Context-free Graph Research Articles

VPPE: A Novel Visual Parallel Programming Environment

Parallel programming continues to be a challenging task despite the many advances in parallel architectures and their wide availability in the cloud. The need both to partition the workload among various processing elements and to specify communication between them to share code and data, and to coordinate their tasks, requires from the developer a deep understanding of the problem, the parallel architecture and the programming language used in order to develop efficient parallel applications. This problem can be reduced significantly through the use of visual programming languages to hide most aspects related to the specification of communication and processes management. This paper presents VPPE, a novel Visual Parallel Programming Environment that allows developers to program parallel applications through organising workflows of interconnected icons. VPPE is a cloud environment that supports icons for specifying: I/O operations, workflow organisation, communication, and processing. Processing computing patterns supported so far include Single Program Multiple Data, Multiple Program Multiple Data, Pipeline, and Master–Slave. The paper highlights the design of VPPE based on a context-free graph grammar, its current implementation based on Java-MPI, its use in developing various parallel applications, and its evaluation compared to Java-MPI text-based programming.

A Framework for Rewriting Families of String Diagrams

We describe a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. The framework is based on context-free families of string diagrams which we represent using context-free graph grammars. We model equations between infinite families of diagrams using rewrite rules between context-free grammars. Our framework represents equational reasoning about concrete string diagrams and context-free families of string diagrams using double-pushout rewriting on graphs and context-free graph grammars respectively. We prove that our representation is sound by showing that it respects the concrete semantics of string diagrammatic reasoning and we show that our framework is appropriate for software implementation by proving the membership problem is decidable.

Context-free graph P system

Graph grammar is a rewriting system generating graph languages. Context-free graph grammars are studied developing a theory similar to that of context-free string languages. In this paper we define context-free node replacement graph P system with conditional communication and context-free node replacement graph rewriting P system. Results on the notions such as the minimum number of membranes required to generate a family of context-free graph languages are discussed.

Context-free graph P system

Context-free graph P system

Reachability analysis of reversal-bounded automata on series\u2013parallel graphs

Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular verification problems. In this paper, we consider a generalization of automata-theoretic infinite-state verification from strings to labelled series–parallel graphs. We define a model of non-deterministic, 2-way, concurrent automata working on series–parallel graphs and communicating through shared registers on the nodes of the graph. We consider the following verification problem: given a family of series–parallel graphs described by a context-free graph transformation system (GTS), and a concurrent automaton over series–parallel graphs, is some graph generated by the GTS accepted by the automaton? The general problem is undecidable already for (one-way) multi-head automata over strings. We show that a bounded version, where the automata make a fixed number of reversals along the graph and use a fixed number of shared registers is decidable, even though there is no bound on the sizes of series–parallel graphs generated by the GTS. Our decidability result is based on establishing that the number of context switches can be bounded and on an encoding of the computation of bounded concurrent automata that allows us to reduce the reachability problem to the emptiness problem for pushdown automata.

Generalizing a categorization of students’ interpretations of linear kinematics graphs

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.Received 23 September 2015DOI:https://doi.org/10.1103/PhysRevPhysEducRes.12.010108This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasConcepts & principlesEpistemology, attitudes, & beliefsPhysics Education Research

Reachability Analysis of Reversal-bounded Automata on Series-Parallel Graphs

Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular verification problems. In this paper, we consider a generalization of automata-theoretic infinite-state verification from strings to labeled series-parallel graphs. We define a model of non-deterministic, 2-way, concurrent automata working on series-parallel graphs and communicating through shared registers on the nodes of the graph. We consider the following verification problem: given a family of series-parallel graphs described by a context-free graph transformation system (GTS), and a concurrent automaton over series-parallel graphs, is some graph generated by the GTS accepted by the automaton? The general problem is undecidable already for (one-way) multi-head automata over strings. We show that a bounded version, where the automata make a fixed number of reversals along the graph and use a fixed number of shared registers is decidable, even though there is no bound on the sizes of series-parallel graphs generated by the GTS. Our decidability result is based on establishing that the number of context switches is bounded and on an encoding of the computation of bounded concurrent automata to reduce the emptiness problem to the emptiness problem for pushdown automata.

