Algebra of Transient States of Postan Signals

Abstract

The m-element Post algebra of m-order, m≥2, is successfully used to describe the steady states of Postan signals in multiple-valued switching circuits. The quasi-Post algebra is introduced to describe both the steady and non-steady states of the Postan signals the similar way as the three-element quasi-Boolean algebra describes the steady and non-steady states of the Boolean signals. The quasi-Post algebra is constructed in such a way that the Post algebra is the subalgebra of the quasi-Post algebra. Operations on steady and transient states of Postan signals are defined and properties of those operations are presented. The algebraic functions of the quasi-Post algebra can be used to study transient states and hazards in multiple-valued combinational logic networks.