Structural Equivalence of Topological Machines
Eugene S. Santos · Journal of Cybernetics · 1974
Recently, there has been a fair amount of interest in the study of topological machines, e.g. Day [2], Norris [4] and Sikdar [5]. Due to the topological structures endowed in the input, output, and state spaces of the topological machines, most of the results of conventional deterministic machines do not admit of an immediate generalization to the topological case. In this paper, we shall study the structural equivalences of topological machines. Various concepts are defined including quotient submachines, irreducibility, reduced forms, homomorphisms, minimality, and minimal forms. It is shown that every topological machine has a unique reduced form and has a minimal form which is unique up to iseomorphism. Moreover, it is shown that a topological machine is irreducible if and only if it is minimal.