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Computational Complexity of Current GPSG Theory
 Proceedings of the 24th annual Meeting of the Association for Computational Linguistics
, 1986
"... An important goal of computational linguistics has been to use linguistic theory to guide the construction of computationally efficient realworld natural language processing systems. At first glance, generalized phrase structure grammar (GPSG) appears to be a blessing on two counts. First, the prec ..."
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An important goal of computational linguistics has been to use linguistic theory to guide the construction of computationally efficient realworld 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 fransparent guide for parser design and implementation. Second, since GPSG has weak contextfree generative power and contextfree languages can be parsed in O(n ~) by a wide range of algorithms, GPSG parsers would appear to run in polynomial time. This widelyassumed GPSG "efficient parsability " result is misleading: here we prove that the universal recognition problem for current GPSG theory is exponentialpolynomial 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. 1
Practical Parsing of Generalized Phrase Structure Grammars
 Computational Linguistics
, 1989
"... this paper. Because a GPSG is so closely related to a CFG, it was thought that the wellknown efficient parsing techniques for CFGs could be applied, with modifications, to GPSGs, and that GPSGs would therefore be computationally tractable. Recently, however, Ristad (1985) has shown that this is no ..."
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this paper. Because a GPSG is so closely related to a CFG, it was thought that the wellknown efficient parsing techniques for CFGs could be applied, with modifications, to GPSGs, and that GPSGs would therefore be computationally tractable. Recently, however, Ristad (1985) has shown that this is not the case, and that the unrestricted GPSG parsing problem is NPcomplete (on the total problem size, viz. grammar plus input sentence) . Even before Ristad's result was known, workers in this field had found the practical problems caused by the interaction of FCRs, FSDs, and the propagation conventions difficult to surmount. Briscoe's comments (1986) are typical: "Finally, the concept of privileged feature, its interaction with feature specification defaults and the bidirectionality of the head feature convention are all so complex that it is debatable how much use they would be in a practical system (even if we did manage to implement them)" (p. 1); "The interaction of feature cooccurrence restrictions, feature specification defaults and feature propagation proved very hard to implement/understand" (p. 2)
Practical Parsing of Generalised Phrase Structure Grammars
, 1987
"... An efficient algorithm is described for parsing a dialect of generalised phrase structure grammar (GPSG). A practical parsing system, based on the algorithm, is presented. The dialect of GPSG which the parsing system accepts is smaller, but considerably "purer" (closer to the original defi ..."
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An efficient algorithm is described for parsing a dialect of generalised phrase structure grammar (GPSG). A practical parsing system, based on the algorithm, is presented. The dialect of GPSG which the parsing system accepts is smaller, but considerably "purer" (closer to the original definition of GPSG) and mathematically "cleaner" than that which is accepted by other practical parsing systems. In particular, the parsing system correctly implements feature cooccurrence restrictions, subject only to the restriction that the FCR set can be expressed in clausal form as a set of Horn clauses.
On the Complexity of ID/LP Parsing
, 1985
"... this paper have illustrated, contextfree generarive power does not guarantee efficient parsability. Every ID/LP grammar technically generates a contextfree language, but the potentially large size of the corresponding CFG means that we can't count on that fact to give us efficient parsing. Th ..."
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this paper have illustrated, contextfree generarive power does not guarantee efficient parsability. Every ID/LP grammar technically generates a contextfree language, but the potentially large size of the corresponding CFG means that we can't count on that fact to give us efficient parsing. Thus it is impossible to sustain this particular argument for the advantages of such formalisms as (early) GPSG over other linguistic theories; instead, GPSG and other modern theories seem to be (very roughly) in the same boat with respect to complexity. In such a situation, the linguistic merits of various theories are more important than complexity results. (See Berwick (1982), Berwick and Weinberg (1982, 1984), and Ristad (1985) for further discussion.) The reduction does not rule out the use of formalisms that decouple ID and LP constraints; note that Shieber's direct parsing algorithm wins out over the use of the object grammar. However, if we assume that natural languages are efficiently parsable (EP), then computational difficulties in parsing a formalism do indicate that the formalism itself does not tell the whole story. That is, they point out that the range of possible languages has been incorrectly characterized: the additional constraints that guarantee efficient parsability remain unstated. Since the general case of parsing ID/LP grammars is computationally difficult, if the linguistically relevant ID/LP grammars are to be efficiently parsable, there must be additional factors that guarantee a certain amount of constraint from some source. TM (Constraints beyond the bare ID/LP formalism are required on linguistic grounds as well.) Note that the subset principle of language acquisition (cf. Berwick and Weinberg 1984:233) would lead the language learner to initially hyp...