Showing papers on "Tree-adjoining grammar published in 1972"

Some aspects of text grammars

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Some decidability results on grammatical inference and complexity

Abstract: The problem of grammatical inference is considered and a number of positive answers to decidability questions obtained. Conditions are prescribed under which it is possible for a machine to infer a grammar (or the best grammar) for even the general rewriting systems.

On the Covering and Reduction Problems for Context-Free Grammars

Abstract: A formal definition of one grammar \"covering\" another grammar is presented. I t is argued that this definition has the property that G' covers G when and only when the ability to parse G' suffices for parsing G. I t is shown that every grammar may be covered by a grammar in canonical two form. Every A-free grammar is covered by an operator normal form grammar while there exist grammars which cannot be covered by any grammar in Greibach form. Any grammar may be covered by an invertible grammar. Each A-free and chain reduced LR(k) (bounded right context) grammar is covered by a precedence detectable, LR(k) (bounded right context) reducible grammar.

Some restrictive devices for context-free grammars

Abstract: For context-free grammars the restrictive devices of unordered scattered context, random context, partial ordering of productions and concatenation of productions in matrices are compared with respect to their generative power. This leads to two new characterizations of the family of type O languages in terms of unordered scattered context grammars and random context grammars, respectively. Languages generated by context-free grammars by imposing one of the above-mentioned restrictive devices or programming, regular control language, periodic time-variance or context-sensitivity are shown to have in the case of finite index a property similar to the “uvwxyproperty≓ of context-free languages.

Matrix Grammars with a Leftmost Restriction

Abstract: The family of languages generated by matrix grammars with context-free (context-free λ -free) core productions and with a leftmost restriction on derivations equals the family of recursively enumerable (context-sensitive) languages.

Probabilistic grammars and automata

Abstract: A mathematical formulation of probabilistic grammars, as well as the random languages generated by probabilistic grammars, is introduced. Various types of probabilistic grammars are considered. The relations between these grammars and the corresponding types of probabilistic automata are examined.

Terminal Context in Context-Sensitive Grammars

Abstract: If every non-context-free rewriting rule of a context-sensitive (with erasing) grammar has as left context a string of terminal symbols and the left context is at least as long as the right context, then the language generated is context-free If every non-context-free rewriting rule of a context-sensitive (with erasing) grammar has as left and right context strings of terminal symbols, then the language generated is context-free

String adjunct grammars: I. Local and distributed adjunction

Abstract: In this paper [and in Joshi et al. (1972) which is a sequel to this paper] a new style of formal grammar called String Adjunct Grammars (AG) has been studied. The rules in an AG have a character essentially different from the “rewrite rule” in a Phrase Structure Grammar (PSG). Such a study of formal grammars of different styles is of great interest because each style is well suited for characterizing certain aspects of natural language structure but has inherent difficulty in characterizing certain other aspects. Several subclasses of AG's motivated by strong linguistic considerations have been studied. Linguistic relevance of these grammars and other grammars suggested by this study has also been discussed.

Generating parsers for affix grammars

Abstract: Affix grammars are two-level grammars which are similar to van Wijngaarden's two-level grammars used in the definition of Algol 68. Affix grammars are shown by Koster to be equal in power to van Wijngaarden grammars. They are much more suited to parsing than are the latter, however. Koster, the inventor of affix grammars, suggests a top-down scheme for parsing them, based on recursive procedures. This paper presents a bottom-up scheme for parsing them, based on an extension of Floyd Production Language (FPL). Included is an algorithm, similar to that of DeRemer's, for converting a large class of affix grammars into FPL. The paper concludes by discussing briefly the applicabilities of the conversion algorithm and affix grammars in general, and some possible extensions to Koster's definition of affix grammars.

String adjunct grammars: II. Equational representation, null symbols, and linguistic relevance

Abstract: In this paper, we continue the study of String Adjunct Grammars (AG) introduced in Joshi et al. (1972). In particular, equational representations of LAG's, LAG's with null symbols, and some special cases of LAG's are studied. Linguistic relevance of these grammars is also discussed in some detail.

On the size of context-free grammars.

