On 2-valued Majority Functions with their Relation to Minimal Clones
Hajime Machida · 2025
A majority function is said to be 2-valued if it is 2-valued on triples with mutually distinct components. To determine all minimal clones generated by 2-valued majority functions, it is sufficient to search generators in three subclasses ${{\mathcal{F}}_{2 - 2}}$, ${{\mathcal{F}}_{4 - 1}}$ and ${{\mathcal{F}}_{4 - 2}}$ of functions.In this paper, we finish the case of ${{\mathcal{F}}_{4 - 1}}$ by proving that the subclass ${{\mathcal{F}}_5}$ of ${{\mathcal{F}}_{4 - 1}}$ is exactly the set of minimal functions in ${{\mathcal{F}}_{4 - 1}}$. Then we investigate the case ${{\mathcal{F}}_{4 - 2}}$ and present a new group of minimal functions extracted from this class.