Article (Scientific journals)
Equivalence of operations with respect to discriminator clones
Lehtonen, Erkko; Szendrei, Ágnes
2009In Discrete Mathematics, 309 (4), p. 673-685
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Keywords :
clone; discriminator function; minor; subfunction; Boolean function
Abstract :
[en] For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of the other using operations from C. In this paper we prove that if C is a discriminator clone on a finite set, then there are only finitely many C-equivalence classes. Moreover, we show that the smallest discriminator clone is minimal with respect to this finiteness property. For discriminator clones of Boolean functions we explicitly describe the associated equivalence relations.
Disciplines :
Mathematics
Identifiers :
UNILU:UL-ARTICLE-2010-135
Author, co-author :
Lehtonen, Erkko ;  Tampere University of Technology, Finland
Szendrei, Ágnes;  Bolyai Institute, University of Szeged, Hungary
Language :
English
Title :
Equivalence of operations with respect to discriminator clones
Publication date :
2009
Journal title :
Discrete Mathematics
ISSN :
0012-365X
Publisher :
Elsevier B.V.
Volume :
309
Issue :
4
Pages :
673-685
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 01 July 2013

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