On the size of Boyer-Moore automata

  • Authors:
  • Ricardo Baeza-Yates;Véronique Bruyère;Olivier Delgrange;Rodrigo Scheihing

  • Affiliations:
  • Yahoo! Research, Blanco Encalada 2120, Santiago, Chile;Service dInformatique Théorique, University of Mons, Place du parc 20 B-7000 Mons, Belgium;Service dInformatique Théorique, University of Mons, Place du parc 20 B-7000 Mons, Belgium;Yahoo! Research, Blanco Encalada 2120, Santiago, Chile

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

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Abstract

In this work we study the size of Boyer-Moore automata introduced in Knuth, Morris & Pratt's famous paper on pattern matching. We experimentally show that a finite class of binary patterns produce very large Boyer-Moore automata, and find one particular case which we conjecture, generates automata of size @W(m^6). Further experimental results suggest that the maximal size could be a polynomial of O(m^7), or even an exponential O(2^0^.^4^m), where m is the length of the pattern.