Abstract: In papers [2] and [3] four criteria of complexity of context-free grammars (CFG's), denoted by Var, Lev, Lev„, and Depth, have been studied. These criteria reflect the intrinsic complexity of CFG's and they induce the criteria of complexity of contextfree languages (CFL's) which reflect the intrinsic complexity of the description of CFL's by CFG's. The criterion Prod (G) = the number of rules of a CFG G, studied in [3] represents the size of CFG's. In the present paper one more criterion of complexity of CFG's, namely Symb (G) = = the number of all occurrences of all symbols in the rules of G, is defined and some results concerning the criteria Prod and Symb are derived.

Program equivalence and context-free grammars

Abstract: This note defines a new equivalence relation among systems of recursion equations and a method for assigning context-free grammars to these systems, such that (1) The new equivalence implies strong equivalence; (2) Systems are equivalent in the new sense iff their grammars generate the same language; (3) There is a nontrivial decidable class of systems whose grammars have the decidability properties of LL(k) grammars Thus, the decidability of generative equivalence for LL(k) grammars mitigates the general undecidability of strong equivalence between arbitrary systems of recursion equations

Compound and serial grammars

Abstract: Two new classes of generative grammars are defined. The first class, the compound grammars, consists of grammars in which the initial symbol is replaced by the language generated by another grammar. The other class, the serial grammars, consists of sequences of compound grammars. The generative power of compound and serial grammars consisting of finite-state grammars is investigated.

Context-Sensitive Grammars Generating Context-Free Languages.

Abstract: Context -sens i t ive g r a m m a r s in which each rule is of the forln a Z f l -~ (-*Tfl are acyclic if the associa ted context-free g r a m m a r wi th the rules Z ~ 3' is acyclic. The prob lem whe the r an in tmt s t r ing is in the language genera ted by an acyclic contextsensi t ive g r a m m a r is NP-conlple te .

Direction controlled programmed grammars

Abstract: A generalization of the notion of a context-free grammar is presented here. It is based on the notion of a programmed grammar. When the underlying context-free rules do not contain erasing, the class of languages obtained is identical with the class of context-sensitive languages. With underlying context-free rules containing erasing one obtains the class of recursively enumerable languages.

Approximation of weighted type 0 languages by formal power series

Abstract: Productions of formal grammars may be given coefficients from certain semirings. These coefficients induce weights for both derivations in the grammar and strings over the terminal alphabet. The weighted grammars can be characterized by sets of equations, which in turn can be used to iteratively generate polynomial approximations to the weighted language. In order to study the sequence of approximations, we introduce the notion of a derivation in top-down form as a formalization of the concept of a derivation which rewrites all antecedents contained in a sentential form simultaneously. The height of a derivation in top-down form is the number of times the sentential form is rewritten. Our main result consists in establishing the relationship between the sequence of approximations of a weighted language and the derivations of a given height. This result is established for grammars in what we call standard form , but is not restricted to those grammars. As a corollary to our work, we show that every recursively enumerable set in V * can be expressed as an intersection of V * with the homomorphic image of a context-free language.

Arbitrary grammars generating context-free languages

Abstract: If G is a grammar such that in each noncontext-free rule of G, the right side contains a string of terminals longer than any terminal string appearing between two nonterminals in the left side; then the language generated by G is context-free Six previous results follow as simple corollaries of this theorem

Stochastic syntactic analysis and syntactic pattern recognition

Abstract: : Stochastic syntactic analysis algorithms for the class of stochastic context-free programmed languages are proposed and their application to pattern classification demonstrated. The area of grammatical inference is briefly reviewed and the possible extension to the inference of stochastic grammars is also studied. A stochastic grammar is formed by assigning a probability to each production associated with a grammar which is a formal system used conveniently to specify a language. The problem of deciding whether or not a stochastic grammar is consistent is called the consistency problem of stochastic languages. It is not yet known whether or not the consistency problem is decidable for stochastic context-sensitive grammars, stochastic programmed grammars and stochastic indexed grammars. Two types of stochastic syntatic analysis algorithms are proposed for stochastic context-free programmed languages. (Author)

Restricted Parallelism and Regular Grammars

Abstract: Title: Restricted Parallelism and Regular Grammars, Author: Robert D. Rosebrugh, Location: Thode

A Note on Bracketed Grammars

Abstract: In this note we show t h a t the family of languages generated by general two-type bracke ted grammars coincides wi th the family of recursively enumerable languages.

Partitioned Grammars and Syntax Analyzers

Abstract: Context-free grammars of programming languages can frequently be partitioned in a natural way, such that: in a well-defined sense, each subgrammar is complete, and each subgrammar possesses its own separate syntax analyzer.