Showing papers on "Context-sensitive grammar published in 1973"

Associate languages and derivational complexity of formal grammars and languages

Abstract: A criterion to measure derivational complexity of formal grammars and languages is proposed and discussed. That is, the associate language and the L-associate language are defined for a grammar such that the former represents all the valid derivations and the latter represents all the valid leftmost derivations. It is shown that for any phrase\3-structure grammar, the associate language is a contex\3-sensitive language and the L\3-associate language is a context\3-free language. Necessary and sufficient conditions for an associate language to be a regular set and to be a context\3-free language are found. The idea in the above necessary and sufficient conditions is extended to the notion of “rank≓ for a measure of derivational complexity of context\3-free grammars and languages. It is shown that for each nonnegative integer k, there exists a context\3-free language whose rank is k. The paper also includes a few solvable decision problems concerning derivational complexity of grammars.

The use of grammatical inference for designing programming languages

Abstract: Both in designing a new programming language and in extending an existing language, the designer is faced with the problem of deriving a “natural” grammar for the language. We are proposing an interactive approach to the grammar design problem wherein the designer presents a sample of sentences and structures as input to a grammatical inference algorithm. The algorithm then constructs a grammar which is a reasonable generalization of the examples submitted by the designer. The implemention is presently restricted to a subclass of operator precedence grammars, but a second algorithm is outlined which applies to a larger class of context-free grammars.

On sentential forms of context-free grammars

Abstract: There is no algorithm for deciding whether two linear context-free grammars generate the same sentential forms. The equivalence problem for propagatingOL-systems is undecidable. The finiteness problem forOL-systems is decidable.SF-languages, i.e., languages which equal the set of sentential forms of a context-free grammar, possess some of the properties of context-free languages but their family is not closed under any of the ordinary operations.

Equivalence between AND/OR graphs and context-free grammars

Abstract: Recent research in artificial intelligence has led to AND/OR graphs as a model of problem decomposition (Nilsson [3]; Simon and Lee [4]). However, AND/OR graphs of a restricted type are equivalent to context-free grammars. This can be set-up formally (the beginnings of a formalism of AND/OR graphs is contained in [4]), but the formalism is so obvious that a brief discussion and example suffice.

How to Make Arbitrary Grammars Look Like Context-Free Grammars

Abstract: Normal form theorems which factor arbitrary phrase-structure grammars into context-free grammars and “a little more” are presented. Every phrase-structure grammar is proven equivalent to one in which each production is either context-free or pure erasing. A pda-like machine is shown to characterize the phrase-structure languages.

Array grammar normal forms

Abstract: The language of an array grammar has been defined as the set of finite, connected terminal arrays, surrounded by #'s, that can be derived from an initial S surrounded by #'s. In the first section of this paper, it is shown that any array language has an array grammar in which all terminal arrays are in fact connected; and that the set of terminal, finite connected components of non #'s that occur in the sentential forms of any array grammar is an array language. Thus several possible ways of defining an array language are in fact all equivalent. In the second section of the paper, it is shown that array grammars need not use #'s as context. It is also shown that array grammars which start with arbitrary initial arrays of S's, and neither create nor destroy #'s, have exactly the same power as monotonic array grammars. In the third section, parallel array grammars are defined, and it is shown that any (monotonic) sequential array language is a (monotonic) parallel array language and vice versa.

On matrix languages

Abstract: The matrix grammar is a well-known concept of a grammar with restricted use of productions. By weakening the matrix restrictions imposed on context-free grammars several new types of grammars are introduced; some of them are proved to possess the same generative power as ordinary matrix grammars; for some other types inclusion properties are obtained.

Generalized context-free grammars.

Abstract: 1 . Introduction. Generalized context-free grammars can be thought of as contextfree grammars all rules of which are of the form A where a is a regular expression. Generalized context-free grammars and their representation by a set of finitestate diagrams are a convenient tool to describe context-free languages. In this paper a classification of context-free languages according to the minimal number of non-terminals of generalized context-free grammars is studied and the corresponding decision problems are investigated.

On the structure of context-sensitive grammars

Abstract: It is well known that the family of context-sensitive grammars generate languages which are not context-free and that it is undecidable whether a context-sensitive grammar generates a context-free language. However, the mechanism by which the use of context allows a non-context-free language to be generated is not well understood. In this paper we attempt to focus on this problem by surveying some of the results which speak to two questions: (i) What constraints can be placed on the form of the rules of context-sensitive grammars without restricting the weak generative capacity? (ii) What (nontrivial) constraints can be placed on the form of the rules of context-sensitive grammars such that only context-free languages will be generated?

Normal forms for context-sensitive grammars

Abstract: In this paper, we mainly study the relation between scattered context grammars, which are an example for regulated context-free rewriting devices, and context-sensitive grammars. Emphasis is laid upon both normal form characterizations of context-sensitive grammars and an argument in how far scattered context grammars are stronger, with respect to generative capacity than unordered scattered context grammars.