Grammar-based model transformations: Definition, execution, and quality properties

Model transformation is a key concept in model-driven software engineering. The definition of model transformations is usually based on meta-models describing the abstract syntax of languages. While meta-models are thereby able to abstract from superfluous details of concrete syntax, they often loose structural information inherent in languages, like information on model elements always occurring together in particular shapes. As a consequence, model transformations cannot naturally re-use language structures, thus leading to unnecessary complexity in their development as well as in quality assurance.In this paper, we propose a new approach to model transformation development which allows to simplify the developed transformations and improve their quality via the exploitation of the languages׳ structures. The approach is based on context-free graph grammars and transformations defined by pairing productions of source and target grammars. We show that such transformations have important properties: they terminate and are sound, complete, and deterministic.

Understanding Descriptions of Visual Scenes Using Graph Grammars

Automatic generation of 3D scenes from descriptions has applications in communication, education, and entertainment, but requires deep understanding of the input text. I propose thesis work on language understanding using graph-based meaning representations that can be decomposed into primitive spatial relations. The techniques used for analyzing text and transforming it into a scene representation are based on context-free graph grammars. The thesis develops methods for semantic parsing with graphs, acquisition of graph grammars, and satisfaction of spatial and world-knowledge constraints during parsing.

Amalgams of finite inverse semigroups and deterministic context-free languages

Let S be the amalgamated free product of two finite inverse semigroups. We prove that the Schutzenberger graph of an element of S with respect to a standard presentation of S is a context-free graph in the sense of Muller and Schupp (Theor. Comput. Sci. 37:51–75, 1985), showing that the language L recognized by the Schutzenberger automaton is context-free. Moreover we construct the grammar generating L proving that L is a deterministic context-free language and we use this fact for solving some algorithmic problems.

Context-free pairs of groups I: Context-free pairs and graphs

Let G be a finitely generated group, A a finite set of generators and K a subgroup of G. We define what it means for (G,K) to be a context-free pair; when K is trivial, this specializes to the standard definition of G to be a context-free group.We derive some basic properties of such group pairs. Context-freeness is independent of the choice of the generating set. It is preserved under finite index modifications of G and finite index enlargements of K. If G is virtually free and K is finitely generated then (G,K) is context-free. A basic tool is the following: (G,K) is context-free if and only if the Schreier graph of (G,K) with respect to A is a context-free graph.

Context-free pairs of groups II — Cuts, tree sets, and random walks

This is a continuation of the study, begun by Ceccherini-Silberstein and Woess (2009) [5], of context-free pairs of groups and the related context-free graphs in the sense of Muller and Schupp (1985) [22]. The graphs under consideration are Schreier graphs of a subgroup of some finitely generated group, and context-freeness relates to a tree-like structure of those graphs. Instead of the cones of Muller and Schupp (1985) [22] (connected components resulting from deletion of finite balls with respect to the graph metric), a more general approach to context-free graphs is proposed via tree sets consisting of cuts of the graph, and associated structure trees. The existence of tree sets with certain “good” properties is studied. With a tree set, a natural context-free grammar is associated. These investigations of the structure of context free pairs, resp. graphs are then applied to study random walk asymptotics via complex analysis. In particular, a complete proof of the local limit theorem for return probabilities on any virtually free group is given, as well as on Schreier graphs of a finitely generated subgoup of a free group. This extends, respectively completes, the significant work of Lalley (1993, 2001) [18,20].

Graph grammars with string-regulated rewriting

Multicellular organisms undergo a complex developmental process, orchestrated by the genetic information in their cells, in order to form a newborn individual from a fertilized egg. This complex process, not completely understood yet, is believed to have a key role in generating the impressive biotic diversity of organisms found on earth. Inspired by mechanisms of Eukaryotic genetic expression, we propose and analyse graph grammars with string-regulated rewriting. In these grammatical systems a genome sequence is represented by a regulatory string, a graph corresponds to an organism, and a set of graph grammar rules represents different forms of implementing cell division. Accordingly, a graph derivation by the graph grammar resembles the developmental process of an organism. We give examples of the concept and compare its generative power to the power of the traditional context-free graph grammars. We demonstrate that the power of expression increases when genetic regulation is included in the model, as compared to non-regulated grammars. Additionally, we propose a hierarchy of string-regulated graph grammars, arranged by expressive power. These results highlight the key role that the transmission of regulatory information during development has in the emergence of biological diversity.

