Decomposition theorems for finite sequential machines

In this work we present a different proof of results by K.B. Krohn and J. L. Rhodes [1], and give a new result on the same lines. These authors proved that every function computed by a finite state machine can be constructed by "elementary operations" on a set of "prime functions." By extending the scope of elementary operations, we now show that all functions computed by finite machines are built from a single function.