Context-free graph grammars and concatenation of graphs

An operation of concatenation is defined for graphs. This allows strings to be viewed as expressions denoting graphs, and string languages to be interpreted as graph languages. For a class of string languages, is the class of all graph languages that are interpretations of languages from . For the classes REG and LIN of regular and linear context-free languages, respectively, . is the smallest class of graph languages containing all singletons and closed under union, concatenation and star (of graph languages). equals the class of graph languages generated by linear HR (= Hyperedge Replacement) grammars, and is generated by the corresponding -controlled grammars. Two characterizations are given of the largest class such that . For the class CF of context-free languages, lies properly inbetween and the class of graph languages generated by HR grammars. The concatenation operation on graphs combines nicely with the sum operation on graphs. The class of context-free (or equational) graph languages, with respect to these two operations, is the class of graph languages generated by HR grammars. Received 16 October 1995 / 18 September 1996     

Parallel communicating grammar systems with terminal transmission

We introduce a new variant of PC grammar systems, called PC grammar systems with terminal transmission, PCGSTT for short. We show that right-linear centralized PCGSTT have nice formal language theoretic properties: they are closed under gsm mappings (in particular, under intersection with regular sets and under homomorphisms) and union; a slight variant is, in addition, closed under concatenation and star; their power lies between that of n-parallel grammars introduced by Wood and that of matrix languages of index n, and their relation to equal matrix grammars of degree n is discussed. We show that membership for these language classes is complete for NL. In a second part of the paper, we discuss questions concerning grammatical inference of these systems. More precisely, we show that PCGSTT whose component grammars are terminal distinguishable right-linear, a notion introduced by Radhakrishnan and Nagaraja in [33,34], are identifiable in the limit if certain data communication information is supplied in addition.     

Monadic second-order definable text languages

Atext is a word together with a (additional) linear ordering. Each text has a generic tree representation, called itsshape. Texts are considered in a logical and in an algebraic framework. It is proved that, for texts of bounded primitivity, the class of monadic second-order definable text languages coincides with both the class of recognizable text languages and the class of text languages generated by right-linear text grammars. In particular it is demonstrated that the construction of the shape of a text can be formalized in terms of our monadic second-order logic. This approach can be extended to the case of graphs. This research was supported by the EBRA Working Group ASMICS 2.     

On the structure of node-label-controlled graph languages

A new kind of graph grammars (called NLC grammars) is introduced. The main theorem is a result on the combinatorial structure of graph languages generated by NLC grammars; it resembles the pumping theorem for context-free string languages.     

右线性文法与有限自动机等价性的一个新证明

迄今为止,左、右线性文法与有限自动机的等价性都是通过相互模拟构造来证明的。文章首先引入字母表上的右线性方程组及其最小解的概念,证明了最小解的存在性与有效可解性,描述了最小解的结构;其次通过右线性方程组及其最小解,证明了右线性文法与有限自动机的等价性。完全类似地,可以引入字母表上的左线性方程组及其最小解,并且证明左线性文...     

On the generative power of sequential and parallel programmed graph grammars

Programmed graph grammars are formally introduced and their generative power is investigated. Programmed graph grammars differ from other approaches to graph grammars in the so-called control diagram which controls the application order of productions. Restricting the form of the productions of a programmed graph grammar we get several classes of graph languages. These are compared mutually as well as with the hierarchy introduced by Nagl [18]. For unrestricted and monotone productions corresponding classes of graph languages coincide, while the class of context free programmed graph languages is properly contained in the class of context free graph languages in the sense of [18].     

Parsing and translation of (attributed) expansive graph languages for scene analysis

In this paper, we suggest a class of (attributed) expansive graph grammars which generate languages contained in a graph family ?. It turns out that by means of node renumbering using a very effi-cient algorithm, any graph in ? can be converted into a standard form, which enables the use of related string representation for that graph to facilitate the syntax analysis. As a consequence, the syntax analysis of (attributed) expansive graph language is very efficient and almost like the parsing of tree languages. Furthermore, a syntax-directed transla-tion can be established for mapping one (attributed) expansive graph language to another. Finally, since many relational graphs for scene analysis can be considered as belonging to these graph languages, the proposed graph grammar model appears to be quite attractive from the application point of view.     

The covering problem for linear context-free grammars

Language equivalence, grammatical covering and structural equivalence are all notions of similarity defined on context-free grammars. We show that the problem of determining whether an arbitrary linear context-free grammar covers another is complete for the class of languages accepted by polynomially space bounded Turing machines. We then compare the complexity of this problem with the analogous problems for language equivalence and structural equivalence, not only for linear grammars, but also for regular grammars and unrestricted context-free grammars. As a step in obtaining the main result of this paper, we show that the equivalence problem for linear s-grammars is decidable in polynomial time.     

Restrictions, extensions, and variations of NLC grammars

This paper continues the basic research on node-label-controlled graph grammars (NLC grammars). In particular three topics are investigated quite thoroughly: (1) the role of the connection relation in an NLC grammar, (2) “context-freeness” of NLC grammars, and (3) the ability of NLC grammars to generate string languages.     

