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Characterizing Structural Descriptions Produced By Various Grammatical Formalisms
 IN PROCEEDINGS OF THE 25TH ANNUAL MEETING OF THE ASSOCIATION FOR COMPUTATIONAL LINGUISTICS
, 1987
"... We consider the structural descriptions produced by various grammatical formalisms in terms of the complexity of the paths and the relationship between paths in the sets of structural descriptions that each system can generate. In considering the relationship between formalisms, we show that it is u ..."
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We consider the structural descriptions produced by various grammatical formalisms in terms of the complexity of the paths and the relationship between paths in the sets of structural descriptions that each system can generate. In considering the relationship between formalisms, we show that it is useful to abstract away from the details of the formalism, and examln the nature of their derivation process as reflected by properties of their derivation trees. We find that several of the formalisms considered can be seen as being closely related since they have derivation ee sets with the same structure as those produced by ContextFree Grammars. On the basis of this observation, we describe a class of formalisms which we call Linear Context Free Rewritin Systems, and show they are recognizable in polynomial time and generate only semilinear languages.
A Descriptive Approach to LanguageTheoretic Complexity
, 1996
"... Contents 1 Language Complexity in Generative Grammar 3 Part I The Descriptive Complexity of Strongly ContextFree Languages 11 2 Introduction to Part I 13 3 Trees as Elementary Structures 15 4 L 2 K;P and SnS 25 5 Definability and NonDefinability in L 2 K;P 35 6 Conclusion of Part I 57 DRAFT ..."
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Cited by 59 (3 self)
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Contents 1 Language Complexity in Generative Grammar 3 Part I The Descriptive Complexity of Strongly ContextFree Languages 11 2 Introduction to Part I 13 3 Trees as Elementary Structures 15 4 L 2 K;P and SnS 25 5 Definability and NonDefinability in L 2 K;P 35 6 Conclusion of Part I 57 DRAFT 2 / Contents Part II The Generative Capacity of GB Theories 59 7 Introduction to Part II 61 8 The Fundamental Structures of GB Theories 69 9 GB and Nondefinability in L 2 K;P 79 10 Formalizing XBar Theory 93 11 The Lexicon, Subcategorization, Thetatheory, and Case Theory 111 12 Binding and Control 119 13 Chains 131 14 Reconstruction 157 15 Limitations of the Interpretation 173 16 Conclusion of Part II 179 A Index of Definitions 183 Bibliography DRAFT 1<
Systematic Parameterized Complexity Analysis in Computational Phonology
, 1999
"... Many computational problems are NPhard and hence probably do not have fast, i.e., polynomial time, algorithms. Such problems may yet have nonpolynomial time algorithms, and the nonpolynomial time complexities of these algorithms will be functions of particular aspects of that problem, i.e., the a ..."
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Cited by 18 (3 self)
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Many computational problems are NPhard and hence probably do not have fast, i.e., polynomial time, algorithms. Such problems may yet have nonpolynomial time algorithms, and the nonpolynomial time complexities of these algorithms will be functions of particular aspects of that problem, i.e., the algorithm's running time is upper bounded by f(k)jxj c where f is an arbitrary function, jxj is the size of the input x to the algorithm, k is an aspect of the problem, and c is a constant independent of jxj and k. Given such algorithms, it may still be possible to obtain optimal solutions for large instances of NPhard problems for which the appropriate aspects are of small size or value. Questions about the existence of such algorithms are most naturally addressed within the theory of parameterized computational complexity developed by Downey and Fellows. This thesis considers the merits of a systematic parameterized complexity analysis in which results are derived relative to all subsets of a specied set of aspects of a given NPhard problem. This set of results denes an \intractability map " that shows relative to
On Descriptive Complexity, Language Complexity, and GB
, 1995
"... ..., a monadic secondorder language for reasoning about trees which characterizes the strongly ContextFree Languages in the sense that a set of nite trees is de nable in L2 K�P i it is (modulo a projection) a Local Set  the set of derivation trees generated by aCFG. This provides a exible appro ..."
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Cited by 6 (4 self)
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..., a monadic secondorder language for reasoning about trees which characterizes the strongly ContextFree Languages in the sense that a set of nite trees is de nable in L2 K�P i it is (modulo a projection) a Local Set  the set of derivation trees generated by aCFG. This provides a exible approach to establishing languagetheoretic complexity results for formalisms that are based on systems of wellformedness constraints on trees. We demonstrate this technique by sketching two such results for Government and Binding Theory. First, we show that freeindexation, the mechanism assumed to mediate a variety of agreement and binding relationships in GB, is not definable in L2 K�P and therefore not enforcible by CFGs. Second, we showhow, in spite of this limitation, a reasonably complete GB account of English can be defined in L2 K�P. Consequently, the language licensed by that account is strongly contextfree. We illustrate some of the issues involved in establishing this result by looking at the definition, in L2 K�P,ofchains. The limitations of this definition provide some insight into the types of natural linguistic principles that correspond to higher levels of language complexity. We close with some speculation on the possible significance
On the Mathematical Properties of Linguistic Theories
, 1984
"... This paper surveys some of these results and discusses their significance for linguistic theory. However, we will avoid entirely the issue of whether one theory is more descrip tively adequate than another. We will consider context free, transformational, lexicalfunctional, generalized phrase st ..."
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This paper surveys some of these results and discusses their significance for linguistic theory. However, we will avoid entirely the issue of whether one theory is more descrip tively adequate than another. We will consider context free, transformational, lexicalfunctional, generalized phrase structure, tree adjunct, and stratificational grammars) Although this paper focuses on metatheoretic results as arbiters among theories as models of human linguistic capacities, they may have other uses as well. Complexity results could be utilized for making decisions about the implementation of parsers as components of computerbased languageunderstanding systems. However, as Stanley Peters has pointed out, no one should underestimate "the pleasure to be derived from ferreting out these results! 3 2. Preliminary Definitions We assume that the reader is familiar with the basic defi nitions of regular, contextfree (CF), contextsensitive (CS), recursive, and recursively enumerable (r.e.) languages, as well as with their acceptors (see Hopcroft and Ullman 1979). We will be much concerned with the problem of recognizing whether a string is contained in a given language (the recognition problem) and with that of 1 This research was sponsored in part by the National Science and Engineering Research Council of Canada under Grant A9285. It was made possible in part by a gift from the Systems Development Foundation. An earlier version of this paper appeared in the Proceedings of the 21st ,4nnual Meeting of the ,4ssociation for Computational Linguistics, Cambridge, MA, June 1983