Abstract
A generalization of the Krohn-Rhodes theorem is presented that holds for finite as well as for infinite automata. In the finite case the statement is sharper than the usual version of the Krohn-Rhodes theorem in so far as it shows that for any automaton M there exists a cascade decomposition of M with the property that each composition factor of a maximal subgroup of the semigroup of M appears at most once as a component of the decomposition.
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Literaturverzeichnis
Arbib, M. A., Theories of Abstract Automata, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1969)
Clifford, A. H., und G. B. Preston, The Algebraic Theory of Semigroups, Amer. Math. Soc, Providence, R.I., Vol. I (1961)
Krohn, K. B., und J. L. Rhodes, Algebraic Theory of Machines. I. Prime Decomposition Theorem for Finite Semigroups and Machines, Trans. Amer. Math. Soc. 116, 450–464 (1965)
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© 1973 Springer-Verlag
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Hotzel, E. (1973). Der Kaskadenzerlegungssatz für Halbautomaten. In: GI Gesellschaft für Informatik e. V. 1. Fachtagung über Automatentheorie und Formale Sprachen. Lecture Notes in Computer Science, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039138
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DOI: https://doi.org/10.1007/BFb0039138
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