Affiliations: Institut für Formale Methoden der Informatik, Universität Stuttgart, Stuttgart, Germany, [email protected] | Institut für Formale Methoden der Informatik, Universität Stuttgart, Stuttgart, Germany, [email protected] | City College of New York, Department of Mathematics, New York, USA, [email protected]
Note: [] Address for correspondence: University of Stuttgart, FMI, Universitätsstr. 38, 70569 Stuttgart, Germany
Note: [] The second author was supported by the German Research Foundation (DFG) under grant DI 435/5-1.
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.
