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Contextual petri nets, asymmetric event structures and processes
 Information and Computation
, 2001
"... We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (readonly operations). A basic rôle is played by asymmetric event structures, a generalization of Winskel’s prime event structure ..."
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Cited by 40 (15 self)
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We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (readonly operations). A basic rôle is played by asymmetric event structures, a generalization of Winskel’s prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality, used to represent a new kind of dependency between events arising in contextual nets. Extending Winskel’s seminal work on safe nets, the truly concurrent event based semantics of contextual nets is given at categorical level via a chain of coreflections
Unfolding and Event Structure Semantics for Graph Grammars
 PROCEEDINGS OF THE 5TH INTERNATIONAL WORKSHOP ON GRAPH GRAMMARS AND THEIR APPLICATION TO COMPUTER SCIENCE, VOLUME 1073 OF LNCS
, 1996
"... We propose an unfolding semantics for graph transformation systems in the doublepushout (DPO) approach. Mimicking Winskel’s construction for Petri nets, a graph grammar is unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the ..."
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Cited by 36 (21 self)
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We propose an unfolding semantics for graph transformation systems in the doublepushout (DPO) approach. Mimicking Winskel’s construction for Petri nets, a graph grammar is unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the possible computations of the original grammar. The unfolding can be abstracted naturally to a prime algebraic domain and then to an event structure semantics. We show that such event structure coincides both with the one defined by Corradini et al. [3] via a
U.: Adhesive HighLevel Replacement Categories and Systems
 Proceedings of ICGT 2004. Volume 3256 of LNCS
, 2004
"... Abstract. Adhesive highlevel replacement (HLR) systems have been recently introduced as a new categorical framework for graph tranformation in the double pushout (DPO) approach. They combine the wellknown concept of HLR systems with the concept of adhesive categories introduced by Lack and Soboci ..."
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Cited by 34 (11 self)
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Abstract. Adhesive highlevel replacement (HLR) systems have been recently introduced as a new categorical framework for graph tranformation in the double pushout (DPO) approach. They combine the wellknown concept of HLR systems with the concept of adhesive categories introduced by Lack and Sobociński. While graphs, typed graphs, attributed graphs and several other variants of graphs together with corresponding morphisms are adhesive HLR categories, such that the categorical framework of adhesive HLR systems can be applied, this has been claimed also for Petri nets. In this paper we show that this claim is wrong for place/transition nets and algebraic highlevel nets, although several results of the theory for adhesive HLR systems are known to be true for the corresponding Petri net transformation systems. In fact, we are able to define a weaker version of adhesive HLR categories, called weak adhesive HLR categories, which is still sufficient to show all the results known for adhesive HLR systems. This concept includes not only all kinds of graphs mentioned above, but also place/transition nets, algebraic highlevel nets and several other kinds of Petri nets. For this reason weak adhesive HLR systems can be seen as a unifying framework for graph and Petri net transformations. 1
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 31 (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...
Horizontal and Vertical Structuring of Typed Graph Transformation Systems
, 1996
"... this paper we concentrate on structuring and refinement concepts for graph transformation systems. Conceptually, we distinguish between two kinds of structuring. We speak of horizontal structuring if a large specification is obtained by combining and modifying smaller ones, possibly sharing some com ..."
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Cited by 31 (18 self)
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this paper we concentrate on structuring and refinement concepts for graph transformation systems. Conceptually, we distinguish between two kinds of structuring. We speak of horizontal structuring if a large specification is obtained by combining and modifying smaller ones, possibly sharing some common parts. Instead, if we consider the relationship between a more abstract and a more concrete version of the same specification, or between a specification and its implementation, we speak of vertical structuring.
A Combined Reference Model and ViewBased Approach to System Specification
, 1997
"... this paper we present a specification technique based on graph transformations which supports such a development approach. The use of graphs and graph transformations supports an intuitive understanding and an integration of static and dynamic aspects on a welldefined semantical base. On this backg ..."
