Bibliographic Details
| Title: |
Clonoids of Boolean functions with essentially unary, linear, semilattice, or 0- or 1-separating source and target clones. |
| Authors: |
Lehtonen, Erkko1 (AUTHOR) erkko.lehtonen@ku.ac.ae |
| Source: |
International Journal of Algebra & Computation. Feb2026, Vol. 36 Issue 1, p17-50. 34p. |
| Subjects: |
Boolean functions, Lattice theory, Linear operators, Cardinal numbers, Semilattices, Mathematical functions |
| Abstract: |
Extending Sparks's theorem, we determine the cardinality of the lattice of (C 1 , C 2) -clonoids of Boolean functions for certain pairs (C 1 , C 2) of clones of essentially unary, linear, or 0 - or 1 -separating functions or semilattice operations. When such a (C 1 , C 2) -clonoid lattice is uncountable, the proof is in most cases based on exhibiting a countably infinite family of functions with the property that distinct subsets thereof always generate distinct (C 1 , C 2) -clonoids. In the cases when the lattice is finite, we enumerate the corresponding (C 1 , C 2) -clonoids. We also provide a summary of the cardinalities of (C 1 , C 2) -clonoid lattices of Boolean functions. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
