An extension of the Krohn-Rhodes decomposition of automata

  • Zoltán Esik
Chapter 2 Machines
Part of the Lecture Notes in Computer Science book series (LNCS, volume 381)


The notion of an irreducible semigroup has been fundamental to the Krohn-Rhodes decomposition. In this paper we study a similar concept and point out its equivalence with the Krohn-Rhodes irreducibility. We then use the new aspect of irreducible semigroups to provide cascade decompositions of automata in a situation when a strict letter-to-letter replacement is essential. The results are stated in terms of completeness theorems. Our terminology follows [10], so that the cascade composition is referred to as the α0-product.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Zoltán Esik
    • 1
  1. 1.Bolyai InstituteA. József UniversitySzegedHungary

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