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An Inductive View of Graph Transformation
 In Workshop on Algebraic Development Techniques
, 1998
"... . The dynamic behavior of rulebased systems (like term rewriting systems [24], process algebras [27], and so on) can be traditionally determined in two orthogonal ways. Either operationally, in the sense that a way of embedding a rule into a state is devised, stating explicitly how the result i ..."
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Cited by 30 (12 self)
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. The dynamic behavior of rulebased systems (like term rewriting systems [24], process algebras [27], and so on) can be traditionally determined in two orthogonal ways. Either operationally, in the sense that a way of embedding a rule into a state is devised, stating explicitly how the result is built: This is the role played by (the application of) a substitution in term rewriting. Or inductively, showing how to build the class of all possible reductions from a set of basic ones: For term rewriting, this is the usual definition of the rewrite relation as the minimal closure of the rewrite rules. As far as graph transformation is concerned, the operational view is by far more popular: In this paper we lay the basis for the orthogonal view. We first provide an inductive description for graphs as arrows of a freely generated dgsmonoidal category. We then apply 2categorical techniques, already known for term and term graph rewriting [29, 7], recasting in this framework the...
A BiCategorical Axiomatisation of Concurrent Graph Rewriting
, 1999
"... In this paper the concurrent semantics of doublepushout (DPO) graph rewriting, which is classically defined in terms of shiftequivalence classes of graph derivations, is axiomatised via the construction of a free monoidal bicategory. In contrast to a previous attempt based on 2categories, the us ..."
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Cited by 18 (10 self)
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In this paper the concurrent semantics of doublepushout (DPO) graph rewriting, which is classically defined in terms of shiftequivalence classes of graph derivations, is axiomatised via the construction of a free monoidal bicategory. In contrast to a previous attempt based on 2categories, the use of bicategories allows to define rewriting on concrete graphs. Thus, the problem of composition of isomorphism classes of rewriting sequences is avoided. Moreover, as a first step towards the recovery of the full expressive power of the formalism via a purely algebraic description, the concept of disconnected rules is introduced, i.e., rules whose interface graphs are made of disconnected nodes and edges only. It is proved that, under reasonable assumptions, rewriting via disconnected rules enjoys similar concurrency properties like in the classical approach.
Concurrent Computing: from Petri Nets to Graph Grammars
 Electronic Notes in Theoretical Computer Science
, 1995
"... Petri nets are widely accepted as a specification formalism for concurrent and distributed systems. One of the reasons of their success is the fact that they are equipped with a rich theory, including wellunderstood concurrent semantics; they also provide an interesting benchmark for tools and tech ..."
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Cited by 9 (0 self)
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Petri nets are widely accepted as a specification formalism for concurrent and distributed systems. One of the reasons of their success is the fact that they are equipped with a rich theory, including wellunderstood concurrent semantics; they also provide an interesting benchmark for tools and techniques for the description of concurrent systems. Graph grammars can be regarded as a proper generalization of Petri nets, where the current state of a system is described by a graph instead as by a collection of tokens. In this tutorial paper I will review some basic definitions and constructions concerning the concurrent semantics of nets, and I will show to what extent corresponding notions have been developed for graph grammars. Most of such results come out from a joint research by the Berlin and Pisa COMPUGRAPH groups. 1 Introduction The nets which owe their name to Carl Adam Petri [28,29] have been the first formal tool proposed for the specification of the behaviour of systems which...
Synchronized Composition of Graph Grammar Productions
, 1995
"... . In the framework of the doublepushout approach to graph grammars, we propose a new notion of parallel composition, called synchronized composition, of production applications. Our aim is to allow (pairs of) productions which are possibly not parallel independent, to be applied in parallel, provid ..."
