SOME APPLICATIONS OF TERNARY ALGEBRAS

J. A. BRZOZOWSKI
Department of Computer Science
University of Waterloo
Waterloo, Ontario, Canada N2L 3G1
August 1996

Abstract

A De Morgan algebra is a distributive lattice with 0 and 1 that has a quasi-complementation operation satisfying De Morgan's laws. A ternary algebra is a De Morgan algebra that has a third constant X that satisfies (a + ~a) + X = a + ~a, (a * ~a) * X = a * ~a, and X = ~X. In this paper we first briefly describe three older applications of ternary algebras, namely, the detection of static hazards in combinational circuits, the computation of outcomes of transitions in sequential circuits, and modelling of CMOS circuits. Next, we discuss a new application of special ternary algebras called process spaces to the specification of interacting systems. We survey some old and new results concerning ternary algebras, and we describe a recent set-theoretic characterization of finite ternary algebras.

Index Terms CMOS circuit, combinational circuit, interacting system, lattice, process space, sequential circuit, static hazard, Stone's theorem subset-pair algebra, ternary algebra.

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