Showing papers on "Tree-adjoining grammar published in 1978"

Syntactic Pattern Recognition: An Introduction

Abstract: This book provides an introduction to basic concepts and techniques of syntactic pattern recognition. The presentation emphasizes fundamental and practical material rather than strictly theoretical topics, and numerous examples illustrate the principles. The subject is developed according to the following topics: introduction (background, patterns and pattern classes, approaches to pattern recognition, elements of a pattern recognition system, concluding remarks); elements of formal language theory (introduction; string grammars and languages; examples of pattern languages and grammars; equivalent context-free grammars; syntax-directed translations; deterministic, nondeterministic, and stochastic systems; concluding remarks); higher-dimensional grammars (introduction; tree grammars; web grammars; plex grammars; shape gammars; concluding remarks); recognition and translation of syntactic structures (introduction; string language recognizers; automata for simple syntax-directed translation; parsing in string languages; recognition of imperfect strings; tree automata; concluding remarks); stochastic grammars, languages, and recognizers (introduction; stochastic grammars and languages; consisting of stochastic context-free grammars; stochastic reocgnizers; stochastic syntax-directed translations; modified Cocke-Younger-Kasami parsing algorithm for stochastic errors of changed symbols; concluding remarks); and grammatical inference (introduction; inference of regular grammars; inference of context-free grammars; inference of tree grammars; inference of stochastic grammar; concluding remarks). 155 references, 93 figures, 4 tables. (RWR)

Context-Free Graph Grammars*

Abstract: In this paper we develop a theory of context-free graph grammars. Formal properties of such grammars are proven, with particular attention to graph language recognizability.

A class of linearly parsable graph grammars

Abstract: Specializing an existing graph grammar model we look in detail at node context-free graph grammars. With a slight generalization the parse trees for context-free Chomsky grammars can be used to describe derivations of these graph grammars. As shown already in former works the precedence graph grammars are defined as a subclass of context-free graph grammars by certain algebraic restrictions on the form of the rules. Then we can prove that every precedence grammar is unambiguous and additionally the reduction process in such a grammar read as replacement system is finite. The most important aim in defining the predence relations was a simple parsing method. This is realized because it is shown that the syntactic analysis for precedence graph grammars can be done in a time which linearly depends on the size of the input graph. The whole method has been implemented and a documentation is available.

A parsing method for Montague grammars

Abstract: The main result in this paper is a method for obtaining derivation trees from sentences of certain formal grammars. No parsing algorithm was previously known to exist for these grammars. Applied to Montague's FTQ the method produces all parses that cou!d correspond to different meanings. The technique directly addresses scope and reference and provides a framework for examining these phenomena. The solution for FTQ is implemented in an efficient and useful computer program. This paper describes an original parsing algorithm that handles quantifier scope and pronoun reference. The parsing method is applicable to formal grammars that use substitution rules ta bind variables. The parsing prob- lem for these grammars has not previously been investigated. In develop- ing the algorithm we had in mind the grammar presented by Richard Montague in The proper treatment of quantification in ordinary i3nglish (PTQ). Our solution provides a general framework in which to consider problems of scope and reference. It is implemented in a practical parsing system that can be used in linguistic investigations. The parsing method obtains derivation trees from sentences of a gram- mar. A major difficulty arises because each sentence in such a grammar has infinitely many derivations. Our method obtains a finite set of represen- tative parses that is adequate to characterize the full infinite set. The finite set contains all parses that could reasonably correspond to different mean- ings. The interesting and difficult part of the problem is how to incorporate the rules of quantification. Our algorithm solves this in a natural way that provides a more general framework in which to address problems related to scope and reference.

On Constructing Efficient Evaluators for Attribute Grammars

Abstract: An attribute grammar is an ordinary context-free grammar augmented with attributes and semantic rules for describing the semantics of terminal strings generated by the underlying context-free grammar. The meaning of a terminal string is revealed in two steps: first a parse tree is constructed for the string, and then a so-called evaluator defines the values of attribute instances attached to the parse tree. Many of these values are very temporary in nature, making it important to use the space allocated for them repeatedly.

