Analysis of Hypergraph Transformation Systems in AGG based on M-Functors: Extended Version

Hypergraph transformation systems are examples ofM-adhesive transformation systems based on M-adhesive categories. For typed attributed graph transformation systems, the tool environment Agg allows the modelling, the simulation and the analysis of graph transformations. A corresponding tool for analysis of hypergraph transformation systems does not exist up to now. The purpose of this paper is to establish a formal relationship between the corresponding M- adhesive transformation systems, which allows us the translation of hypergraph transformations into typed attributed graph transformations with equivalent behavior, and, vice versa, the creation of hypergraph transformations from typed attributed graph transformations. This formal relationship is based on the general theory ofM-functors between differentM-adhesive transformation systems. We construct a functor between the M-adhesive categories of hypergraphs and of typed attributed graphs, and show that our construction yields an M-functor with suitable properties. We then use existing results for M-functors to show that analysis results for hypergraph transformation systems can be obtained using Agg by analysis of the translated typed attributed graph transformation system. This is shown in general and for a concrete example

Analysis of Hypergraph Transformation Systems in AGG based on M-Functors

Hypergraph transformation systems are examples of M-adhesive transformation systems based on M-adhesive categories. For typed attributed graph transformation systems, the tool environment AGG allows the modelling, the simu-lation and the analysis of graph transformations. A corresponding tool for analysis of hypergraph transformation systems does not exist up to now. The purpose of this paper is to establish a formal relationship between the corresponding M-adhesive transformation systems, which allows us the translation of hypergraph transformations into typed attributed graph transformations with equivalent behavior, and, vice versa, the creation of hypergraph transformations from typed attributed graph transformations. This formal relationship is based on the general theory of M-functors between different M-adhesive transformation systems. We construct a functor between the M-adhesive categories of hypergraphs and of typed attributed graphs, and show that our construction yields an M-functor with suitable properties. We then use existing results for M-functors to show that analysis results for hypergraph transformation systems can be obtained using AGG  by analysis of the translated typed attributed graph transformation system. This is shown in general and for a concrete example

Simulating Multigraph Transformations Using Simple Graphs

Application of graph transformations for software verification and model transformation is an emergent field of research. In particular, graph transformation approaches provide a natural way of modelling object oriented systems and semantics of object-oriented languages.\ud \ud There exist a number of tools for graph transformations that are often specialised in a particular kind of graphs and/or graph transformation approaches, depending on the desired application domain. The main drawback of this diversity is the lack of interoperability.\ud \ud In this paper we show how (typed) multigraph production systems can be translated into (typed) simple-graph production systems. The presented construction enables the use of multigraphs with DPO transformation approach in tools that only support simple graphs with SPO transformation approach, e.g. the GROOVE tool

Towards Model Checking Reconfigurable Petri Nets using Maude

This paper introduces an approach to model checking of reconfigurable Petri nets. The main task is to flatten the two levels of dynamic behavior that reconfigurable nets provide, the firing of transitions on the one hand and the transformation of the nets on the other hand. We show how to translate a reconfigurable net into  Maude modules. Maude's LTL model-checker is then used to verify properties of these modules

Reconfigurable component connectors

This thesis provides formal methods for reconfigurable component connectors.UBL - phd migration 201

A Unifying Theory for Graph Transformation

The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO

Matrix Graph Grammars

This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars -- Matrix Graph Grammars in particular -- study dynamics of graphs. Ideally, this algebraization would enforce our understanding of grammars in general, providing new analysis techniques and generalizations of concepts, problems and results known so far.Comment: 321 pages, 75 figures. This book has is publisehd by VDM verlag, ISBN 978-363921255