2025/04/06 by Erkko Lehtonen, Lehtonen, Erkko
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #Computational Drug Discovery Methods #FOS: Mathematics #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2504.04481
openalex publication_date 2025/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Extending Sparks's theorem, we determine the cardinality of the lattice of (C1,C2)-clonoids of Boolean functions for certain pairs (C1,C2) of clones of Boolean functions. Namely, when C1 is a subclone (a proper subclone, resp.) of the clone of all linear (affine) functions and C2 is a subclone of the clone generated by a semilattice operation and constants (a subclone of the clone of all 0- or 1-separating functions, resp.), then the lattice of (C1,C2)-clonoids is uncountable. Combining this fact with several earlier results, we obtain a complete classification of the cardinalities of the lattices of (C1,C2)-clonoids for all pairs (C1,C2) of clones on \0,1\.