Algebraic Properties of Operator Precedence Languages

Abstract: This paper presents new results on the algebraic ordering properties of operator precedence grammars and languages. This work was motivated by, and applied to, the mechanical acquisition or inference of operator precedence grammars. A new normal form of operator precedence grammars called homogeneous is defined. An algorithm is given to construct a grammar, called max-grammar, generating the largest language which is compatible with a given precedence matrix. Then the class of free grammars is introduced as a special subclass of operator precedence grammars. It is shown that operator precedence languages corresponding to a given precedence matrix form a Boolean algebra.

On the inference of stochastic regular grammars

Abstract: The relevance of grammatical inference techniques to the semiautomatic construction from empirical data, of a model of human decision making, is outlined. A grammatical inference problem is presented in which the least complex stochastic regular grammar is sought which describes a given set of strings. An upper bound on the complexity of the best grammar for a given data set is found, and some properties of the grammars which are less complex than the bound are proved. The technique of splitting grammars is used to organize a search of these grammars. An initial grammar is defined, and it is established that any best grammar is obtainable by repeated splitting of the initial grammar. The performance of a program based on these results is described.

Normal-form transformations of context-free grammars.

Abstract: We discuss three normal form transformations Tj, r2 and r:: of grammars G which are in Chomsky normal form into grammars Gi, G, and G3 respectively. G1 is in Greibach normal form with nonterminal productions restricted to z — tp such that t ^ T and pf_Z+ and length The nonterminal productions of G2 and G3 are of the form z^ipr such that t, r£ T and p£Z, length or length ( p ) s 3 , respectively. It is shown that these transformations do not increase the multiplicity of words in the generated languages. Furthermore we show that certain functorial relations between languages are preserved under these transformations. The restriction of r, to one sided linear grammars produces the minimal grammars. r2 and r3 do not preserve the LR{k) property of grammars, r, preserves LL(k) for ksO and LR(k) for ¿ > 1 , LR(Q) may be transformed into LR{ 1) as we show in the following paper. X UNIVERSITÄT DES S A A R L A N D E S D-66 S A A R B R Ü C K E N

Attribute Grammars and Mathematical Semantics

Abstract: Attribute grammars and mathematical semantics are rival language definition methods. We show that any attribute grammar G has a reformulation MS(G) within mathematical semantics. Most attribute grammars have properties that discipline the sets of equations the grammar gives to derivation trees. We list six such properties, and show that for a grammar G with one of these properties both MS(G) and the compiler for G can be simplified. Because these compiler-friendly properties are of independent interest, the paper is written in such a way that the first and last sections do not depend on the other sections.

On the complexity of formal grammars

Abstract: The time and space complexity of the class of languages generated in linear time by context-sensitive grammars is investigated. Among other results it is shown that the membership question for languages in the class is NP-complete.

A direct proof of the equivalence of free categorial grammars and simple phrase structure grammars

Abstract: In [2], Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars (SPGs) defined by Chomsky are equivalent in a certain sense to Bar-Hillel's bidirectional categorial grammars (BCGs). On the other hand, Cohen [3] proves the equivalence of the latter ones to what the calls free categorial grammars (FCGs). They are closely related to Lambek's syntactic calculus which, in turn, is based on the idea due to Ajdukiewicz [1]. For the reasons which will be discussed in the last section, Cohen's proof seems to be at least incomplete. This paper yields a direct proof of the equivalence ofFCGs andSPGs.

Two-Level Graph Grammars

Abstract: Two-level graph grammars (2GG) combine the concepts of (one-level) graph grammars — as defined by PRATT — and of two-level (string) grammars — as introduced by v. WIJNGAARDEN for the formal definition of ALGOL 68. 2GG's settle both the inadequacies of one-level graph grammars and of two-level string grammars, the former resulting from the lack of parameters, the latter from the general lack of structure of string manipulation systems. As a field of application of 2GG's, the formal description of programming languages is focussed.

