Clonoids of Boolean functions with a monotone or discriminator source clone
Abstract
Extending Sparks's theorem, we determine the cardinality of the lattice of (C1,C2)-clonoids of Boolean functions in the cases where the target clone C2 is the clone of projections. Moreover, we explicitly describe the (C1,C2)-clonoids of Boolean functions in the cases where the source clone C1 is one of the four clones of monotone functions or contains the discriminator function.
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