Majority-closed minions of Boolean functions

TL;DR

This paper classifies 93 minions of Boolean functions stable under specific composition rules, providing a comprehensive understanding of their structure and implications for stable classes under certain clones.

Contribution

It explicitly describes all minions stable under composition with the clone of self-dual monotone functions, extending the understanding of Boolean function stability.

Findings

93 minions of Boolean functions are characterized.

All (C_1,C_2)-stable classes are determined for relevant clones.

Provides a complete classification of these minions.

Abstract

The 93 minions of Boolean functions stable under left composition with the clone of self-dual monotone functions are described. As an easy consequence, all $(C_1,C_2)$-stable classes of Boolean functions are determined for an arbitrary clone $C_1$ and for any clone $C_2$ containing the clone of self-dual monotone functions.