Adaptive star grammars and their languages

Motivated by applications that require mechanisms for describing the structure of object-oriented programs, adaptive star grammars are introduced, and their fundamental properties are studied. In adaptive star grammars, rules are actually schemata which, via the cloning of so-called multiple nodes, may adapt to potentially infinitely many contexts when they are applied. This mechanism makes adaptive star grammars more powerful than context-free graph grammars. Nevertheless, they turn out to be restricted enough to share some of the basic characteristics of context-free devices. In particular, the underlying substitution operator enjoys associativity and confluence properties quite similar to those of context-free graph grammars, and the membership problem for adaptive star grammars is decidable.

Syntactic Characterization of the Two-Dimensional Grid Graphs

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.

The recognizability of sets of graphs is a robust property

Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite congruences. Applications to the construction of efficient algorithms and to the theory of context-free sets of graphs follow naturally. The class of recognizable sets depends on the signature of graph operations. We consider three signatures related respectively to Hyperedge Replacement ( HR) context-free graph grammars, to Vertex Replacement ( VR) context-free graph grammars, and to modular decompositions of graphs. We compare the corresponding classes of recognizable sets. We show that they are robust in the sense that many variants of each signature (where in particular operations are defined by quantifier-free formulas, a quite flexible framework) yield the same notions of recognizability. We prove that for graphs without large complete bipartite subgraphs, HR-recognizability and VR-recognizability coincide. The same combinatorial condition equates HR-context-free and VR-context-free sets of graphs. Inasmuch as possible, results are formulated in the more general framework of relational structures.

On spectra of sentences of monadic second order logic with counting

Abstract.We show that the spectrum of a sentence ϕ in Counting Monadic Second Order Logic (CMSOL) using one binary relation symbol and finitely many unary relation symbols, is ultimately periodic, provided all the models of ϕ are of clique width at most k, for some fixed k. We prove a similar statement for arbitrary finite relational vocabularies τ and a variant of clique width for τ-structures. This includes the cases where the models of ϕ are of tree width at most k. For the case of bounded tree-width, the ultimate periodicity is even proved for Guarded Second Order Logic GSOL. We also generalize this result to many-sorted spectra, which can be viewed as an analogue of Parikh's Theorem on context-free languages, and its analogues for context-free graph grammars due to Habel and Courcelle.Our work was inspired by Gurevich and Shelah (2003), who showed ultimate periodicity of the spectrum for sentences of Monadic Second Order Logic where only finitely many unary predicates and one unary function are allowed. This restriction implies that the models are all of tree width at most 2, and hence it follows from our result.

MDL-BASED CONTEXT-FREE GRAPH GRAMMAR INDUCTION AND APPLICATIONS

We present an algorithm for the inference of context-free graph grammars from examples. The algorithm builds on an earlier system for frequent substructure discovery, and is biased toward grammars that minimize description length. Grammar features include recursion, variables and relationships. We present an illustrative example, demonstrate the algorithm's ability to learn in the presence of noise, and show real-world examples.

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

Abstract This lecture surveys about 15 years of research about context-free graph grammars, graph operations, graph transformations and monadic second-order logic done in cooperation with participants of the European network GETGRATS and of previous European projects related with graph grammars and graph transformations.

Context-free hypergraph grammars with node rewriting

Abstract The generalisation of confluent node rewriting, a context-free graph grammar approach, to hypergraphs yields the most powerful known context-free technique to define hypergraph languages. This paper, which summarises part of the author's doctoral thesis, substantiates that claim by reporting on the generative power of the so-called C-hNCE grammars.