Clonoids of Boolean functions with a monotone or discriminator source clone

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发表日期：

2025年12月22日

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Erkko Lehtonen

摘要

Extending Sparks’s theorem, we determine the cardinality of the lattice of $(C_1,C_2)$ $(C_{1}, C_{2})$ -clonoid of Boolean functions in the cases where the target clone $C_2$ $C_{2}$ is the clone of projections. Moreover, we explicitly describe the $(C_1,C_2)$ $(C_{1}, C_{2})$ -clonoid of Boolean functions in the cases where the source clone $C_1$ $C_{1}$ is one of the four clones of monotone functions or contains the discriminator function.