Splittability of bilexical context-free grammars is undecidable

  • Authors:
  • Mark-Jan Nederhof;Giorgio Satta

  • Affiliations:
  • University of St. Andrews;University of Padua

  • Venue:
  • Computational Linguistics
  • Year:
  • 2011

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Abstract

Bilexical context-free grammars (2-LCFGs) have proved to be accurate models for statistical natural language parsing. Existing dynamic programming algorithms used to parse sentences under these models have running time of O(â聢拢wâ聢拢4), where w is the input string. A 2-LCFG is splittable if the left arguments of a lexical head are always independent of the right arguments, and vice versa. When a 2-LCFGs is splittable, parsing time can be asymptotically improved to O(â聢拢wâ聢拢3). Testing this property is therefore of central interest to parsing efficiency. In this article, however, we show the negative result that splittability of 2-LCFGs is undecidable.