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Choosing Word Occurrences for the Smallest Grammar Problem

  • Rafael Carrascosa
  • François Coste
  • Matthias Gallé
  • Gabriel Infante-Lopez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6031)

Abstract

The smallest grammar problem - namely, finding a smallest context-free grammar that generates exactly one sequence - is of practical and theoretical importance in fields such as Kolmogorov complexity, data compression and pattern discovery. We propose to focus on the choice of the occurrences to be rewritten by non-terminals. We extend classical offline algorithms by introducing a global optimization of this choice at each step of the algorithm. This approach allows us to define the search space of a smallest grammar by separating the choice of the non-terminals and the choice of their occurrences. We propose a second algorithm that performs a broader exploration by allowing the removal of useless words that were chosen previously. Experiments on a classical benchmark show that our algorithms consistently find smaller grammars then state-of-the-art algorithms.

Keywords

Production Rule Data Compression Pattern Discovery Kolmogorov Complexity Repeated Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Rafael Carrascosa
    • 1
  • François Coste
    • 2
  • Matthias Gallé
    • 2
  • Gabriel Infante-Lopez
    • 1
    • 3
  1. 1.Grupo de Procesamiento de Lenguaje NaturalUniversidad Nacional de CórdobaArgentina
  2. 2.Symbiose ProjectIRISA/INRIA Rennes-Bretagne AtlantiqueFrance
  3. 3.Consejo Nacional de Investigaciones CientíficasArgentina

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