Generalised Stream X-Machines and Cooperating Distributed Grammar Systems

Stream X-machines are a general and powerful computational model. By coupling the control structure of a stream X-machine with a set of formal grammars a new machine called a generalised stream X-machine with underlying distributed grammars, acting as a translator, is obtained. By introducing this new mechanism a hierarchy of computational models is provided. If the grammars are of a particular class, say regular or context-free, then finite sets are translated into finite sets, when ?k, = k derivation strategies are used, and regular or context-free sets, respectively, are obtained for ?k, * and terminal derivation strategies. In both cases, regular or context-free grammars, the regular sets are translated into non-context-free languages. Moreover, any language accepted by a Turing machine may be written as a translation of a regular set performed by a generalised stream X-machine with underlying distributed grammars based on context-free rules, under = k derivation strategy. On the other hand the languages generated by some classes of cooperating distributed grammar systems may be obtained as images of regular sets through some X-machines with underlying distributed grammars. Other relations of the families of languages computed by generalised stream X-machines with the families of languages generated by cooperating distributed grammar systems are established. At the end, an example dealing with the specification of a scanner system illustrates the use of the introduced mechanism as a formal specification model. Received September 1999 / Accepted in revised form October 2000     

Structuring of Large-scale Complex Hybrid Systems: from Illustrative Analysis toward Modelization

System structuring is paramount to the development of large-scale complex hybrid systems (LCHS). However, there is no well-established and effective methodology for the structuring of LCHS. Using the approach of illustrating and abstracting, this paper investigates the structuring of LCHS based on a wide variety of applications. First, intrinsic attributes of LCHS are explored. Then, a unified framework-based analysis is made of six typical examples of LCHS, i.e. human brain-body systems, autonomous robot systems, autonomous fed-batch reactor systems, human-car driving systems, autonomous urban traffic systems, and autonomous production (manufacturing/industrial process) systems. In this way, common characteristics among typical examples, e.g., perception–decision link, distributing, nesting, hierarchy, multiple gradation and hybrid dynamics over a spectrum of time drivers, and, incidentally, wide application orientations of LCHS, are illustrated. Furthermore, after basic concepts for the modelization of LCHS are formulated, two novel general-purpose information-processing modules are proposed and constructed, called perception cube and decision spheroid. Based on them, a novel block diagram based model is originally proposed and established for LCHS.     

Parameter reduction and automata evaluation for grammar-compressed trees

Trees can be conveniently compressed with linear straight-line context-free tree grammars. Such grammars generalize straight-line context-free string grammars which are widely used in the development of algorithms that execute directly on compressed structures (without prior decompression). It is shown that every linear straight-line context-free tree grammar can be transformed in polynomial time into a monadic (and linear) one. A tree grammar is monadic if each nonterminal uses at most one context parameter. Based on this result, polynomial time algorithms are presented for testing whether a given (i) nondeterministic tree automaton or (ii) nondeterministic tree automaton with sibling-constraints or (iii) nondeterministic tree walking automaton, accepts a tree represented by a linear straight-line context-free tree grammar. It is also shown that if tree grammars are nondeterministic or non-linear, then reducing their numbers of parameters cannot be done without an exponential blow-up in grammar size.     

Grammatical Inference: Introduction and Survey-Part II

Inference of high-dimensional grammars is discussed. Specifically, techniques for inferring tree grammars are briefly presented. The problem of inferring a stochastic grammar to model the behavior of an information source is also introduced and techniques for carrying out the inference process are presented for a class of stochastic finite-state and context-free grammars. The possible practical application of these methods is illustrated by examples.     

Approximation of fuzzy context-free grammars

Fuzzy context-free max- grammar (or FCFG, for short), as a straightforward extension of context-free grammar, has been introduced to express uncertainty, imprecision, and vagueness in natural language fragments. Li recently proposed the approximation of fuzzy finite automata, which may effectively deal with the practical problems of fuzziness, impreciseness and vagueness. In this paper, we further develop the approximation of fuzzy context-free grammars. In particular, we show that a fuzzy context-free grammar under max- compositional inference can be approximated by some fuzzy context-free grammar under max-min compositional inference with any given accuracy. In addition, some related properties of fuzzy context-free grammars and fuzzy languages generated by them are studied. Finally, the sensitivity of fuzzy context-free grammars is also discussed.     

