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International Colloquium on Automata, Languages, and Programming

ICALP 2000: Automata, Languages and Programming pp 536–546Cite as

On the Centralizer of a Finite Set

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1853))

Abstract

We prove two results on commutation of languages. First, we show that the maximal language commuting with a three element language, i.e. its centralizer, is rational, thus giving an affirmative answer to a special case of a problem proposed by Conway in 1971. Second, we characterize all languages commuting with a three element code. The characterization is similar to the one proved by Bergman for polynomials over noncommuting variables, cf. Bergman, 1969 and Lothaire, 2000: A language commutes with a three element code X if and only if it is a union of powers of X.

The authors acknowledge the support from the Academy of Finland under project 44087.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Turku andTurku Centre for Computer Science (TUCS), Turku, 20014, Finland

    Juhani Karhumäki & Ion Petre

Authors
  1. Juhani Karhumäki
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  2. Ion Petre
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Editor information

Editors and Affiliations

  1. Department of Computer Sciences, University of Pisa, Corso Italia, 40, 56125, Pisa, Italy

    Ugo Montanari

  2. Center for Computer Sciences, University of Geneva, 24, Rue Général Dufour, 1211, Geneva 4, Switzerland

    José D. P. Rolim

  3. Department of Computer Sciences, ETH Zurich, 8092, Zurich, Switzerland

    Emo Welzl

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© 2000 Springer-Verlag Berlin Heidelberg

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Karhumäki, J., Petre, I. (2000). On the Centralizer of a Finite Set. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_45

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  • DOI: https://doi.org/10.1007/3-540-45022-X_45

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67715-4

  • Online ISBN: 978-3-540-45022-1

  • eBook Packages: Springer Book Archive

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