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<Paper uid="P86-1006">
  <Title>COMPUTATIONAL COMPLEXITY OF CURRENT GPSG THEORY</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> 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. Generalized Phrase Structure Grammar (GPSG) linguistic theory holds out considerable promise as an aid in this task. The precise formalisms of GPSG offer the prospect of a direct and transparent guide for parser design and implementation. Furthermore, and more importantly, GPSG's weak context-free generative power suggests an efficiency advantage for GPSG-based parsers. Since context-free languages can be parsed in polynomial time, it seems plausible that GPSGs can also be parsed in polynomial time. This would in turn seem to provide &amp;quot;the beginnings of an explanation for the obvious, but largely ignored, fact thatlhumans process the utterances they hear very rapidly (Gazdar,198\] :155).&amp;quot; 1 In this paper I argue that the expectations of the informal complexity argument from weak context-free generative power are not in fact met. I begin by examining the computational complexity of metarules and the feature system of GPSG and show that these systems can lead to computational intractabil~See also Joshi, &amp;quot;Tree Adjoining Grammars ~ p.226, in Natural Language Parsing (1985) ed. by D. Dowty, L. Karttunen, and A. Zwicky, Cambridge University Press: Cambridge, and aExceptlons to the Rule, ~ Science News 128: 314-315.</Paragraph>
    <Paragraph position="1"> ity. Next I prove that the universal recognition problem for current GPSG theory is Exp-Poly hard, and assuredly intractable. 2 That is, the problem of determining for an arbitrary GPSG G and input string z whether x is in the language L(G) generated by G, is exponential polynomial time hard. This result puts GPSG-Recognition in a complexity class occupied by few natural problems: GPSG-Recognition is harder than the traveling salesman problem, context-sensitive language recognition, or winning the game of Chess on an n x n board. The complexity classification shows that the fastest recognition algorithm for GPSGs must take exponential time or worse. One role of a computational analysis is to provide formal insights into linguistic theory. To this end, this paper pinpoints sources of complexity in the current GPSG theory and concludes with some linguistically and computationally motivated restrictions.</Paragraph>
  </Section>
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