A characterization of context-free string languages by directed node-label controlled graph grammars

Summary Directed node-label controlled graph grammars (DNLC grammars) are sequential graph rewriting systems. In a direct derivation step of a DNLC grammar a single node is rewritten. Both the rewriting of a node and the embedding of a daughter graph in a host graph are controlled by the labels of nodes only. We study the use of those grammars to define string languages. In particular we provide a characterization of the class of context-free string languages in terms of DNLC grammars.     

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     

基于量子逻辑的自动机和文法理论

初步建立了基于量子逻辑的自动机和文法理论的基本框架.引入了量子文法(称为l值文法),特别是证明了任意l值正规文法生成的语言(称为量子语言)等价于某种基于量子逻辑且含动作(的自动机(称为l值自动机)识别的语言,反之,任意l值自动机识别的语言等价于某l值正规文法生成的语言.建立了l值泵引理,并得到量子语言的判定性刻画.最后简要讨论了正规文法与量子文法(即l值正规文法)的关系.因此,为进一步研究更复杂的量子自动机(如量子下推自动机和Turing机)和量子文法(如量子上下文无关文法和上下文有关文法)奠定了基础.     

Parsers for indexed grammars

Three classes of parsable indexed grammars are defined. The new parsing mechanisms are derived by extending those that have been most successful for contextfree grammars, the LR and LL algorithms. Design criteria for the new grammar classes include membership decidability and unambiguity. We show that all three parsers operate in linear time for at least some grammars in our new classes. One of our new classes generates all the deterministic contextfree languages, along with some noncontextfree languages. We also show that the flag strings generated by indexed grammars are regular sets. This is done by showing that they can be generated by regular canonical systems.     

Control sets on grammars using depth-first derivations

Control sets on grammars are extended to depth-first derivations. It is proved that a context-free language is generated by the depth-first derivations of an arbitrary context-free grammar controlled by an arbitrary regular set. This result is sharpened to obtain a new characterization of the family of derivation-bounded languages: a languageL is derivation bounded if and only if it is generated by the depth-first derivations of a context-free grammarG controlled by a regular subsetR of the Szilard language ofG. The left-derivation-bounded languages are characterized analogously using leftmost derivations. It is proved that a grammarG is nonterminal bounded if and only if the Szilard language defined using only the depth-first derivations ofG is regular. Finally, it is proved that if a family of languagesC is a trio, a semi-AFL, an AFL, or an AFL closed under -free substitution, then the family of languages generated using arbitrary context-free grammars controlled by members ofC is full, is closed under reversal, and has the closure properties assumed ofC.     

Spinal-Formed Context-Free Tree Grammars

In this paper we introduce a restricted model of context-free tree grammars called spine grammars, and study their formal properties including considerably simple normal forms. Recent research on natural languages has suggested that formalisms for natural languages need to generate a slightly larger class of languages than context-free grammars, and for that reason tree adjoining grammars have been widely studied relating them to natural languages. It is shown that the class of string languages generated by spine grammars coincides with that of tree adjoining grammars. We also introduce acceptors called linear pushdown tree automata, and show that linear pushdown tree automata accept exactly the class of tree languages generated by spine grammars. Linear pushdown tree automata are obtained from pushdown tree automata with a restriction on duplicability for the pushdown stacks. Received May 29, 1998, and in revised form April 27, 1999, and in final form May 10, 1999.     

Graph grammars with neighbourhood-controlled embedding

A central feature that distinguishes graph grammars (we consider grammars generating sets of node-labelled undirected graphs only) from string grammars is that in the former one has to provide a mechanism by which a daughter graph (the right-hand side of a production) can be embedded in the rest of the mother graph, while in the latter this embedding is provided automatically by the structure that all strings possess (left-to-right orientation). In this paper we consider a possible classification of embedding mechanisms for (node-rewriting) graph grammars. This classification originates from the basic ideas of [9]. On the one hand it allows one to fit a number of existing notions of a graph grammar into a common framework and on the other hand it points out new “natural” possibilities for defining the embedding mechanism in a graph grammar. The relationship between the graph-language generating power of graph grammars using various embedding mechanisms is established.     

On labelled graph grammars

According to the classification of labelled graph grammars by Nagl [4], it can be shown that the class of context-sensitive graph languages is equivalent to the class of context-free graph languages and the context-free graph languages properly include the regular graph languages.     

The equivalence of four extensions of context-free grammars

There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This paper concerns the relationship between the class of string languages generated by several such formalisms, namely, combinatory categorial grammars, head grammars, linear indexed grammars, and tree adjoining grammars. Each of these formalisms is known to generate a larger class of languages than context-free grammars. The four formalisms under consideration were developed independently and appear superficially to be quite different from one another. The result presented in this paper is that all four of the formalisms under consideration generate exactly the same class of string languages.This work has been supported by NSF Grants MCS-82-19116-CER, MCS-82-07294, DCR-84-10413, IRI-8909810, ARO Grant DAA29-84-9-0027, and DARPA Grant N0014-85-K0018.     

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.     

Büchi context-free languages

We define context-free grammars with Büchi acceptance condition generating languages of countable words. We establish several closure properties and decidability results for the class of Büchi context-free languages generated by these grammars. We also define context-free grammars with Müller acceptance condition and show that there is a language generated by a grammar with Müller acceptance condition which is not a Büchi context-free language.