InforLorV4, Main, Exploration, bibRecord, 000733

A complete classification of equational classes of threshold functions included in clones

Identifieur interne : 000733 ( Main/Exploration ); précédent : 000732; suivant : 000734

A complete classification of equational classes of threshold functions included in clones

Auteurs : Miguel Couceiro [France] ; Erkko Lehtonen [Luxembourg (pays)] ; Karsten Schölzel [Luxembourg (pays)]

Source :

RAIRO - Operations Research [ 0399-0559 ] ; 2015.

RBID : Hal:hal-01090621

Abstract

The class of threshold functions is known to be characterizable by functional equations or, equivalently, by pairs of relations, which are called relational constraints. It was shown by Hellerstein that this class cannot be characterized by a finite number of such objects. In this paper, we investigate classes of threshold functions which arise as intersections of the class of all threshold functions with clones of Boolean functions, and provide a complete classification of such intersections in respect to whether they have finite characterizations. Moreover, we provide a characterizing set of relational constraints for each class of threshold functions arising in this way.

Url:

https://hal.archives-ouvertes.fr/hal-01090621

DOI: 10.1051/ro/2014034

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 000607
to stream Hal, to step Curation: 000607
to stream Hal, to step Checkpoint: 000747
to stream Main, to step Merge: 000722
to stream Main, to step Curation: 000733

Le document en format XML

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<front><div type="abstract" xml:lang="en">The class of threshold functions is known to be characterizable by functional equations or, equivalently, by pairs of relations, which are called relational constraints. It was shown by Hellerstein that this class cannot be characterized by a finite number of such objects. In this paper, we investigate classes of threshold functions which arise as intersections of the class of all threshold functions with clones of Boolean functions, and provide a complete classification of such intersections in respect to whether they have finite characterizations. Moreover, we provide a characterizing set of relational constraints for each class of threshold functions arising in this way.</div>
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A complete classification of equational classes of threshold functions included in clones

A complete classification of equational classes of threshold functions included in clones

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