Showing papers on "Tree-adjoining 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.

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.

A Universal Syntax-Directed Top-Down Analyzer

Abstract: An algorithm is described that will recognize, and fully analyze, strings of unbounded length, using the rewriting rules of any context-free grammar. It uses a finite random access store, three pushdown tapes, and a counter. It imposes no restrictions on the grammar defined by the rewriting rules, excepting only that it be a context-free phrase structure grammar. The analysis printed out is a linearized form of the structural description tree (or trees, in an ambiguous case) of the input string. A proof that the analyzer will always stop in a finite time is provided. The upper bound on the running time increases exponentially with input string length.

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.