InforLorV4, Hal, Curation, bibRecord, 000483

A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones

Identifieur interne : 000483 ( Hal/Curation ); précédent : 000482; suivant : 000484

A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones

Auteurs : Miguel Couceiro [France] ; Lucien Haddad [Canada] ; Karsten Schölzel [Luxembourg (pays)] ; Tamas Waldhauser [Hongrie]

Source :

RBID : Hal:hal-01090640

Abstract

The following natural problem, first considered by D. Lau, has been tackled by several authors recently: Let C be a total clone on 2 := {0, 1}. Describe the interval I(C) of all partial clones on 2 whose total component is C. We establish some results in this direction and combine them with previous ones to show the following dichotomy result: For every total clone C on 2, the set I(C) is either finite or of continuum cardinality.

Url:

https://hal.archives-ouvertes.fr/hal-01090640

DOI: 10.1109/ISMVL.2013.7

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Le document en format XML

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<front><div type="abstract" xml:lang="en">The following natural problem, first considered by D. Lau, has been tackled by several authors recently: Let C be a total clone on 2 := {0, 1}. Describe the interval I(C) of all partial clones on 2 whose total component is C. We establish some results in this direction and combine them with previous ones to show the following dichotomy result: For every total clone C on 2, the set I(C) is either finite or of continuum cardinality.</div>
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<sourceDesc><biblStruct><analytic><title xml:lang="en">A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones</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">Lucien</forename>
<surname>Haddad</surname>
</persName>
<idno type="halAuthorId">1103904</idno>
<affiliation ref="#struct-130123"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Karsten</forename>
<surname>Schölzel</surname>
</persName>
<idno type="halAuthorId">1103930</idno>
<affiliation ref="#struct-106066"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Tamas</forename>
<surname>Waldhauser</surname>
</persName>
<idno type="halAuthorId">1103876</idno>
<affiliation ref="#struct-409319"></affiliation>
</author>
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<monogr><meeting><title>IEEE 43rd International Symposium on Multiple-Valued Logic (ISMVL), 2013</title>
<date type="start">2013-05-22</date>
<date type="end">2013-05-24</date>
<settlement>Toyama</settlement>
<country key="JP">Japan</country>
</meeting>
<imprint><date type="datePub">2013</date>
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<idno type="doi">10.1109/ISMVL.2013.7</idno>
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<abstract xml:lang="en">The following natural problem, first considered by D. Lau, has been tackled by several authors recently: Let C be a total clone on 2 := {0, 1}. Describe the interval I(C) of all partial clones on 2 whose total component is C. We establish some results in this direction and combine them with previous ones to show the following dichotomy result: For every total clone C on 2, the set I(C) is either finite or of continuum cardinality.</abstract>
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A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones

A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones

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