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A complete classification of equational classes of threshold functions included in clones
Couceiro, Miguel; Lehtonen, Erkko; Schölzel, Karsten
2013
 

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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.
Disciplines :
Mathematics
Author, co-author :
Couceiro, Miguel
Lehtonen, Erkko ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
Schölzel, Karsten ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
A complete classification of equational classes of threshold functions included in clones
Publication date :
2013
Available on ORBilu :
since 19 November 2013

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