Cascade synthesis of finite-state machines

One can construct any finite-state machine as a cascade interconnection of machines whose inputs either permute the states or reset them all to one state. Each permutation group needed in the construction is a homomorphic image of a group generated by the action of a set of input sequences on a state subset of the original machine. Proofs of these facts will be given and their application to the Krohn-Rhodes theory described

Automata & Sequential Machines, A Survey

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryContract DA-36-039-TR US AMC 02208(E