Infinitely Generated Classes of 01-Functions of Three-Valued Logic
Sergey Seraphimovich Marchenkov · Moscow University Computational Mathematics and Cybernetics · 2021
Infinitely generated closed classes $$\Pi_{1}{-}\Pi_{4}$$ of 01-functions of three-valued logic are investigated. The property of maximality is proved for classes $$\Pi_{3}$$ and $$\Pi_{4}$$ . Each proper extension of classes leads to finitely generated closed classes. It is proved that there is no base in class $$\Pi_{1}$$ . All of the simplest two- and three-variable functions obtainable by superposition from an arbitrary function not belonging to class $$\Pi_{1}$$ are found.