Computational complexity of current GPSG theory

  • Authors:
  • Eric Sven Ristad

  • Affiliations:
  • MIT Artificial Intelligence Lab, Cambridge, MA

  • Venue:
  • ACL '86 Proceedings of the 24th annual meeting on Association for Computational Linguistics
  • Year:
  • 1986

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Abstract

An important goal of computational linguistics has been to use linguistic theory to guide the construction of computationally efficient real-world natural language processing systems. At first glance, generalized phrase structure grammar (GPSG) appears to be a blessing on two counts. First, the precise formalisms of GPSG might be a direct and transparent guide for parser design and implementation. Second, since GPSG has weak context-free generative power and context-free languages can be parsed in O(n3) by a wide range of algorithms, GPSG parsers would appear to run in polynomial time. This widely-assumed GPSG "efficient parsability" result is misleading: here we prove that the universal recognition problem for current GPSG theory is exponential-polynomial time hard, and assuredly intractable. The paper pinpoints sources of complexity (e.g. metarules and the theory of syntactic features) in the current GPSG theory and concludes with some linguistically and computationally motivated restrictions on GPSG.