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Short 3-Collapsing Words over a 2-Letter Alphabet

  • Alessandra Cherubini
  • Achille Frigeri
  • Brunetto Piochi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)

Abstract

Let \(\mathcal{A}=(Q,\Sigma,\delta)\) be a finite deterministic complete automaton. \(\mathcal{A}\) is called k-compressible if there is a word w ∈ Σ +  such that the image of the state set Q under the action of w has at most size |Q| − k, in such case the word w is called k-compressing for \(\mathcal{A}\). A word w ∈ Σ +  is k-collapsing if it is k-compressing for each k-compressible automaton of the alphabet Σ and it is k-synchronizing if it is k-compressing for each k-compressible automaton with k + 1 states (see [1,2] for details).

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References

  1. 1.
    Ananichev, D.S., Petrov, I.V., Volkov, M.V.: Collapsing words: A progress report. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 11–21. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Cherubini, A.: Synchronizing and collapsing words. Milan J. Math. 75, 305–321 (2007)MathSciNetCrossRefGoogle Scholar
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    Margolis, S.W., Pin, J.-E., Volkov, M.V.: Words guaranteeing minimum image. Internat. J. Foundations Comp. Sci. 15, 259–276 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
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    Sauer, N., Stone, M.G.: Composing functions to reduce image size. Ars. Combinatoria 1, 171–176 (1991)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Alessandra Cherubini
    • 1
  • Achille Frigeri
    • 1
  • Brunetto Piochi
    • 2
  1. 1.Politecnico di MilanoItaly
  2. 2.Università di FirenzeItaly

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