From Nerode's congruence to suffix automata with mismatches

  • Authors:

  • M. Crochemore;C. Epifanio;A. Gabriele;F. Mignosi

  • Affiliations:

  • Kings College London, UK and Institut Gaspard-Monge, Université Paris-Est, France;Dipartimento di Matematica e Applicazioni, Università di Palermo, Italy;Dipartimento di Matematica e Applicazioni, Università di Palermo, Italy;Dipartimento di Informatica, Università dellAquila, Italy

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

In this paper we focus on the minimal deterministic finite automaton S"k that recognizes the set of suffixes of a word w up to k errors. As first result we give a characterization of the Nerode's right-invariant congruence that is associated with S"k. This result generalizes the classical characterization described in [A. Blumer, J. Blumer, D. Haussler, A. Ehrenfeucht, M. Chen, J. Seiferas, The smallest automaton recognizing the subwords of a text, Theoretical Computer Science, 40, 1985, 31-55]. As second result we present an algorithm that makes use of S"k to accept in an efficient way the language of all suffixes of w up to k errors in every window of size r of a text, where r is the repetition index of w. Moreover, we give some experimental results on some well-known words, like prefixes of Fibonacci and Thue-Morse words. Finally, we state a conjecture and an open problem on the size and the construction of the suffix automaton with mismatches.