A class of linearly parsable graph grammars

Summary 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.     

格值下推自动机与格值上下文无关文法

引入了格值下推自动机、格值上下文无关文法及它们的语言的概念,证明了格值下推自动机以两种不同方式接受的语言类的等价性,研究了格值Chomsky范式文法、格值上下文无关文法及其派生所产生的语言的等价条件,揭示了在一定条件下,格值下推自动机接受的语言类与格值上下文无关文法产生的语言类的等价性,证明了有理格值语言均被格值下推自动机识别。     

Learning context-free grammar using improved tabular representation

This paper describes an improved version of TBL algorithm [Y. Sakakibara, Learning context-free grammars using tabular representations, Pattern Recognition 38(2005) 1372–1383; Y. Sakakibara, M. Kondo, GA-based learning of context-free grammars using tabular representations, in: Proceedings of 16th International Conference in Machine Learning (ICML-99), Morgan-Kaufmann, Los Altos, CA, 1999] for inference of context-free grammars in Chomsky Normal Form. The TBL algorithm is a novel approach to overcome the hardness of learning context-free grammars from examples without structural information available. The algorithm represents the grammars by parsing tables and thanks to this tabular representation the problem of grammar learning is reduced to the problem of partitioning the set of nonterminals. Genetic algorithm is used to solve NP-hard partitioning problem. In the improved version modified fitness function and new delete specialized operator is applied. Computer simulations have been performed to determine improved a tabular representation efficiency. The set of experiments has been divided into 2 groups: in the first one learning the unknown context-free grammar proceeds without any extra information about grammatical structure, in the second one learning is supported by a partial knowledge of the structure. In each of the performed experiments the influence of partition block size in an initial population and the size of population at grammar induction has been tested. The new version of TBL algorithm has been experimentally proved to be not so much vulnerable to block size and population size, and is able to find the solutions faster than standard one.     

A Toolkit for Generating Sentences from Context-Free Grammars

Producing sentences from a grammar, according to various criteria, is required in many applications. It is also a basic building block for grammar engineering. This paper presents a toolkit for context-free grammars, which mainly consists of several algorithms for sentence generation or enumeration and for coverage analysis for context-free grammars. The toolkit deals with general context-free grammars. Besides providing implementations of algorithms, the toolkit also provides a simple graphical user interface, through which the user can use the toolkit directly. The toolkit is implemented in Java and is available at http://lcs.ios.ac.cn/~zhiwu/toolkit.php. In the paper, the overview of the toolkit and the major algorithms implemented in the toolkit are presented, and experimental results and preliminary applications of the toolkit are also contained.     

Context-free hypergraph grammars have the same term-generating power as attribute grammars

Context-free hypergraph grammars and attribute grammars generate the same class of term languages. Extending the context-free hypergraph grammar with a context-free grammar and a semantic domain, a syntax-directed translation device is obtained that is equivalent to the attribute grammar.     

A survey of normal form covers for context free grammars

Summary An overview is given of cover results for normal forms of context-free grammars. The emphasis in this paper is on the possibility of constructing ɛ-free grammars, non-left-recursive grammars and grammars in Greibach normal form. Among others it is proved that any ɛ-free context-free grammar can be right covered with a context-free grammar in Greibach normal form. All the cover results concerning the ɛ-free grammars, the non-left-recursive grammars and the grammars in Greibach normal form are listed, with respect to several types of covers, in a cover-table.     

Grammar constraints

With the introduction of the Regular Membership Constraint, a new line of research has opened where constraints are based on formal languages. This paper is taking the next step, namely to investigate constraints based on grammars higher up in the Chomsky hierarchy. We devise a time- and space-efficient incremental arc-consistency algorithm for context-free grammars, investigate when logic combinations of grammar constraints are tractable, show how to exploit non-constant size grammars and reorderings of languages, and study where the boundaries run between regular, context-free, and context-sensitive grammar filtering.     

