Existence of finite total equivalence systems for certain closed classes of 3-valued logic functions (Q2342799)

The aim of the paper is to find finite total equivalence systems (FTES) for some classes of functions on finite sets. A reference monograph on this topic is [\textit{D. Lau}, Function algebras on finite sets. A basic course on many-valued logic and clone theory. Berlin: Springer (2006; Zbl 1105.08001)]. For more details, we quote the paper summary. ``The article deals with finding finite total equivalence systems for formulas based on an arbitrary closed class of functions of several variables defined on the set \(\{0,1,2\}\) and taking values in the set \(\{0,1\}\) with the property that the restrictions of its functions to the set \(\{0,1\}\) constitutes a closed class of Boolean functions. We consider all classes whose restriction closure is either the set of all functions of two-valued logic or the set \(T_a\) of functions preserving \(a, a \in \{0, 1\}\). In each of these cases, we find a finite total equivalence system, construct a canonical type for formulas, and present a complete algorithm for determining whether any two formulas are equivalent.''