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Equivalence of operations with respect to discriminator clones

Authors
  • Lehtonen, Erkko
  • Szendrei, Ágnes
Publication Date
Jan 01, 2009
Source
ORBilu
Keywords
Language
English
License
Unknown
External links

Abstract

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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