Some remarks on state grammars and matrix grammars

Abstract: The context-free matrix grammar and the state grammar without any restriction in applying productions are considered. It turned out that these grammars are equivalent in the generative power. Another type of state grammar called the state grammar with unconditional transfer is introduced, and it is shown that each context-free matrix language is a homomorphic image of the intersection of a state language with unconditional transfer and a regular set.

Structural Descriptions, Transformational Rules, and Pattern Analysis.

Abstract: : In the paper two equivalent notations are defined for describing the structure assigned to graph-like patterns by web grammar derivations. The notion of a transformational rule for webs is defined and the use of transformational rules for describing structural relations among webs that cannot be indicated by context-free web grammars is illustrated. (Author)

On ordered context-free grammars

Abstract: An extension for the concept of the finite index of context-free grammars is introduced and regular control languages are derived for the resulting family of languages generated by ordered context-free grammars.

Constructions of Grammars for Formal Languages.

Abstract: The present invention relates to novel 1-azaxanthone-3-carboxylic acid and its derivatives usable for effective medicines for the treatment of allergic diseases, which are shown by the following formula (I) (I) wherein R1 is hydrogen, alkyl, phenyl, carboxyl, hydroxyl, alkoxy or amino group which may be unsubstituted or substituted by one alkyl, m is 0, 1 or 2 and R2 is alkyl, alkoxy, halogen, nitro, hydroxy, carboxyl, butadienylene (-CH=CH-CH=CH-) which forms a benzene ring with any adjacent carbon atoms or amino group which may be unsubstituted or substituted by at least one alkyl, and their physiologically acceptable salts.

Periodic representation of equal matrix grammars

Abstract: A substantial amount of research in formal grammars recently has been to impose constraints on the use of rules in addition to the restrictions on the form of the rules of grammars. Time-variant grammars and equal matrix grammars are amoung them. It has been shown here that for each equal matrix grammar, there is a procedure to systematically construct the almost right linear periodic grammar equivalent to it.

On the Representation of Generative Grammars as First-Order Theories

Abstract: As is well known, a generative grammar is considered by Chomsky as a set of rules that, in particular, generates the sentences of a language. In this paper I shall try to make it plausible that for each such generative rule system a corresponding first-order theory can be effectively constructed such that, roughly speaking, what can be generated by the grammar, can be logically derived within this theory. A grammar represented as a first-order theory will provide thus, above all, a deductive nomological explanation of the sentences of a language in the sense of theory of knowledge (Wang, 1971b). We shall treat at first the problem of representation of the well-defined context-free grammar and then that of the less formalized transformational grammar.

SENTENCE GRAMMAR, TEXT GRAMMAR, AND THE EVALUATION PROBLEM Some Remarks Concerning the Theoretical Foundation and the Possible Application of Text Grammars

Abstract: O. The text grammars set up so far generalize the formal properties of specific types of sentence grammar.! This procedure, widely accepted among text linguists, led us to the assumption that text grammars developed from a specific type of sentence grammar will have the formal and empirical prop­ erties of this model sentence grammar. This assumption will be dealt with in this paper.2 Another feature of the text grammars set up so far is closely connected with the theoretical and practical aims such text grammars try to meet: We think that not only the sentence grammar chosen as a model for the construction of a text grammar and the practical interests which led to its construction determine its theoretical power but also its supposed domain of application. Thus the meta-theoretical part of a text grammar may in­ clude the postulate that the grammar must reconstruct the semantic relations between two arbitrary texts belonging to a certain extensionally delimitable subset of the set of all texts of a natural language. This subset might e.g. consist of the legal texts valid during some time interval. The domain of application of the text grammar in question would then be this subset of the set of all texts of a given natural language. 3 If two text grammars are said to obey the same theoretical postulates and to cover the same domain of application it may be inferred that the text grammars in question are equi­ valent relative to the underlying theoretical postulates and the chosen domain of application. Supposing now that one grammar out of the two proves to be more successful in meeting the theoretical postulates and in covering the pre-set domain of application, then this success would naturally count strongly against the other type of text grammar. The test as to whether two text grammars are equivalent relative to a given domain of application may thus serve as an evaluation procedure and, as far as we can judge, this kind of evaluation, informal and intuitive as it may be, is at least one possible way to get better and more powerful text grammars. It must be added that the 1 Cf. e.g. J. S. Pet6fi'sgoal to set up a text grammar according to the principles of generative semantics in [19], pp. 248-273, [21], pp. 33-47 and [24]; van Dijk treats somewhat ana­ logous problems in [7], pp. 12-23 and 34-159; the question of the generalizability ofPSGs is discussed in [30], [31], [32], and [33]. 2 This hypothesis was discussed first in [3], [32], and [33]. 3 This specific domain of application was chosen for practical reasons, cf. [3], [27], and [28] for further information. Other interesting domains of application are discussed by T. A. van Dijk, J. Ihwe and J. S. Pet6fi in their contributions to this volume.