Boundary graph grammars with dynamic edge relabeling

AbstractMost NLC-like graph grammars generate node-labeled graphs. As one of the exceptions, eNCE graph grammars generate graphs with edge labels as well. We investigate this type of graph grammar and show that the use of edge labels (together with the NCE feature) is responsible for some new properties. Especially boundary eNCE (B-eNCE) grammars are considered. First, although eNCE grammars have the context-sensitive feature of “blocking edges,” we show that B-eNCE grammars do not. Second, we show the existence of a Chomsky normal form and a Greibach normal form for B-eNCE grammars. Third, the boundary eNCE languages are characterized in terms of regular tree and string languages. Fourth, we prove that the class of (boundary) eNCE languages properly contains the closure of the class of (boundary) NLC languages under node relabelings. Analogous results are shown for linear eNCE grammars

On the membership problem for regular DNLC grammars

AbstractThere are (at least) three motivations to study the class of regular directed node-label controlled graph grammars (regular DNLC grammars for shor): (1) it fits very well into the hierarchy of subclasses of DNLC grammars, (2) it generalizes naturally right-linear string grammars and (3) it provides a useful framework for the theory of concurrent systems based on the theory of traces.The complexity of (the membership problem for) the class of regular DNLC grammars is investigated

Symbol–Relation Grammars: A Formalism for Graphical Languages

AbstractA common approach to the formal description of pictorial and visual languages makes use of formal grammars and rewriting mechanisms. The present paper is concerned with the formalism of Symbol–Relation Grammars (SR grammars, for short). Each sentence in an SR language is composed of a set of symbol occurrences representing visual elementary objects, which are related through a set of binary relational items. The main feature of SR grammars is the uniform way they use context-free productions to rewrite symbol occurrences as well as relation items. The clearness and uniformity of the derivation process for SR grammars allow the extension of well-established techniques of syntactic and semantic analysis to the case of SR grammars. The paper provides an accurate analysis of the derivation mechanism and the expressive power of the SR formalism. This is necessary to fully exploit the capabilities of the model. The most meaningful features of SR grammars as well as their generative power are compared with those of well-known graph grammar families. In spite of their structural simplicity, variations of SR grammars have a generative power comparable with that of expressive classes of graph grammars, such as the edNCE and the N-edNCE classes

Theory of traces

AbstractThe theory of traces, originated by A. Mazurkiewicz in 1977, is an attempt to provide a mathematical description of the behavior of concurrent systems. Its aim is to reconcile the sequential nature of observations of the system behavior on the one hand and the nonsequential nature of causality between the actions of the system on the other hand.One can see the theory of traces to be rooted in formal string language theory with the notion of partial commutativity playing the central role. Alternatively one can see the theory of traces to be rooted in the theory of labeled acyclic directed graphs (or even in the theory of labeled partial orders).This paper attempts to present a major portion of the theory of traces in a unified way. However, it is not a survey in the sense that a number of new notions are introduced and a number of new results are proved. Although traditionally most of the development in the theory of traces follows the string-language-theoretic line, we try to demonstrate to the reader that the graph-theoretic point of view may be more appropriate.The paper essentially consists of two parts. The first one (Sections 1 through 4) is concerned with the basic theory of traces. The second one (Section 5) presents applications of the theory of traces to the theory of the behavior of concurrent systems, where the basic system model we have chosen is the condition/event system introduced by C.A. Petri

FEAT-REP : representing features in CAD/CAM

When CAD/CAM experts view a workpiece, they perceive it in terms of their own expertise. These terms, called features, which are build upon a syntax (geometry) and a semantic (e.g. skeletal plans in manufacturing or functional relations in design), provide an abstraction mechanism to facilitate the creation, manufacturing and analysis of workpieces. Our goal is to enable experts to represent their own feature-language via a feature-grammar in the computer to build feature-based systems e.g. CAPP systems. The application of formal language terminology to the feature definitions facilitates the use of well-known formal language methods in conjunction with our flexible knowledge representation formalism FEAT-REP which will be presented in this paper

When Stars Control a Grammar's Work

Graph-controlled insertion-deletion (GCID) systems are regulated extensions of insertion-deletion systems. Such a system has several components and each component contains some insertion-deletion rules. The components are the vertices of a directed control graph. A rule is applied to a string in a component and the resultant string is moved to the target component specified in the rule. The language of the system is the set of all terminal strings collected in the final component. We impose the restriction in the structure of the underlying graph to be a star structure where there is a central, control component which acts like a master and transmits a string (after applying one of its rules) to one of the components specified in the (applied) rule. A component which receives the string can process the obtained string with any applicable rule available in it and sends back the resultant string only to the center component. With this restriction, we obtain computational completeness for some descriptional complexity measuresComment: In Proceedings AFL 2023, arXiv:2309.0112

Criteria for Designing Computer Facilities for Linguistic Analysis

Abstract: In the natural-language-processing research community, the usefulness of computer tools for testing linguistic analyses is often taken for granted. Linguists, on the other hand, have generally been unaware of or ambivalent about such devices. We discuss several aspects of computer use that are preeminent in establishing the utility for linguistic research of computer tools and describe several factors that must be considered in designing such computer tools to aid in testing linguistic analyses of grammatical phenomena. A series of design alternatives, some theoretically and some practically motivated, is then based on the resultant criteria. We present one way of pinning down these choices which culminates in a description of a particular grammar formalism for use in computer linguistic tools. The PATR-II formalism this serves to exemplify our general perspective.Engineering and Applied Science