Reference : Equivalence of operations with respect to discriminator clones
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Equivalence of operations with respect to discriminator clones
Lehtonen, Erkko mailto [Tampere University of Technology, Finland]
Szendrei, Ágnes mailto [Bolyai Institute, University of Szeged, Hungary]
Discrete Mathematics
Elsevier B.V.
Yes (verified by ORBilu)
[en] clone ; discriminator function ; minor ; subfunction ; Boolean function
[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.

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