30/06/2025, 16:00 — 17:00 Unusual schedule —
Room P3.10, Mathematics Building
Erkko Lehtonen, Khalifa University of Science and Technology, Abu Dhabi
On clones, minions, and clonoids, especially those of Boolean functions
We provide a brief introduction to the theory of clones, minions, and clonoids, which are sets of functions of several arguments with certain closure conditions defined in terms of function class composition. These notions arise in a natural way in universal algebra and they have proved useful in the analysis of computational complexity of constraint satisfaction problems. Our primary focus is on clonoids of Boolean functions, and we present classifications of clonoids in the spirit of Post's classification of clones. Moreover, we propose refinements and strengthenings to Sparks's theorem on the cardinalities of clonoid lattices.
