Mutual Generation of the Choice and Majority Functions

Abstract

The k-valued (in particular ternary) computing has been becoming more and more relevant during the last decade. The research and development of algorithms based on k-valued logic is very relevant in many fields of science and engineering. A fundamentally essential problem—the problem of full description of closed classes of three-valued logic functions—must be solved to make the implementation of such algorithms are possible. A continuum of closed classes on the superposition operation appeared in the transition to a multivalued logic (greater than two). We can’t construct a complete description in this case. In this paper, we consider the problem of verifying the finite generation of classes containing some subclass of functions of one variable. We also give a description of the over lattices of classes in $$ P_k $$ containing some precomplete class of unary functions. The finite generation of overlattices has been proved.