Showing papers on "Context-sensitive grammar published in 1969"

Practical translators for lr(k) languages

Abstract: A context-free syntactical translator (CFST) is a machine which defines a translation from one context-free language to another. A transduction grammar is a formal system based on a context-free grammar and it specifies a context-free syntactical translation. A simple suffix transduction grammar based on a context-free grammar which is LR(k) specifies a translation which can be defined by a deterministic push-down automation (DPDA). A method is presented for automatically constructing CFSTs (DPDAs) from those simple suffix transduction grammars which are based on the LR(k) grammars. The method is developed by first considering grammatical analysis from the string-manipulation viewpoint, then converting the resulting string-manipulation.

Probabilistic and weighted grammars

Abstract: Devices for the generation of languages, corresponding to the probabilistic recognition devices or probabilistic automata, are introduced and the resulting families of languages are investigated. Comparisons are made with some other recently introduced grammars, where restrictions are imposed not only on the form of the rewriting rules but also on the use of them. A uniform representation for such grammars is provided by the notion of a grammar with a prescribed control language for the derivations.

Properties of deterministic top down grammars

Abstract: The class of context free grammars that can be deterministically parsed in a top down manner with a fixed amount of look-ahead is investigated. These grammars, called LL(k) grammars where k is the amount of look-ahead are first defined and a procedure is given for determining if a context free grammar is LL(k) for a given value of k. It is shown that e-rules can be eliminated from an LL(k) grammar, at the cost of increasing the value of k by one, and a description is given of a canonical pushdown machine for recognizing LL(k) languages. It is shown that for each value of k there are LL(k+l) languages that are not LL(k) languages. It is shown that the equivalence problem is decidable for LL(k) grammars. Additional properties are also given.

On equal matrix languages

Abstract: A generative grammar called equal matrix grammar which generates a class which meets both context-sensitive and context-free languages is defined and the formal power series generated by context-free grammars is extended to grammars of this system. The Parikh mapping of this family of languages is shown to be semilinear. The Boolean and closure properties of a certain subfamily are examined. For this subfamily, the generative power of equal matrix grammar is higher than that of context-free grammars. For certain inherently ambiguous context-free languages, including that of Parikh, unambiguous grammars of this class exist. The application of equal matrix grammar to the generation of Tamil kernel sentences is given in the appendix.

Context-free grammars on trees

Abstract: In this paper we discuss still another version of indexed grammars 1 and macro grammars3,gaining some geometric intuition about the structure of these systems. An ordinary context-free grammar is a rewriting system for strings; we find that a macro grammar is a rewriting system for trees. CF grammars on strings form a special case since strings can be thought of as trees without branching nodes. We consider the special case of finite-state grammars in this report. We define the tree analogue of a non deterministic generalized sequential machine and obtain results about the domain and range of such a mapping. We relate these results to the theory of generalized finite automata6.

Some properties of precedence languages

Abstract: The classes of languages definable by operator precedence grammars1 and by Wirth-Weber precedence grammars2 are studied. A grammar is backwards-deterministic3 if no two productions have the same right part. Operator precedence grammars have no more generative power than backwards deterministic operator precedence grammars, but Wirth-Weber precedence grammars (i.e., grammars having unique Wirth-Weber precedence relations) are more powerful than backwards-deterministic Wirth-Weber precedence grammars; indeed they can generate any context-free language. An algorithm is developed for finding a Wirth-Weber precedence grammar equivalent to a given operator precedence grammar, a result of possible practical significance. The operator precedence languages are shown to be a proper subclass of the backwards-deterministic Wirth-Weber precedence languages which in turn are a proper subclass of the deterministic context-free languages.

A Syntax-Analysis Procedure for Unambiguous Context-Free Grammars

Abstract: A syntax-analys is Mgorithm is presented for a language generated by an unambiguous context-free grammar in a number of e lementary operat ions proportional to n = log n, where n is the length of a given string, using a random access memory. The amount of memory required for the a lgor i thm is proport ional to n 2 log n. The proposed algori thm is a modified version of Cocke's a lgor i thm and utilizes a eertair, proper ty of unambiguous normal grammars .

String adjunct grammars

Abstract: In this paper, we have introduced a new style of formal grammars called String Adjunct Grammars (AG) The rules in an AG have a considerably different formal character as compared to the 'rewrite rule' in a Phrase Structure Grammar (PSG) Such a study of formal grammars of different styles (ie, formal character of rules) is of great interest because each style is well suited for characterizing certain aspects of natural language structure and is awkward for characterizing certain other aspects Several subclasses of AG's motivated by strong linguistic considerations have been studied, comparing them with PSG's Linguistic relevance of these grammars (and other gram mars suggested by this study) has been discussed at the end

Property grammars and table machines

Abstract: A method is given for generalizing context free grammars to include infinite terminal sets. The new grammar has many of the properties of context free grammars (e.g. membership is decidable and recognition by a suitably generalized nondeterministic pushdown device is always possible). Yet, treating each identifier as a separate terminal symbol, the grammar has enough power to describe all of the syntactic and semantic constraints of the declaration structure for variables and labels in ALGOL-60.

