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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 Context-Free 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.

There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This paper concerns the relationship between the class of string languages generated by several such formalisms viz. Combinatory Categorial Grammars, Head Grammars, Linear Indexed Grammars and Tree Adjoining Grammars. Each of these formalisms is known to generate a larger class of languages than Context-Free Grammars. The four formalisms under consideration were developed independently and appear superficially to be quite different from one another. The result presented in this paper is that all four of the formalisms under consideration generate exactly the same class of string languages. 1 Introduction There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This is based on the argument that a grammar formalism should not merely be viewed as a notation, but as part o...

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this paper we present a scheme to extend a recognition algorithm for Context-Free Grammars (CFG) that can be used to derive polynomial-time recognition algorithms for a set of formalisms that generate a superset of languages generated by CFG. We describe the scheme by developing a Cocke-Kasami-Younger (CKY)-like pure bottom-up recognition algorithm for Linear Indexed Grammars and show how it can be adapted to give algorithms for Tree Adjoining Grammars and Combinatory Categorial Grammars. This is the only polynomial-time recognition algorithm for Combinatory Categorial Grammars that we are aware of

this paper, we present a generalized form of SVG, which supports additional biologically-relevant operations by going beyond homomorphisms, instead uniformly applying substitutions in either a forward or reverse direction (see Definition 2.1) to bindings of logic variables. We give a constructive proof of our conjecture [26] that the languages describable by SVG are contained in the indexed languages, and furthermore show that the containment is proper, thus refining the position of an important class of biological sequences in the hierarchy of languages. We also describe a simple grammar translator, give a number of examples of mathematical and biological languages, discuss the distinctions between SVG, DG, TAG, and RPDAs, and suggest extensions well-suited to the overlapping languages of genes. Finally, we describe a large-scale implementation of a domain-specific parser called GenLang which incorporates a practical version of these ideas, and which has been successful in parsing several types of genes from DNA sequence data [9, 30], in a form of pattern-matching search termed syntactic pattern recognition [10]. 6 2. STRING VARIABLE GRAMMAR

This paper introduces a paradigm of context-dependent grammar (CDG) and an acquisition system that, through interactive teaching sessions, accumulates the CDG rules. The resulting context-sensitive rules are used by a stack-based, shift~reduce parser to compute unambiguous syntactic structures of sentences. The acquisition system and parser have been applied to the phrase structure and case analyses of 345 sentences, mainly from newswire stories, with 99 % accuracy. Extrapolation from our current grammar predicts that about 25 thousand CDG rule examples will be sufficient to train the system in phrase structure analysis of most news stories. Overall, this research concludes that CDG is a computationally and conceptually tractable approach for the construction of sentence grammar for large subsets of natural language text. 1.

An account of grammatical acquisition is developed within the parametersetting framework applied to a generalized categorial grammar (GCG). The GCG is embedded in a default inheritance network yielding a natural partial ordering (reflecting generality) of parameters which determines a partial order for parameter setting. Computational simulation shows that several resulting acquisition procedures are effective on a parameter set expressing major typological distinctions based on constituent order, and defining 70 distinct full languages and over 200 subset languages. The effects on acquisition of inductive bias, that is, of differing initial parameter settings, are explored via computational simulation. Computational simulation of populations of language learners and users instantiating the acquisition model show: 1) that variant acquisition procedures, with differing inductive biases, exert differing selective pressures on the evolution of language(s); 2) acquisition proc...

This paper outlines a simple and general notion of syntactic category on a metatheoretical level, independent of the notations and substantive claims of any particular grammatical framework. We define a class of formal objects called "category structures" where each such object provides a constructive definition for a space of syntactic categories. A unification operation and subsumption and identity relations are defined for arbitrary syntactic categories. In addition, a formal language for the statement of constraints on categories is provided. By combining a category structure with a set of constraints, we show that one can define the category systems of several well-known grammatical frameworks: phrase structure grammar, tagmemics, augmented phrase structure grammar, relational grammar, transformational grammar, generalized phrase structure grammar, systemic grammar, categorial grammar, and indexed grammar. The problem' of checking a category for conformity to constraints is shown to be soivable in linear time. This work provides in effect a unitary class of data structures for the representation of syntactic categories in a range of diverse grammatical frameworks. Using such data structures should make it possible for various pseudo-issues in natural language processing research to be avoided. We conclude by examining the questions posed by set-valued features and sharing of values between distinct feature specifications, both of which fall outside the scope of the formal system developed in this paper