Adaptive star grammars and their languages

Graph Operations, Graph Transformations and Monadic Second-Order Logic A survey

Graph Operations, Graph Transformations and Monadic Second-Order Logic:: A survey

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 \(K\) of string languages, \({\rm Int}(K)\) is the class of all graph languages that are interpretations of languages from \(K\). For the classes REG and LIN of regular and linear context-free languages, respectively, \({\rm Int}({\rm REG}) = {\rm Int}({\rm LIN})\). \({\rm Int}({\rm REG})\) is the smallest class of graph languages containing all singletons and closed under union, concatenation and star (of graph languages). \({\rm Int}({\rm REG})\) equals the class of graph languages generated by linear HR (= Hyperedge Replacement) grammars, and \({\rm Int}(K)\) is generated by the corresponding \(K\)-controlled grammars. Two characterizations are given of the largest class \(K'\) such that \({\rm Int}(K') = {\rm Int}(K)\). For the class CF of context-free languages, \({\rm Int}({\rm CF})\) lies properly inbetween \({\rm Int}({\rm REG})\) 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.

Vigna and Ghezzi showed that the language of grid graphs could not be constructed by their context-free graph grammars [1]. In this paper, we construct a context-sensitive graph grammar for the two-dimensional grid graphs.

In this paper we discuss the use of views to address the problem of providing useful answers to provenance queries while ensuring that privacy concerns are met. In particular, we propose a hierarchical workflow model, based on context-free graph grammars, in which fine-grained dependencies between the inputs and outputs of a module are explicitly specified. Using this model, we examine how privacy concerns surrounding data, module function, and workflow structure can be addressed.

Recursive queries and context-free graph grammars

On the Complexity of Pattern Matching for Highly Compressed Two-Dimensional Texts

In each graph-grammar approach it is defined how and under which conditions graph productions can be applied to a given graph in order to obtain a derived graph. The conditions under which productions can be applied are called application conditions. Although the generative power of most of the known general graph-grammar approaches is sufficient to generate any recursively enumerable set of graphs, it is often convenient to have specific application conditions for each production. Such application conditions, on the one hand, include context conditions like the existence or non-existence of nodes, edges, or certain subgraphs in the given graph as well as embedding restrictions concerning the morphisms from the left-hand side of the production to the given graph. In this paper, the concept of application conditions introduced by Ehrig and Habel is restricted to contextual conditions, especially negative ones. In addition to the general concept, we state local confluence and the Parallelism Theorem for derivations with application conditions. Finally we study context-free graph grammars with application conditions with respect to their generative power.

Given a sample from an unknown probability distribution over strings, there exist algorithms for inferring the structure and parameters of stochastic grammatical representations of the unknown distribution, i.e. string grammars. Despite the fact that research on grammatical representations of sets of graphs has been conducted since the late 1960’s, almost no work has considered the possibility of stochastic graph grammars and no algorithms exist for inferring stochastic graph grammars from data. This paper presents PEGG, an algorithm for estimating the parameters of stochastic context-free graph grammars given a sample from an unknown probability distribution over graphs. It is established formally that for a certain class of graph grammars PEGG finds parameter estimates in polynomial time that maximize the likelihood of the data, and preliminary empirical results demonstrate that the algorithm performs well in practice.KeywordsGraph TransformationGraph GrammarMaximum Likelihood ParameterStart SymbolEstimate Maximum Likelihood ParameterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Layout graph grammars are extensions of context-free graph grammars and are introduced as a tool for syntax directed constructions of graph layouts. The constructions are based on a layout specification of the productions, which are consistently transferred to the derivations. The layout specification consists of rules for a placement of the vertices and a partial routing of the edges. It specifies minimal distances between the vertices in X- or Y-dimension. These distances can be optimized according to some formal cost measures.

The fundamental properties of a gas-sensitive device for the recognition of odoriferous gases made of a surface acoustic wave (SAW) device and Langmuir-Blodgett (LB) film were studied. An SAW device can be operated at a higher oscillation frequency than a quartz oscillator, and an organic ultrathin film, such as the LB film, was used as the gas-sensitive film on the SAW device. The relationship between gassensitivity and the molecular orientation, as well as the thickness and the counterion of LB film, was investigated. The molecular orientation and the thickness of the LB films affected the gassensitivity. The gassensitivity of LB films incorporating counterions was largely dependent on the electronegativity of the counterion. The characteristics of the gas-sensitive device were elucidated and were utilized to realize the recognition system for odoriferous gases.

Context-free graph grammars

We give examples to show that not even c-edNCE, the most general known notion of context-free graph grammar, is suited for the specification of some common data structures.

This paper describes an object-oriented lexical representation language based on Unification Categorial Grammar (UCG) that encodes linguistic and semantic information uniformly as classes and objects and an efficient bottom-up parsing method for UCG using selection sets technique. The lexical representation language, implemented in the logic and object-oriented programming language LIFE, introduces several new information sharing mechanisms to enable natural, declarative, modular and economial construction of large and complex computational lexicons. The selection sets are deduced from a transformation between UCG and Context-Free Grammar (CFG) and used to reduce search space for the table-driven algorithm. The experimental tests on a spoken English corpus show that the hierarchical lexicon achieves a dramatic reduction on redundant information and that selection sets significantly improve parsing UCG with a polynomial time complexity.

Chapter 1 - Type-II Superlattice Infrared Detectors