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21
Distributed Graph Transformation Units
 International Journal on Software Engineering and Knowledge Engineering
, 2002
"... Transformation units are a structuring principle for graph transformation systems. In this paper we introduce distributed transformation units that can be used to model distributed graph transformation systems. A distributed transformation unit consists of a set of local transformation units which a ..."
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Cited by 24 (21 self)
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Transformation units are a structuring principle for graph transformation systems. In this paper we introduce distributed transformation units that can be used to model distributed graph transformation systems. A distributed transformation unit consists of a set of local transformation units which are connected via interface units. Semantically, a distributed transformation unit transforms distributed graphs consisting of a set of local graphs connected via interface graphs, in such a way that every local graph with its interfaces is transformed by a local transformation unit. Since the interface graphs can be modified concurrently by various local transformation units we introduce a concurrent semantics of transformation units. The presented concepts are illustrated with a running example of a simple game where two different actors access a common game board randomly.
Model Checking Graph Grammars
, 2003
"... We sketch a setup in which transition systems are generated from graph grammars andsubsequently checked for properties expressed in a temporal logic on graphs. We envisage this as part of an approach where graph grammars are used to express the behavioural semantics ofobjectoriented programs, thus ..."
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Cited by 21 (8 self)
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We sketch a setup in which transition systems are generated from graph grammars andsubsequently checked for properties expressed in a temporal logic on graphs. We envisage this as part of an approach where graph grammars are used to express the behavioural semantics ofobjectoriented programs, thus enabling automatic verification of those programs. This paper describes work in progress.
Compositional Semantics for Open Petri Nets based on Deterministic Processes
, 2001
"... In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect ..."
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Cited by 19 (4 self)
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In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect this extension, we define a truly concurrent semantics for open nets by extending the GoltzReisig process semantics of Petri nets. We introduce a composition operation over open nets, characterized as a pushout in the corresponding category, suitable to model both interaction through open places and synchronization of transitions. The deterministic process semantics is shown to be compositional with respect to such composition operation. If a net Z 3 results as the composition of two nets Z 1 and Z 2 , having a common subnet Z 0 , then any two deterministic processes of Z 1 and Z 2 which "agree" on the common part, can be "amalgamated" to produce a deterministic process of Z 3 . Vice versa, any deterministic process of Z 3 can be decomposed into processes of the component nets. The amalgamation and decomposition operations are shown to be inverse to each other, leading to a bijective correspondence between the deterministic processes of Z 3 and pair of deterministic processes of Z 1 and Z 2 which agree on the common subnet Z 0 . Technically, our result is similar to the amalgamation theorem for datatypes in the framework of algebraic specification. A possible application field of the proposed constructions and results is the modeling of interorganizational workflows, recently studied in the literature. This is illustrated by a running example.
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.
Compositional modeling of reactive systems using open nets
, 2001
"... In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect ..."
Abstract

Cited by 17 (6 self)
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In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect this extension, we define a truly concurrent semantics for open nets by extending the GoltzReisig process semantics of Petri nets. We introduce a composition operation over open nets, characterized as a pushout in the corresponding category, suitable to model both interaction through open places and synchronization of transitions. The process semantics is shown to be compositional with respect to such composition operation. Technically, our result is similar to the amalgamation theorem for datatypes in the framework of algebraic specifications. A possible application field of the proposed constructions and results is the modeling of interorganizational workflows, recently studied in the literature. This is illustrated by a running example.
Classification and comparison of module concepts for graph transformation systems
 In Ehrig et
, 1999
"... In this chapter we use a threelevel approach for analyzing module concepts for graph transformation systems. Based on the observation that module architectures consist of basic specifications like body or export interface and relations like the implementation relation between them, or the import re ..."
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Cited by 13 (0 self)
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In this chapter we use a threelevel approach for analyzing module concepts for graph transformation systems. Based on the observation that module architectures consist of basic specifications like body or export interface and relations like the implementation relation between them, or the import relation between a client and a server module, module concepts are characterized by answering the questions 1. What are the basic specifications? 2. Which relations between specifications are used? 3. How are specifications and relations combined to module architectures? These three questions are investigated for five module concepts available in the literature. As a reference example, a sample modular specification of resource management in distributed operating systems is presented.
A ViewBased Approach To System Modeling Based On Open Graph Transformation Systems
 In [11
, 1999
"... this paper, we follow a constructive approach, where different views are automatically integrated. This means that two operations from different views are merged into one operation in the resulting overall system specification. The common underlying reference model indicates and identifies the overl ..."
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Cited by 9 (6 self)
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this paper, we follow a constructive approach, where different views are automatically integrated. This means that two operations from different views are merged into one operation in the resulting overall system specification. The common underlying reference model indicates and identifies the overlapping part
Autonomous units and their semantics  the sequential case
 ICGT 2006. LNCS
, 2006
"... In this paper, we introduce the notion of a community of autonomous units as a rulebased and graphtransformational device to model processes that run interactively but independently of each other in a common environment. The emphasis of the approach is laid on the study of the formal semantics of ..."
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Cited by 5 (5 self)
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In this paper, we introduce the notion of a community of autonomous units as a rulebased and graphtransformational device to model processes that run interactively but independently of each other in a common environment. The emphasis of the approach is laid on the study of the formal semantics of a community as a whole and of each of its member units separately. We concentrate on the sequential case where only one unit can act at a time and the rule applications of the involved units are interleaved with each other.
Tile Transition Systems as Structured Coalgebras
 Fundamentals of Computation Theory, volume 1684 of LNCS
, 1999
"... . The aim of this paper is to investigate the relation between two models of concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules with side effects which are endowed with operations of parallel and sequential composition and synchronization. Their models can be described ..."
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Cited by 4 (2 self)
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. The aim of this paper is to investigate the relation between two models of concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules with side effects which are endowed with operations of parallel and sequential composition and synchronization. Their models can be described as monoidal double categories. Coalgebras can be considered, in a suitable mathematical setting, as dual to algebras. They can be used as models of dynamical systems with hidden states in order to study concepts of observational equivalence and bisimilarity in a more general setting. In order to capture in the coalgebraic presentation the algebraic structure given by the composition operations on tiles, coalgebras have to be endowed with an algebraic structure as well. This leads to the concept of structured coalgebras, i.e., coalgebras for an endofunctor on a category of algebras. However, structured coalgebras are more restrictive than tile models. Those models which can be presented as st...