SGML and XML Document Grammars and Exceptions

The Standard Generalized Markup Language (SGML) and the Extensible Markup Language (XML) allow users to define document-type definitions (DTDs), which are essentially extended context-free grammars expressed in a notation that is similar to extended Backus–Naur form. The right-hand side of a production, called a content model, is both an extended and a restricted regular expression. The semantics of content models for SGML DTDs can be modified by exceptions (XML does not allow exceptions). Inclusion exceptions allow named elements to appear anywhere within the content of a content model, and exclusion exceptions preclude named elements from appearing in the content of a content model. We give precise definitions of the semantics of exceptions, and prove that they do not increase the expressive power of SGML DTDs when we restrict DTDs according to accepted SGML practice. We prove the following results:1. Exceptions do not increase the expressive power of extended context-free grammars.2. For each DTD with exceptions, we can obtain a structurally equivalent extended context-free grammar.3. For each DTD with exceptions, we can construct a structurally equivalent DTD when we restrict the DTD to adhere to accepted SGML practice.4. Exceptions are a powerful shorthand notation—eliminating them may cause exponential growth in the size of an extended context-free grammar or of a DTD.     

Analyzing ambiguity of context-free grammars

It has been known since 1962 that the ambiguity problem for context-free grammars is undecidable. Ambiguity in context-free grammars is a recurring problem in language design and parser generation, as well as in applications where grammars are used as models of real-world physical structures.We observe that there is a simple linguistic characterization of the grammar ambiguity problem, and we show how to exploit this by presenting an ambiguity analysis framework based on conservative language approximations. As a concrete example, we propose a technique based on local regular approximations and grammar unfoldings. We evaluate the analysis using grammars that occur in RNA analysis in bioinformatics, and we demonstrate that it is sufficiently precise and efficient to be practically useful.     

Learning context-free grammars using tabular representations

We present a novel algorithm using new hypothesis representations for learning context-free grammars from a finite set of positive and negative examples. We propose an efficient hypothesis representation method which consists of a table-like data structure similar to the parse table used in efficient parsing algorithms for context-free grammars such as Cocke-Younger-Kasami algorithm. By employing this representation method, the problem of learning context-free grammars from examples can be reduced to the problem of partitioning the set of nonterminals. We use genetic algorithms for solving this partitioning problem. Further, we incorporate partially structured examples to improve the efficiency of our learning algorithm, where a structured example is represented by a string with some parentheses inserted to indicate the shape of the derivation tree of the unknown grammar. We demonstrate some experimental results using these algorithms and theoretically analyse the completeness of the search space using the tabular method for context-free grammars.     

THE COMPUTATIONAL COMPLEXITY OF THE UNIVERSAL RECOGNITION PROBLEM FOR PARALLEL MULTIPLE CONTEXT-FREE GRAMMARS

A number of grammatical formalisms have been proposed to describe the syntax of natural languages, and the universal recognition problems for some of those classes of grammars have been studied. A universal recognition problem for a class Q of grammars is the one to decide, taking a grammar G ∈ G and a string ui as an input, whether G can generate w or not. In this paper, the computational complexities of the universal recognition problems for parallel multiple context-free grammars, multiple context-free grammars, and their subclasses are discussed.     

Context-free like restrictions on selective rewriting

Selective substitution grammars based on ‘context-free’ productions form a possible framework for the study of ‘grammatically oriented’ formal language theory. Such grammars (with no control governing the composition of derivation steps) are studied in this paper. In particular we study the effect of various conditions on selectors (which define the way that rewriting is performed); those conditions are aimed to formalize the notion of ‘using information about the context’ during the rewriting process. Each of them captures a particular feature of a rewriting according to a context-free grammar or an EOS system (essentially a context-free grammar that can also rewrite terminal symbols). Some of those conditions yield characterizations of the class of context-free languages for other conditions the lower and upper bound on the language generating power are given. Also a natural notion of a class of ‘simple’ rewriting systems is introduced (pattern grammars) and it is demonstrated that they possess surprisingly high language generating power.