Transformational classes of grammars

Abstract: Given two Chomsky grammars G and \-G, a homomorphism φ from G to \-G is, roughly speaking, a map which assigns to every derivation of G a derivation of \-G in such a manner that φ is uniquely determined by its restriction to the set of productions of G. Two grammars are contained in the same transformational class, if the one can be transformed into the other by a sequence of homomorphisms. If two grammars are related in such a manner, then there are two relations, one concerning the words of the languages generated and the other regarding the derivations of these words. We establish several classifications of context-free grammars in transformational classes which are recursively solvable.

Properties of formal grammars with mixed types of rules and their linguistic relevance

Abstract: In this paper, we will study a class of formal grammars with mixed types of rules. The reason for considering such grammars is that no single style (i.e., formal character of rules) of formal grammars is able to represent the various aspects of language structure in a natural way. Various considerations for setting up such grammars have been discussed. Generation schemes which map strings in the language of one mixed grammar into strings in the language of another mixed grammar (both strings being 'well-formed') have been studied. Linguistic relevance of these concepts has also been discussed.

A system for designing fast programming language translators

Abstract: This paper demonstrates a straightforward algorithm for converting programming language grammars into pushdown-store automata translators. The language grammar is written as a "translation grammar" in which, for each syntactic rule, there is a corresponding "rule of translation" that recursively specifies the reverse Polish string translation of the objects in the syntactic rule. This augmented grammar is transformed directly into a flow chart for the appropriate translator.

Parallel leveled grammars

Abstract: A new type of grammar, called a parallel leveled grammar, is introduced. The families of languages generated by such grammars with contextfree, linear or right-linear subrules are studied. Right-linear parallel finite-leveled languages can be displayed as nested vector expressions, which are extensions of regular expressions. Various hierarchy theorems for these families of languages are obtained. A normal form for context-free parallel leveled grammars is derived and connections of these with other families of languages are investigated.

A note on enumerable grammars

Abstract: A concept of a generalized grammar with an enumerable set of productions is introduced. Some of the generalized grammars, called “ω-regular grammars”, are considered. The recursiveness of languages generated by ω-regular grammars is proved.

A note on top-down deterministic languages

Abstract: In recent years attempts have been made to characterize those languages to which deterministic top-down analysis is applicable. This note examines the relationships between the various classes of grammars that are known to this author.

Generating parsers for BNF grammars

Abstract: The procedure described herein is in essence an extension, albeit a simplification, of the work Earley which in turn was based on Evans, Feldman, Floyd, and Standish. For a large subset of grammars, the procedure maps the Backus Naur Form (BNF) definition of the grammar of a language into a deterministic, left-to-right parser for the sentences in that language. It is shown below that the procedure by design, covers all bounded right context grammars and, as a by-product, some LR(k) grammars which are not bounded right context. See Knuth for the definitions of these classes of grammars. If two parameters are incorporated a priori into the procedure, one limiting the look-back and the other limiting the look-ahead capabilities of the parser to be generated, an algorithm results. For each BNF grammar G the algorithm either rejects G as not bounded right context for the specified limits or it generates a parser for G.

A note on one-sided context-sensitive grammars.

Abstract: In this note it is proved that so called one-sided context-sensitive grammars can generate languages which cannot be generated by any context-free grammar. This fact is not quite new. It has been proved in [3], [4] and [5] (as far as the author knows). In [3] it is proved that a special one-sided context-sensitive grammar suggested by Dr. Fris ([1]) generates a language {a m b'\"c\"; Hn^ m} which is not context-free. In [5] an example of a one-sided context-sensitive grammar is given and in [4] there is proved, concerning this grammar, that it generates a well-known language {a\"b\"c\"; n £ 1}. The proofs given in [3] and [4] are rather complicated though the grammars in question contain about 20 rules only. The aim of the present note is to give a simple proof of the above-mentioned statement. Let us define a one-sided context-sensitive grammar G = (V T , V N , R, S> as follows:

Decidability of a class of grammars

Abstract: A PROOF is given of the decidability of some family of classes of grammars to which the class et, described in [ll belongs. The construction used in the proof is close in idea to the construction used by Knuth [2l to prove the decidability of the important class LR t/d. It should be mentioned that the results obtained in 121 became known to the author only while the present paper was being prepared for press. 1. We will call a context-free grammar a system