An inverse automata algorithm for recognizing 2-collapsing words

  • Authors:

  • Dmitry S. Ananichev;Alessandra Cherubini;Mikhail V. Volkov

  • Affiliations:

  • Department of Mathematics and Mechanics, Ural State University, Ekaterinburg, Russia;Dipartimento di Matematica "Francesco Brioschi", Politecnico di Milano, Milano, Italia;Department of Mathematics and Mechanics, Ural State University, Ekaterinburg, Russia

  • Venue:
  • DLT'02 Proceedings of the 6th international conference on Developments in language theory
  • Year:
  • 2002

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Abstract

A word ω over a finite alphabet Σ is n-collapsing if for an arbitrary DFA A = {Q,Σ, δ}, the inequality |δ(Q,ω)| ≤ |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 ω is 2-collapsing. In contrast to our previous group-theoretic algorithm, the present algorithm is of a geometric nature, and if the word ω ∈ Σ* is not 2-collapsing, it directly produces a DFA Aω = {Q,Σ,δ} such that |Q| Q, u)| ≤ |Q| - 2 for some word u ∈ Σ* , but |δ(Q, ω)| ≥ |Q| - 1.