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

Couceiro, Miguel; Lehtonen, Erkko; Schölzel, Karsten (2015), A complete classification of equational classes of threshold functions included in clones, RAIRO - Operations Research, 49, 1, p. 39-66. 10.1051/ro/2014034

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01090621
Date
2015
Journal name
RAIRO - Operations Research
Volume
49
Number
1
Pages
39-66
Publication identifier
Metadata
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Author(s)
Couceiro, Miguel
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lehtonen, Erkko cc
University of Luxembourg, Computer Science Department
Schölzel, Karsten
Mathematics Research Unit
Abstract (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.
Subjects / Keywords
Boolean functions; threshold functions; constraints; clones; equational classes