Factorization of synchronous context-free grammars in linear time

  • Authors:
  • Hao Zhang;Daniel Gildea

  • Affiliations:
  • University of Rochester, Rochester, NY;University of Rochester, Rochester, NY

  • Venue:
  • SSST '07 Proceedings of the NAACL-HLT 2007/AMTA Workshop on Syntax and Structure in Statistical Translation
  • Year:
  • 2007

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Abstract

Factoring a Synchronous Context-Free Grammar into an equivalent grammar with a smaller number of nonterminals in each rule enables synchronous parsing algorithms of lower complexity. The problem can be formalized as searching for the tree-decomposition of a given permutation with the minimal branching factor. In this paper, by modifying the algorithm of Uno and Yagiura (2000) for the closely related problem of finding all common intervals of two permutations, we achieve a linear time algorithm for the permutation factorization problem. We also use the algorithm to analyze the maximum SCFG rule length needed to cover hand-aligned data from various language pairs.