Methods of the algebraic theory of machines: I. Decomposition theorem for generalized machines; Properties preserved under series and parallel compositions of machines

Abstract

In previous papers, Krohn and Rhodes exploited the natural connection between finite semigroups and finite-state sequential machines to prove a ptime decomposition theorem for finite semigroups and machines. The present paper uses the methdos of this algebraic approach to obtain a prime decomposition theorem for generalized machines together with the determination of properties preserved under siries and parallel (or cascade) composition of sequential machines.