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Properties of factorization forests

  • Imre Simon
Mathematical Foundations Of The Theory Of Automata
Part of the Lecture Notes in Computer Science book series (LNCS, volume 386)

Abstract

It has been proved that every morphism f: A+S, with S a finite semigroup, admits a Ramseyan factorization forest of height at most 9|S|. In this paper we show that, up to a constant factor, this result is best possible. More precisely, we show that if S is a finite rectangular band and f(A) = S then every Ramseyan factorization forest admitted by f has height at least |S|.

In the second part, using induction on the height of vertices of factorization forests we obtain a new proof of a Theorem of T. C. Brown on locally finite semigroups. Our proof is constructive.

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References

  1. [1]
    T. C. Brown. An interesting combinatorial method in the theory of locally finite semigroups. Pacific J. Math., 36:285–289, 1971.Google Scholar
  2. [2]
    I. Simon. Factorization Forests of Finite Height. Technical Report 87-73, Laboratoire d'Informatique Théorique et Programmation, Paris, 1987.Google Scholar
  3. [3]
    H. Straubing. The Burnside problem for semigroups of matrices. In L. J. Cummings, editor, Combinatorics on Words, Progress and Perspectives, pages 279–295, Academic Press, New York, NY, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Imre Simon
    • 1
  1. 1.Instituto de Matemática e EstatísticaUniversidade de São PauloSão Paulo, SPBrasil

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