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Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach
 HANDBOOK OF GRAPH GRAMMARS AND COMPUTING BY GRAPH TRANSFORMATION, VOLUME 1: FOUNDATIONS
, 1996
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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...
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.
Hierarchically Distributed Graph Transformation
 Proc. 5th Int. Workshop on Graph Grammars and their Application to Computer Science
, 1994
"... . Hierarchically distributed graph transformation offers means to model different aspects of open distributed systems very intuitively in a graphical way. The distribution topology as well as local object structures are represented graphically. Distributed actions such as local actions, network ..."
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Cited by 9 (1 self)
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. Hierarchically distributed graph transformation offers means to model different aspects of open distributed systems very intuitively in a graphical way. The distribution topology as well as local object structures are represented graphically. Distributed actions such as local actions, network activities, communication and synchronization can be described homogeneously using the same method: graph transformation. This new approach to graph transformation follows the lines of algebraic and categorical graph grammars and fits into the framework of doublepushout highlevel replacement systems. Keywords: Graph transformation, distributed systems, communication, synchronization 1 Introduction Graphical representations are an obvious means to describe different aspects of systems. Modeling distributed and concurrent systems graphs are often used to describe the topological structure of the system. The graphical structure shows then which parts are involved and what are the ways of...
Parallel HighLevel Replacement Systems
 Theoretical Computer Science
, 1994
"... Highlevel replacement systems are an axiomatic categorical framework based on doublepushouts in order to unify replacement systems like grammars for different kinds of graphs and relational structures or other types of structures like algebraic specifications. Parallel highlevel replacement syste ..."
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Cited by 6 (4 self)
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Highlevel replacement systems are an axiomatic categorical framework based on doublepushouts in order to unify replacement systems like grammars for different kinds of graphs and relational structures or other types of structures like algebraic specifications. Parallel highlevel replacement systems are introduced to formalize parallel rewriting of these highlevel structures. On one hand this concept generalizes and extends parallel graph grammars presented so far in the algebraic approach by allowing other structures than graphs, on the other hand the kinds of replacement introduced for highlevel replacement systems are extended by different types of parallel replacement which are compared to each other in different parallel replacement theorems. An abstract version of a windowbased graph editor and movement of objects in configuration spaces are presented as examples of parallel highlevel replacement systems. Contents 1 Introduction 2 2 Basic concepts of highlevel replacement...
From Abstract Data Types to Algebraic Development Techniques: A Shift . . .
 In Proc. of Workshop on Algebraic Development Techniques
, 1998
"... Data Types to Algebraic Development Techniques: A Shift of Paradigms H. Ehrig, M. Gajewsky, U. Wolter email: fehrig, gajewsky, wolterg@cs.tuberlin.de Technical University of Berlin Abstract. The concept of abstract data types and the corresponding series of ADTworkshops have been most frui ..."
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Cited by 3 (2 self)
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Data Types to Algebraic Development Techniques: A Shift of Paradigms H. Ehrig, M. Gajewsky, U. Wolter email: fehrig, gajewsky, wolterg@cs.tuberlin.de Technical University of Berlin Abstract. The concept of abstract data types and the corresponding series of ADTworkshops have been most fruitful for the development of algebraic specification techniques within the last two decades. Since abstract data types by now are wellestablished in all areas of Computer Science and algebraic specification techniques go far beyond their classical roots of universal algebra the name of the ADTworkshop has been changed to "Workshop on Algebraic Development Techniques", where the acronym ADT has now a new interpretation. In this paper we discuss this shift of paradigms from "Abstract Data Types" to "Algebraic Development Techniques". We show how the scope of algebraic development techniques has been extended from algebraic specification to several other formal specification approache...
Towards Synchronous and Asynchronous Graph Transformations
, 1996
"... Synchronous and asynchronous graph transformations are discussed on the basis of distributed graph transformations. All types of graph transformations presented are formulated in the singlepushout approach to graph transformations and compared with each other. Some criteria are given to preserve or ..."
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Cited by 2 (1 self)
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Synchronous and asynchronous graph transformations are discussed on the basis of distributed graph transformations. All types of graph transformations presented are formulated in the singlepushout approach to graph transformations and compared with each other. Some criteria are given to preserve or reestablish synchrony according to the definition proposed in this paper. 1 Introduction Graphs and graph transformations have been used to model different kinds of parallel and distributed systems. (See, for example, the approaches of Degano and Montanari [3], Ehrig et.al. [5], Schneider [14], Goering [8], Kaplan et.al. [10], Janssens and Rozenberg [9], Ehrig and Lowe [7], Schied [13], Korff [11], etc.) In [5] and [7] the algebraic approach is used to model concepts of concurrency and distribution. In this framework graphs correspond to states of a system and graph transformations to operations or actions on these states. Distribution of graphs is modeled by splitting global state graphs ...
A Parallel Solution Strategy For Irregular, Dynamic Problems
, 1996
"... Parallelizing irregular, dynamic data structures can be a very difficult problem. An efficient solution often demands that work on the data structure be divided up among processors, yet despite the large and growing number of such applications there has been little work done on general approaches to ..."
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Cited by 2 (0 self)
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Parallelizing irregular, dynamic data structures can be a very difficult problem. An efficient solution often demands that work on the data structure be divided up among processors, yet despite the large and growing number of such applications there has been little work done on general approaches to such situations. In part this is due to the extreme difficulty of ensuring enough generality to be useful, while still efficiently addressing each individual problem; irregular and dynamic problems can vary dramatically, and direct, efficient solutions simply do not exist. Most attempts have therefore either concentrated on problemspecific areas, where good results can be obtained at the expense of generality, or have defaulted to heuristic methods applicable to almost any possible situation. In this thesis we present a hybrid method, combining a direct and problemspecific approach with a system general enough to be applicable to the majority of applications. Our method is based on local g...