Computational Complexity of Current GPSG Theory
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, the entirely new generalized phrase structure grammar (GPSG) theory of Gazdar, Klein, Pullum, and Sag (1985) appears to be a blessing on two counts. First, their precise formal system and the broad empirical coverage of their published English grammar might be a direct guide for a transparent 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 parsbility" result is misleading: here we prove that the universal recognition problem for the new GPSG theory is exponentially-polynomial time hard, and assuredly intractable. The paper pinpoints sources of intractability (e.g. metarules and syntactic features in the GPSG formal system and concludes with some linguistically and computationally motivated restrictions on GPSG.