Corradini, A.; Montanari, U.; Rossi, F.; Ehrig, H.; Heckel, R.; and Lowe, M. 1997. Algebraic approaches to graph transformation, volume 1. World Scientific.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....or has complex semantics, or does not make the relationship between recon guration and computation very clear. To overcome these disadvantages, we have proposed an algebraic framework [20] using categorical diagrams to represent architectures, the double pushout graph transformation approach [5] to specify recon gurations, and a program design language with explicit state to describe computations. In this paper we re ne our approach, introducing the notions of productive recon guration step and architectural style. To accommodate the latter, we have made the underlying mathematical de ....

A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic approaches to graph transformation, part I: Basic concepts and double pushout approach. Technical Report TR-96-17, University of Pisa, Mar. 1996.

....or does not make the relationship between reconfiguration and computation clear enough. To overcome these disadvantages, we have proposed in the last ESEC FSE an algebraic approach [29] using categorical diagrams to represent architectures, the double pushout graph transformation approach [6] to specify reconfigurations, and a program design language with explicit state to describe computations [17] In [30] we have further refined and extended the work, using typed graphs to represent simple topological invariants for the reconfiguration process. We have shown that our approach has ....

....#sa# SalaryAccount node sa balance bal avgbal avg number num salary sal NormalAccount node vnodes 1 balance bal avgbal avg number num Figure 1: Semantics of n : create NormalAccount with balance : s.a.balance # avgbal : s.a.avgbal # number : s.a. number rewriting techniques [6]) The approach also provides a strict separation between computation and (re)configuration, while keeping them explicitly related. This was already done at the formal level in our previous papers [29, 30] and the language presented herein complies with that principle: the components do not have ....

A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. L owe. Algebraic approaches to graph transformation, part I: Basic concepts and double pushout approach. Technical Report TR-96-17, University of Pisa, Mar. 1996.

.... 1997; Ehrig et al. 1999a; Ehrig et al. 1999b) In the original paper (Ehrig, Pfender and Schneider 1973) the left hand sides of transformation rules are matched by injective graph morphisms, but the vast majority of later papers on the double pushout approach including the surveys (Ehrig 1979; Corradini et al. 1997) considers arbitrary, possibly non injective matching morphisms. In this paper we argue that despite this tradition, injective matching makes the approach more expressive. For y This research was partly supported by the ESPRIT Working Group APPLIGRAPH. The work of J. M uller was also supported ....

....morphisms both in the right hand sides of rules and for matching to obtain three other variants in the next section by requiring injectivity for one or both of the relevant morphisms. For a comprehensive survey of the traditional approach DPO i=a , the reader may consult (Ehrig 1979; Corradini et al. 1997). y A label alphabet C = hC V ; CE i is a pair of sets of node labels and edge labels. A graph over C is a system G = VG ; EG ; s G ; t G ; l G ; mG ) consisting of two nite sets VG and EG of nodes (or vertices) and edges, two source and target functions s G ; t G : EG VG , and two labelling ....

Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R. and Lowe, M. (1997) Algebraic approaches to graph transformation. Part I: Basic concepts and double pushout approach. In G.

....a semantics, given by an operation that transforms the architectural diagram into an equivalent component representing the whole system on which computations are performed. This relates the architectural and computational levels. Reconfiguration is specified through algebraic graph rewriting [5], a formalism with many years of research into its theory and application. Together with the representation of components, the approach guarantees that components are removed in a quiescent state [16] i.e. when not interacting with other components) and are introduced in a properly initialized ....

....d 0 , there is a unique morphism k : d d 0 . This ensures that d, being a component of any other object in the same conditions, is minimal. Object c is called the pushout complement of diagram a f b h d. 1. 6 Graph Transformation The algebraic approach to graph transformation [5] was introduced over 20 years ago in order to generalize grammars from strings to graphs. Hence it was necessary to adapt string concatenation to graphs. The approach is algebraic because the gluing of graphs is done by a pushout in an appropriate category. There are two main variants, the ....

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A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic approaches to graph transformation, part I: Basic concepts and double pushout approach. Technical Report TR-96-17, University of Pisa, Mar. 1996.

....a semantics, given by an operation that transforms the architectural diagram into an equivalent component representing the whole system on which computations are performed. This relates the architectural and computational levels. Recon guration is speci ed through algebraic graph rewriting [5], a formalism with many years of research into its theory and application. Together with the representation of components, the approach guarantees that components are removed in a quiescent state [15] i.e. when not interacting with other components) and are introduced in a properly initialized ....

....d 0 , there is a unique morphism k : d d 0 . This ensures that d, being a component of any other object in the same conditions, is minimal. Object c is called the pushout complement of diagram a f b h d. 1. 5 Graph Transformation The algebraic approach to graph transformation [5] was introduced over 20 years ago in order to generalize grammars from strings to graphs. Hence it was necessary to adapt string concatenation to graphs. The approach is algebraic because the gluing of graphs is done by a pushout in an appropriate category, whose objects are labelled graphs and ....

A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic approaches to graph transformation, part I: Basic concepts and double pushout approach. Technical Report TR-96-17, University of Pisa, Mar. 1996.

