Completeness criterion for functions with delay defined over a domain of three elements
Teruo Hikita · Proceedings of the Japan Academy Series A Mathematical Sciences · 1978
1. Introduction.Let E={0,1,...,k--1} for k22.A k- valued function with delay is.defined to be a pair (f, d), where f is a usual k-valued logical (or switching) function, that is., a function from a cartesian product E E ... E into E, and d is a nonnegative integer.It represents a certain switching element which performs its operation in d units, of time delay.A set of such functions with delay is.called complete if any k-valued function can be realized with some delay by composing the elements in the set "synchronously", i.e., so as to synchronize the delays caused at each part of the composition.A spectrum over E is an infinite sequence of sets of k-valued functions indexed by nonnegative integers., and it is used as an algebraic repre- sentation of a set of functions with delay.A spectrum is complete if