Concurrent Computing: from Petri Nets to Graph Grammars

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Towards rule-based visual programming of generic visual systems

This paper illustrates how the diagram programming language DiaPlan can be used to program visual systems. DiaPlan is a visual rule-based language that is founded on the computational model of graph transformation. The language supports object-oriented programming since its graphs are hierarchically structured. Typing allows the shape of these graphs to be specified recursively in order to increase program security. Thanks to its genericity, DiaPlan allows to implement systems that represent and manipulate data in arbitrary diagram notations. The environment for the language exploits the diagram editor generator DiaGen for providing genericity, and for implementing its user interface and type checker.Comment: 15 pages, 16 figures contribution to the First International Workshop on Rule-Based Programming (RULE'2000), September 19, 2000, Montreal, Canad

From Separate Formal Specifications to Certified Integrated Visual Modelling Techniques and Environments - Position Statement

In this position statement we discuss the state of the art and role of formal specification and modelling techniques in different periods with special focus on the work of the TFS-group at TU-Berlin. In the past (1970 – 1990) single formal specification techniques have been developed with little impact on practical software development. In the present (1990 – 2010) integrated and visual modelling techniques have gained more and more importance. For the future (2010 – 2020) we try to sketch the idea of a Certified Integrated Visual Modelling Technique and Environment based on an integration of graph theory, graph transformation and Petri net theory, short Dynamic Graph and Net Theory

Consistency of a system of equations: What does that mean?

The concept of (structural) consistency also called structural solvability is an important basic tool for analyzing the structure of systems of equations. Our aim is to provide a sound and practically relevant meaning to this concept. The implications of consistency are expressed in terms of explicit density and stability results. We also illustrate, by typical examples, the limitations of the concept

Implementing β-Reduction by Hypergraph Rewriting

AbstractThe aim of this paper is to implement the β-reduction in the lambda;-calculus with a hypergraph rewriting mechanism called collapsed lambda;-tree rewriting. It turns out that collapsed lambda;-tree rewriting is sound with respect to β-reduction and complete with respect to the Gross-Knuth strategy. As a consequence, there exists a normal form for a collapsed lambda;-tree if and only if there exists a normal form for the represented λ-term.I am grateful to Renate Klempien-Hinrichs, Detlef Plump, and to the referees for their helpful comments

A Compositional Approach to Structuring and Refinement of Typed Graph Grammars

Abstract Based on a categorical semantics that has been developed for typed graph grammars we uses colimits (pushouts) to model composition and (reverse) graph grammar morphisms to describe refinements of typed graph grammars. Composition of graph grammars w.r.t. common subgrammars is shown to be compatible with the semantics, i.e. the semantics of the composed grammar is obtained as the composition of the semantics of the component grammars. Moreover, the structure of a composed grammar is preserved during a refinement step in the sense that compatible refinements of the components induce a refinement of the composition. The concepts and results are illustrated by an example

Modelling and analysis of traffic networks based on graph transformation

This is an electronic version of the paper presented at the Symposium on Formal Methods for Automation and Safety in Railway and Automotive Systems, FORMS/FORMATS 2004 , held in Braunschweig on 2004We present the formal definition of a domain specific visual language (Traffic) for the area of traffic networks. The syntax has been specified by means of meta-modelling. For the semantics, two approaches have been followed. In the first one, graph transformation is used to specify an operational semantics. In the second one we include timing information and a denotational semantics is defined in terms of Timed Transition Petri Nets (TTPN). The transformation from the Traffic formalism into TTPN was also defined by graph transformation. Both approaches have been used for the analysis of Traffic models. The ideas have been implemented in the AToM3 tool and are illustrated with examples.Juan de Lara’s work has been partially sponsored by a grant from the E.U. SEGRAVIS research network (HPRN-CT-2002-00) and the Spanish Ministry of Science and Technology (TIC2002-01948). Hans Vangheluwe gratefully acknowledges partial support for this work by a National Sciences and Engineering Research Council of Canada (NSERC) Individual Research Grant