The Krohn-Rhodes Theorem and Local Divisors
Volker Diekert, Manfred Kufleitner, Benjamin Steinberg · Fundamenta Informaticae · 2012
We give a new proof of the Krohn-Rhodes theorem using local divisors. The proof provides nearly as good a decomposition in terms of size as the holonomy decomposition of Eilenberg, avoids induction on the size of the state set, and works exclusively