The Krohn-Rhodes Theorem and Local Divisors

Authors:
Volker Diekert;Manfred Kufleitner;Benjamin Steinberg
Affiliations:
(Correspd.) Institut für Formale Methoden der Informatik, Universität Stuttgart, Stuttgart, Germany, diekert@fmi.uni-stuttgart.de;(Supported by the German Research Foundation (DFG) under grant DI 435/5-1) Institut für Formale Methoden der Informatik, Universität Stuttgart, Stuttgart, Germany, kufleitner@fmi.uni-stu ...;City College of New York, Department of Mathematics, New York, USA, bsteinberg@ccny.cuny.edu
Venue:
Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
Year:
2012

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Abstract

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 with monoids with the base case of the induction being that of a group.