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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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