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Cited by 3 (1 self)
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. In the framework of the doublepushout approach to graph grammars, we propose a new notion of parallel composition, called synchronized composition, of production applications. Our aim is to allow (pairs of) productions which are possibly not parallel independent, to be applied in parallel, provided that they are not mutually exclusive.The notion of synchronized composition we propose is not comparable to amalgamation [BFH87], since two productions which are amalgable are not necessarily synchronizable, and viceversa. Our different idea of which productions should be applicable in parallel comes from our view of graph grammars as a generalization of Petri nets. The definitions and constructions we use are a conservative extension of the ones used in the classical theory of parallelism in the algebraic approach to graph grammars. Moreover, they can be the basis for the development of a more general concept of canonical derivations, and also for a generalization of the recently develop...
Singlepushout rewriting in categories of spans I: The general setting
"... . A unifying view of all constructions of pushouts of partial morphisms considered so far in the literature of singlepushout transformation is given in this paper. Pushouts of partial morphisms are studied in an abstract category of spans formed out of two distinguished subcategories of the base ca ..."
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. A unifying view of all constructions of pushouts of partial morphisms considered so far in the literature of singlepushout transformation is given in this paper. Pushouts of partial morphisms are studied in an abstract category of spans formed out of two distinguished subcategories of the base category, thus generalizing previous studies in singlepushout transformation. Such spans are single pairs of morphisms, instead of equivalence classes, providing then a notion of transformation which is independent of class representatives. A necessary and sufficient condition for the existence of the pushout of two spans is established which involves properties of the base category, from which the category of spans is derived, as well as properties of the spans themselves. Moreover, a necessary and sufficient condition for singlepushout derivations in a category of spans to subsume doublepushout derivations in the base category is established which only involves properties of the base categ...
ASPECTORIENTED CONSTRAINT MANAGEMENT IN METAMODELBASED MODEL TRANSFORMATION STEPS
, 2004
"... A widely applied approach to model transformation uses graph rewriting as the underlying transformation technique. In case of diagrammatic languages, such as the Unified Modeling Language (UML), the exclusive topological matching is found to be not enough. To define the transformation steps precisel ..."
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A widely applied approach to model transformation uses graph rewriting as the underlying transformation technique. In case of diagrammatic languages, such as the Unified Modeling Language (UML), the exclusive topological matching is found to be not enough. To define the transformation steps precisely beyond the structure of the visual models, additional constraints must be specified which ensures the correctness of the attributes, or other properties to be enforced. Dealing with OCL constraints provides a solution for these unsolved issues. The use of OCL as a constraint and query language in modelling is essential. We have shown that it can be applied to model transformations as well. Often, the same constraint is repetitiously applied in many different places in a transformation. It would be beneficial to describe a common constraint in a modular manner, and to mark the places where it is to be applied. This paper discusses (i) the problem of crosscutting constraints in visual model transformation steps, and provides an aspectoriented solution for a consistent constraint management. It introduces the concepts of aspectoriented constraints and a new type of aspect, the constraint aspects. (ii) In general, it is difficult to require a whole transformation to validate, preserve or guarantee certain properties because transformations are built form isolated transformation steps ordered by a control structure. This problem is solved by the provided constraint weaver methods, which weave the constraints into the model transformation steps prior to the execution. (iii) Furthermore, the work presents offline constraint optimization (normalization) algorithms, which are part of the presented weaving process.
Concurrency for Graph Grammars in a Petri net shell
"... Graph grammars are a powerful model of concurrent and distributed systems which can be seen as a proper extension of Petri nets. Inspired by this correspondence we develop truly concurrent semantics for dpo graph grammars based on (deterministic) processes and on a Winskel’s style unfolding construc ..."
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Graph grammars are a powerful model of concurrent and distributed systems which can be seen as a proper extension of Petri nets. Inspired by this correspondence we develop truly concurrent semantics for dpo graph grammars based on (deterministic) processes and on a Winskel’s style unfolding construction, and we show that the two approaches can be reconciled. A basic role is played by the study of contextual and inhibitor nets, two extensions of ordinary nets which can be seen as intermediate models between graph grammars and ordinary Petri nets. Keywords: domains.