Skip to main content
SpringerLink
Log in
Book cover

International Meeting of Young Computer Scientists

IMYCS 1988: Machines, Languages, and Complexity pp 65–71Cite as

An extension of the Krohn-Rhodes decomposition of automata

  • Chapter 2 Machines
  • Conference paper
  • First Online:

  • 126 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 381))

Abstract

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.

This paper has been completed with the assistance of the Alexander von Humboldt Foundation

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arbib, M.A.: (Ed.), Algebraic Theory of Machines, Languages, and Semigroups, with a major contribution by K. Krohn and J.L. Rhodes (Academic Press, New York, 1968).

    Google Scholar 

  2. Dénes, J. and P. Hermann, On the product of all elements in a finite group, Ann. of Discrete Mathematics, 15 (1982), 107–111.

    Google Scholar 

  3. Dömösi, P. and Z. Ésik, On homomorphic realization of automata with α0-products, Papers on Automata Theory, VIII (1986) 63–97.

    Google Scholar 

  4. Dömösi, P. and Z. Ésik, Critical classes for the α0-product, Theoret. Comput. Sci., 61 (1988), 17–24.

    Google Scholar 

  5. Eilenberg, S., Automata, Languages, and Machines, vol. B (Academic Press, New York, 1976).

    Google Scholar 

  6. Ésik, Z., Varieties of automata and transformation semigroups, Acta Math. Hung., to appear.

    Google Scholar 

  7. Ésik, Z., Results on homomorphic realization of automata by α0-products, submitted.

    Google Scholar 

  8. Ésik, Z. and P. Dömösi, Complete classes of automata for the α0-product, Theoret. Comput. Sci., 47 (1986) 1–14.

    Google Scholar 

  9. Ésik, Z. and J. Virágh, On products of automata with identity, Acta Cybernetica, 7 (1986) 299–311.

    Google Scholar 

  10. Gécseg, F., Products of Automata (Springer-Verlag, Berlin,1986).

    Google Scholar 

  11. Ginzburg, A., Algebraic Theory of Automata (Academic Press, New York, 1968).

    Google Scholar 

  12. Hartmanis, J. and R.E. Stearns, Algebraic Structure Theory of Sequential Machines (Prentice-Hall, Englewood Cliffs, 1966).

    Google Scholar 

  13. Lallement, G., Semigroups and Combinatorial Applications (John Wiley, New York, 1979).

    Google Scholar 

  14. Straubing, H., Finite Semigroup varieties of the form V * D, J. of Pure and Appl. Alg., 36 (1985) 53–94.

    Google Scholar 

  15. Thérien, D. and A. Weiss, Graph congurences and wreath products, J. of Pure and Appl. Alg., 36 (1985) 205–215.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bolyai Institute, A. József University, Aradi v. tere 1, 6720, Szeged, Hungary

    Zoltán Esik

Authors
  1. Zoltán Esik
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. Dassow J. Kelemen

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Esik, Z. (1989). An extension of the Krohn-Rhodes decomposition of automata. In: Dassow, J., Kelemen, J. (eds) Machines, Languages, and Complexity. IMYCS 1988. Lecture Notes in Computer Science, vol 381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015928

Download citation

  • DOI: https://doi.org/10.1007/BFb0015928

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51516-6

  • Online ISBN: 978-3-540-48203-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation