44 research outputs found
A note on minors determined by clones of semilattices
The C-minor partial orders determined by the clones generated by a
semilattice operation (and possibly the constant operations corresponding to
its identity or zero elements) are shown to satisfy the descending chain
condition.Comment: 6 pages, proofs improved, introduction and references adde
Equivalence of operations with respect to discriminator clones
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.Comment: 17 page