Graadadjektieven en orientatie

Abstract: In this paper we present a grammar formalism for the generation and parsing of two-dimensional symbolic languages. Linear Positional Grammars (or LPGs for short) are an immediate generalization of the context-free string grammars. Through the use of general spatial relations they allow the definition of pictures whose symbols span on a two-dimensional space. Due to their analogy to context-free string grammars, LPGs can be used to construct an LR-based parser which uses the spatial relations to navigate the input. We study ambiguous grammars and present several ways to solve them. Moreover we provide an algorithm to translate a linear positional grammar into a context-free grammar with actions and suggest a general methodology to parse two-dimensional symbolic languages by making use of the well-known tool YACC (Yet Another Compiler-Compiler [25]). As an example, we construct a parser for a subset of the two-dimensional arithmetical expression language.

Map Grammars: Cycles and the Algebraic Approach

Abstract: Some real world phenomena are essentially two dimensional; they are more naturally modelled by map grammars than graph grammars. The planarity of maps can be captured by cycles and converted into a form suitable for abstract manipulation. This insight suggests (section 1) a new definition of map grammars, (section 2) some theorems, (section 3) and a generalization of the algebraic approach to graph grammars.

On the Parsing and Covering of Simple Chain Grammars

Abstract: A method is presented for obtaining a simple deterministic pushdown transducer which acts as a parser for simple chain grammars. It is shown that a simple deterministic grammar can be constructed which covers the simple chain grammar. To obtain both the simple deterministic pushdown transducer and the cover result, a new type of parse is introduced which differs from the left and right parses which are common for the usual one pass no back-tracking parsing algorithms. For the simple chain grammars this parse, the so-called left part parse, follows from a simple left part property which is satisfied by the grammatical trees of simple chain grammars.

On functional grammars

Abstract: A family of simple relational systems — with a functional grammar as a parameter — can serve as a single framework for many theories of formal languages and automata. This note outlines the principles of the systems and comments their application.

Two infinite hierarchies of languages defined by branching grammars.

Abstract: Two types of branching grammars are introduced inspired from Havel's works about branching automata. They naturally define two infinite hierarchies into the family of regular, respectively, linear languages. Homomorphic characterisations of regular and linear languages >n terms of branching languages are obtained. Finally, the relations between branching grammars and contextual grammars of [5] are investigated.

Inference of high dimensional grammars

Abstract: : Inference of high-dimensional grammars such as tree grammars and web grammars is discussed. The k-tail inference procedure for finite-state grammars is extended to the case of regular tree grammars. The behavior of the k-tail procedure with variable values of k is studied. The derivation diagram of context-free web languages is introduced. A 'semantic teacher' is used for the inference of web grammars. Application examples in picture and scene analysis are presented. (Author)

String and graph grammar characterizations of bounded regular languages

Abstract: Two grammatical characterizations of the bounded regular languages are presented: one in terms of graph grammars, the other using string grammars. First it is shown that a class of state graphs recognizing the bounded regular languages can be generated by a particular second-order contextfree graph grammar. Next we call uniquely recursive a right-linear (string) grammar having at most one right-recursive production for each of its nonterminals. It is then established that the class of languages generated by uniquely recursive, sequential right-linear grammars is exactly the bounded regular languages. Some comments on the relationship between string and graph grammars are made.

Two-level meta-controlled substitution grammars

Abstract: A language-generating mechanism, inspired on the two-level van Wijngaarden syntax for Algol 68, is considered. Its language generating properties are studied and compared to those of well-known classical systems and grammars. The new mechanism is called a 2 MSG, for "two-level metacontrolled substitution grammar."

Grammars with Dynamic Control Sets

Abstract: The use of control strings to direct derivations in context-free grammars is generalized in this paper. Recording grammars (rgs) are introduced. Rgs don't have a pregiven set of control strings, but generate these during the course of derivations. The generative capacity for several models of rgs is studied. The control mechanism inherent to rgs establishes relationships between substrings in words. The nature of these relationships is investigated too. Applicability of rgs within both compiler theory and programming language description methods is demonstrated. New characterizations of a-transducer mappings and Turing-transductions are displayed. It is shown further how rgs can be used to formalize non-contextfree features in programming languages.

The transformation of context-free grammars to Wirth-Weber precedence form.

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