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Cited by 24 (12 self)
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this paper we present a specification technique based on graph transformations which supports such a development approach. The use of graphs and graph transformations supports an intuitive understanding and an integration of static and dynamic aspects on a welldefined semantical base. On this background, formal notions of view and view relation are developed and the behaviour of views is described by a loose semantics. The integration of two views derived from a common reference model is done in two steps. First, dependencies between the views which are not given by the reference model are determined, and the reference model is extended appropriately. This is the task of a model manager. If the two views and the reference model are consistent, the actual view integration can be performed automatically. For the case of more than two views more general scenarios are developed and discussed. All concepts and results are illustrated at the wellknown example of a banking system.
A Generic Graphical Editor for Visual Languages based on Algebraic Graph Grammars
, 1998
"... GENGED is a generic graphical editor supporting the graphical definition of visual languages. Given an alphabet and rules of a specific visual language GENGED generates a syntaxdirected graphical editor for this language. GENGED as well as each visual language defined using GENGED is based on algeb ..."
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Cited by 24 (3 self)
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GENGED is a generic graphical editor supporting the graphical definition of visual languages. Given an alphabet and rules of a specific visual language GENGED generates a syntaxdirected graphical editor for this language. GENGED as well as each visual language defined using GENGED is based on algebraic graph grammars. A sentence is given by a graphical structure consisting of a logical (abstract syntax) and a visual level (concrete syntax). Both levels are connected by layout operations. Visual language rules are defined by graph grammar rules. The underlying logical structure, however, is hidden from the user, but it is essential for a formal presentation and manipulation of graphical structures on both levels. The manipulations are performed by a graph transformation machine working on the logical level, whereas a graphical constraint solver manages the layout the user works with. Keywords: graphical definition of VLs; generation of syntaxdirected graphical editors; visual specifi...
Concurrent semantics of algebraic graph transformation
 Handbook of Graph Grammars and Computing by Graph Transformation
, 1999
"... Graph transformation systems are widely recognized as a powerful formalism for the specification of concurrent and distributed systems. Therefore, the need emerges naturally of developing formal concurrent semantics for graph transformation systems allowing for a suitable description and analysis of ..."
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Cited by 23 (4 self)
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Graph transformation systems are widely recognized as a powerful formalism for the specification of concurrent and distributed systems. Therefore, the need emerges naturally of developing formal concurrent semantics for graph transformation systems allowing for a suitable description and analysis of their computational properties. The aim of this chapter is to review and compare various concurrent semantics for the double pushout (DPO) algebraic approach to graph transformation, using different mathematical structures and describing computations at different levels of abstraction. We first present a trace semantics, based on the classical shift equivalence on graph derivations. Next we introduce graph processes, which lift to the graph transformation framework the notion of nonsequential process for Petri nets. Trace and process semantics are shown to be equivalent, in the sense that given a graph transformation system, the corresponding category of derivation traces and that of (concatenable) processes turns out to be isomorphic. Finally, a more abstract description of graph transformation systems computations is given by defining a semantics based on Winskel’s event structures.
Conflict Detection for Graph Transformation with Negative Application Conditions
 In Proc. Third International Conference on Graph Transformation (ICGT’06), volume 4178 of LNCS
, 2006
"... Abstract. This paper introduces a new theory needed for the purpose of conflict detection for graph transformation with negative application conditions (NACs). Main results are the formulation of a conflict notion for graph transformation with NACs and a conflict characterization derived from it. A ..."
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Cited by 21 (10 self)
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Abstract. This paper introduces a new theory needed for the purpose of conflict detection for graph transformation with negative application conditions (NACs). Main results are the formulation of a conflict notion for graph transformation with NACs and a conflict characterization derived from it. A critical pair definition is introduced and completeness of the set of all critical pairs is shown. This means that for each conflict, occuring in a graph transformation system with NACs, there exists a critical pair expressing the same conflict in a minimal context. Moreover a necessary and sufficient condition is presented for parallel independence of graph transformation systems with NACs. In order to facilitate the implementation of the critical pair construction for a graph transformation system with NACs a correct construction is formulated. Finally, it is discussed how to continue with the development of conflict detection and analysis techniques in the near future. 1
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 20 (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.