Showing papers on "Context-sensitive grammar published in 1968"

Indexed Grammars—An Extension of Context-Free Grammars

Abstract: A new type of grammar for generating formal languages, called an indexed grammar, is presented. An indexed grammar is an extension of a context-free grammar, and the class of languages generated by indexed grammars has closure properties and decidability results similar to those for context-free languages. The class of languages generated by indexed grammars properly includes all context-free languages and is a proper subset of the class of context-sensitive languages. Several subclasses of indexed grammars generate interesting classes of languages.

Control sets on grammars

Abstract: Given a setC of strings of rewriting rules of a phrase structure grammarG, we consider the setL c (G) of those words generated by leftmost derivations inG whose corresponding string of rewriting rules is an element ofC. The paper concerns the nature of the setL c (G) whenC andG are assumed to have special form. For example, forG an arbitrary phrase structure grammar,L c (G) is an abstract family of languages ifC is an abstract family of languages, andL c (G) is bounded ifC is bounded.

Grammars with partial ordering of the rules

Abstract: It is proved that the languages generated by context-free grammars, whose rules are partially ordered, constitute an intermediate class between the context-free and context-sensitive languages; the first inclusion is shown to be proper.

A global parser for context-free phrase structure grammars

Abstract: An algorithm for analyzing any context-free phrase structure grammar and for generating a program which can then parse any sentence in the language (or indicate that the given sentence is invalid) is described. The parser is of the “top-to-bottom” type and is recursive. A number of heuristic procedures whose purpose is to shorten the basic algorithm by quickly ascertaining that certain substrings of the input sentence cannot correspond to the target nonterminal symbols are included. Both the generating algorithm and the parser have been implemented in RCA SNOBOL and have been tested successfully on a number of artificial grammars and on a subset of ALGOL. A number of the routines for extracting data about a grammar, such as minimum lengths of N-derivable strings and possible prefixes, are given and may be of interest apart from their application in this particular context.

Derivation-bounded languages

Abstract: A derivation in a phrase-structure grammar is said to be k-bounded if each word in the derivation contains at most k occurrences of nonterminals. A set L is said to be derivation bounded if there exists a phrase-structure grammar G and a positive integer k such that L is the set of words in the language generated by G which have some k-bounded derivation. The main result is that every derivation-bounded set is a contextfree language. Various characterizations of the derivation-bounded languages are then given. For example, the derivation-bounded languages coincide with the standard matching-choice sets discussed by Yntema. They also coincide with the smallest family of sets containing the linear context-free languages and closed under arbitrary substitution.

Property grammars and table machines

Abstract: The purpose of this paper is to generalize the methods of automata theory to accommodate infinite input alphabets and to propose a method of describing computer languages such as ALGOL-60 with more reliance on grammatical methods and less reliance on semantic constraints. Our chief concern is a natural generalization of a context-free grammar which we call a context-free property grammar. The generalization is straight-forward and can be used in similar fashion to define regular property grammars, context-sensitive property grammars, etc. The chief result is that these contextfree property grammars generate precisely the set of languages recognized by a non-determinated pushdown table machine, which is a straight forward generalization of a pushdown machine. Again it is clear that other kinds of automata have corresponding table versions. The language-machine correspondence is preserved in such a matter that efficient processing schemes for context-free property grammars are suggested by the well-known schemes for context free languages. Before beginning, we mention some mathematical conventions used. If A is a set, then A* represents the set of all finite sequences of elements from A. If w is in A*, then l(w) is the length of word w. The symbol ∈ represents the null or length zero word. A typical element of A* will be described by ai...an with the understanding that if n = 0, the null string ∈ is represented and there are no ai in the string. If n is a positive integer, then An represents the set of n dimensional vectors whose components are from A. A typical element of An is represented as (ai,..., an). If I is a set, then AI represents the set of all functions from I to A. Finally 2A represents the set of all subsets of A.

Degrees of Unsolvability in Formal Grammars

Abstract: The following theorem is a refinement of an unsolvability result due to E. Post: For any recursively enumerable degree D of recursive unsolvability there is a recursive class of sequences (of the same length) of nonempty words on an alphabet A such that the Post correspondence decision problem for that class is of degree D. This theorem is proved and then applied to obtain degree analogues of the ambiguity problem and the common program problem for the class of context-free grammars.

Structural Equivalence and LL-k Grammars

Abstract: It has been shown by Lewis and Stearns that LL-k grammars are useful descriptive forms for languages that are to be translated mechanically. The goal of the research reported on here is to develop algorithms for transforming arbitrary context-free grammars into LL-k grammars while retaining the structure imposed on the language by the grammar, if this is possible. A solution is presented for the case where k=1 and there are no ∈-rules. In addition it is shown that every LL-k grammar is structurally equivalent to what we define as an LL*-k grammar, a form with a simpler definition that leads to a simpler parsing algorithm. It is hoped that this latter result will facilitate the generalization of the former result.

Structural equivalance and LL-k grammers

Abstract: It has been shown by Lewis and Stearns that LL-k grammars are useful descriptive forms for languages that are to be translated mechanically. The goal of the research reported on here is to develop algorithms for transforming arbitrary context-free grammars into LL-k grammars while retaining the structure imposed on the language by the grammar, if this is possible. A solution is presented for the case where k=1 and there are no ∈-rules. In addition it is shown that every LL-k grammar is structurally equivalent to what we define as an LL*-k grammar, a form with a simpler definition that leads to a simpler parsing algorithm. It is hoped that this latter result will facilitate the generalization of the former result.

A computer system for writing and testing transformational grammars.

Abstract: : For the past two years the Computational Linguistics Project in the Computer Science Department at Stanford University has been engaged in research leading to computer programs for accepting and manipulating transformational grammars corresponding to a version of the theory based on Chomsky's Aspects of the Theory of Syntax. These programs have been combined into a computer system for transformational grammar which accepts a transformational grammar in a natural format, and carries out the complete generation of sentences, from phrase structure generation, through lexical insertion and transformation. These programs are the first to handle complete sentence generation. The project has made some interesting contributions to linguistic theory, particularly in the areas of formal definition of grammars, lexical insertion, and traffic rules for transformations. The results obtained are described in reports which have been issued during the course of the project. To summarize these results the abstracts of the more important papers are included here. The bibliography attached to this report contains a list of current reports produced by the project. (Author)