An Inverse Automata Algorithm for Recognizing 2-Collapsing Words

  • Dmitry S. Ananichev
  • Alessandra Cherubini
  • Mikhail V. Volkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2450)

Abstract

A word w over a finite alphabet Σ is n-collapsing if for an arbitrary DFA A = 〈Q,Σ, δ〉, the inequality ∣δ(Q,w)∣ ≤ ∣Q∣ - n holds provided that ∣δ(Q, u)∣ ≤ ∣Q∣ - n for some word u ∈, Σ+ (depending on A ).We give a new algorithm to test whether a word w is 2-collapsing. In contrast to our previous group-theoretic algorithm, the present algorithm is of a geometric nature, and if the word w ∈, Σ* is not 2-collapsing, it directly produces a DFA Aw = 〈Q,Σ, δ〉 such that ∣Q∣ < max{∣w∣, 4}, ∣δ(Q, u)∣ ≤ ∣Q∣- 2 for some word u ∈, Σ*, but ∣δ(Q,w)∣ ≥ ∣Q∣ - 1.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Dmitry S. Ananichev
    • 1
  • Alessandra Cherubini
    • 2
  • Mikhail V. Volkov
    • 1
  1. 1.Department of Mathematics and MechanicsUral State UniversityEkaterinburgRussia
  2. 2.Dipartimento di Matematica “Francesco Brioschi”Politecnico di MilanoMilanoItalia

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