On connecting modules together uniformly to form a modular computer

Abstract

We informally define a modular (cellular, iterative) computer to be a device consisting of a large (or, in theory, infinite) number of identical circuit modules connected together in some uniform manner, that is, in such a fashion that every module is connected into the device in the same manner as every other. In this paper we propose a mathematically precise definition of, "connected together in a uniform manner". In brief, we show that the underlying linear graph whose vertices correspond to the modules and whose edges correspond to the cables connecting the modules, is a group-graphs that is, the vertices correspond to the elements of a group G and there is given a finite subset G0 of G such that {g, g1} is an edge of the graph If, and only if, there exists g0 ϵ G0 such that g1 = gg0. We further investigate the effects of restricting G to be an Abelian group and indicate why we feel such a restriction is unwarranted at least in developing the theory of modular computers.