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Clones of pivotally decomposable functions.</title><author role="aut"><persName><forename type="first">Miguel</forename><surname>Couceiro</surname></persName><email></email><idno type="idhal">miguel-couceiro</idno><idno type="halauthor">816609</idno><idno type="arXiv">http://arxiv.org/a/Miguel Couceiro</idno><affiliation ref="#struct-205125"></affiliation></author><author role="aut"><persName><forename type="first">Bruno</forename><surname>Teheux</surname></persName><email></email><idno type="halauthor">1103922</idno><affiliation ref="#struct-264920"></affiliation></author><editor role="depositor"><persName><forename>Miguel</forename><surname>Couceiro</surname></persName><email>miguel.couceiro@inria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2015-07-11 18:08:22</date><date type="whenWritten">2014</date><date type="whenModified">2015-09-22 01:12:42</date><date type="whenReleased">2015-07-11 18:08:22</date><date type="whenProduced">2015-05-18</date></edition><respStmt><resp>contributor</resp><name key="304220"><persName><forename>Miguel</forename><surname>Couceiro</surname></persName><email>miguel.couceiro@inria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">hal-01175698</idno><idno type="halUri">https://hal.inria.fr/hal-01175698</idno><idno type="halBibtex">couceiro:hal-01175698</idno><idno type="halRefHtml">45th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2015), May 2015, Waterloo, Canada. 45th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2015), IEEE Computer Society</idno><idno type="halRef">45th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2015), May 2015, Waterloo, Canada. 45th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2015), IEEE Computer Society</idno></publicationStmt><seriesStmt><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA-TALC" p="LORIA">Traitement automatique des langues et des connaissances</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno></seriesStmt><notesStmt><note type="audience" n="2">International</note><note type="invited" n="0">No</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note><note type="proceedings" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Clones of pivotally decomposable functions.</title><author role="aut"><persName><forename type="first">Miguel</forename><surname>Couceiro</surname></persName><idno type="idHal">miguel-couceiro</idno><idno type="halAuthorId">816609</idno><idno type="arXiv">http://arxiv.org/a/Miguel Couceiro</idno><affiliation ref="#struct-205125"></affiliation></author><author role="aut"><persName><forename type="first">Bruno</forename><surname>Teheux</surname></persName><idno type="halAuthorId">1103922</idno><affiliation ref="#struct-264920"></affiliation></author></analytic><monogr><meeting><title>45th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2015)</title><date type="start">2015-05-18</date><settlement>Waterloo</settlement><country key="CA">Canada</country></meeting><imprint><biblScope unit="serie">45th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2015), IEEE Computer Society.</biblScope></imprint></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><classCode scheme="halDomain" n="info">Computer Science [cs]</classCode><classCode scheme="halDomain" n="math">Mathematics [math]</classCode><classCode scheme="halTypology" n="COMM">Conference papers</classCode></textClass><abstract xml:lang="en">This paper is a contribution to the understanding of the relation between pivotal decompositions of operations on a set A and clones on the same set. In this preliminary study we establish sufficient conditions on a pivotal operation Π so that the corresponding class of Π-decomposable functions constitutes a clone, and discuss the normal form representations that such pivotal operations induce. As a bi-product, we establish thatclones of Π-decomposable functions are determined by the unary sections of their members. We also outline several open questions, providing directions for further research</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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