Collapsing Words: A Progress Report

  • Dmitry S. Ananichev
  • Ilja V. Petrov
  • Mikhail V. Volkov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3572)


A word w over a finite alphabet Σ is n-collapsing if for an arbitrary DFA \({\mathcal A}=\langle Q,\Sigma,\delta\rangle\), the inequality |δ(Q,w)| ≤ |Q| − n holds provided that |δ(Q,u)| ≤ |Q| − n for some word u∈Σ +  (depending on \({\mathcal A}\)). We overview some recent results related to this notion. One of these results implies that the property of being n-collapsing is algorithmically recognizable for any given positive integer n.


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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dmitry S. Ananichev
    • 1
  • Ilja V. Petrov
    • 1
  • Mikhail V. Volkov
    • 1
  1. 1.Department of Mathematics and MechanicsUral State UniversityEkaterinburgRussia

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