Some Closed Classes of Three-Valued Logic Generated by Periodic Symmetric Functions

TL;DR

This paper investigates specific closed classes of three-valued logic generated by periodic symmetric functions, providing criteria for their bases and finite bases existence, advancing understanding of their structural properties.

Contribution

It introduces criteria for the existence of bases and finite bases in closed classes generated by particular three-valued symmetric functions.

Findings

Criteria established for bases existence.

Criteria established for finite bases existence.

Enhanced understanding of the structure of these logic classes.

Abstract

Closed classes of three-valued logic generated by periodic symmetric funtions that equal $1$ in tuples from $\{1,2\}^n$ and equal $0$ on the rest tuples are considered. Criteria for bases existence and finite bases existence for these classes is obtained.