....although little e#orts have been devoted within the graph transformation community to issues of tool support. A few notable exceptions are the systems GraphEd [4] PROGRES [8] Agg [5] and Treebag [3] Grammatica is a prototype implementation of double pushout algebraic graph transformation [2] based on relation algebra [1, 7] It has originated in an investigation of the extent to which algebraic graph transformation can be expressed within relation algebra [6] and has been implemented using Mathematica [11] on top of the Combinatorica [9] package. Therefore, it runs on most ....

....Mathematica with In[n] and the corresponding output is labeled Out[n] as shown in Figure 1. Fig. 1. The user interface of Grammatica shares the notebook interface of Mathematica. The reader is assumed to be familiar with the basic notions of the doublepushout approach to graph transformation [2]. Recall that a (double pushout) production rule is a pair of graph homomorphisms L K R l r and it can be applied to a graph G when there exist a graph homomorphism m : L # G and a diagram L K R G D H m l r d m # l # r # such that both squares in it are ....

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A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic approaches to graph transformation. part I: Basic concepts and double pushout approach. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation, volume 1: Foundations, chapter 3, pages 163--245. World Scientific, 1997.

....main results presented in this paper are a characterization of subsumption and a su#cient condition for redundancy, which involves composite productions. 1 Introduction High level replacement systems [6] generalize the algebraic approach to graph transformation, both the double pushout approach [3] and the single pushout approach [5] to other classes of replacement systems. They provide a common categorical framework for di#erent classes of replacement systems, such as grammars on graphs, relational structures, and algebraic specifications, based on categories and pushouts. This paper ....

A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic Approaches to Graph Transformation. Part I: Basic Concepts and Double Pushout Approach, chapter 3, pages 163--245.

....independent development of single local ViewPoints and the configuration and connection of a set of related ViewPoints in a structured way. The concepts as well as the formal definition of distributed graph transformation are based on the double pushout approach to algebraic graph transformation [1] where basic concepts from category theory are applied. Distributed graph transformation is introduced formally in [11] The ViewPoints framework was devised by A. Finkelstein et al. 5] and B. Nuseibeh [10] to describe complex systems. An overview of other approaches related to multiple ....

Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., and Lwe, M., "Algebraic Approaches to Graph Transformation", in Rozenberg, G. (ed.), Handbook of Graph Grammars and Computing by Graph Transformation, Vol. 1 Foundations, pp 163 -- 245, World Scientific, Singapore, 1997.

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Corradini, A., U. Montanari, F. Rossi, H. Ehrig, R. Heckel and M. Lowe, Algebraic approaches to graph transformation, Part I: Basic concepts and double pushout approach, in: Rozenberg [15] pp. 163-245. 12

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A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic approaches to graph transformation, Part I: Basic concepts and double pushout approach. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, pages 163--245. World Scientific, 1997.

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A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic approaches to graph transformation, Part I: Basic concepts and double pushout approach. In Rozenberg [22], pages 163--245.

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A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic approaches to graph transformation, Part I: Basic concepts and double pushout approach. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, pages 163--245. World Scientific, 1997.

No context found.

A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic approaches to graph transformation, Part I: Basic concepts and double pushout approach. In G. Rozenberg, editor, Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, pages 163--245. World Scientific, 1997.

....if, for all premises L i a 0 :m(a 1 ; a n ) R i , L i [R i = fa 0 ; a 1 ; a n g. We speak of an OO transition system specification if all its rules are object oriented. The notion of sequent in the above definition is reminiscent of a DPO graph production with production name [3]. In fact, given a sequent L e R, the corresponding named production can be obtained as e : L L R , R. The left hand side L represents the precondition of the production, the right hand side R its postcondition, while the intermediate graph L R is needed in the DPO approach for specifying ....

....by another collaboration diagram. In this view, the methods occur and perform implement part of an interpreter of the state chart language. Next, we state more precisely the concept of deduction with graphical SOS rules. We start with a set theoretic presentation of DPO graph transformation [3] which provides us with a concept of matching of sequents with transitions. Definition 4 (sequent and rule instance) Given a graph transition signature Q as above, an instance of a graphical sequent L m(a) R is a sequent G m(b) H over Q together with a graph morphism o : L [R G[H, ....

CORRADINI, A., MONTANARI, U., ROSSI, F., EHRIG, H., HECKEL, R., AND L OWE, M. Algebraic approaches to graph transformation, Part I: Basic concepts and double pushout approach. In Handbook of Graph Grammars and Computing by Graph Transformation, Volume 1: Foundations, G. Rozenberg, Ed. World Scientific, 1997, pp. 163--245.

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Corradini, A.; Montanari, U.; Rossi, F.; Ehrig, H.; Heckel, R.; and Lowe, M. 1997. Algebraic approaches to graph transformation, volume 1. World Scientific.

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Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R. & Lowe, M. (1997), Algebraic Approaches to Graph Transformation, Vol. 1 of Rozenberg (1997), chapter 3, pp. 163--245.

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A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel, and M. Lowe. Algebraic Approaches to Graph Transformation. Part 1: Basic Concepts and Double Pushout Approach. Handbook of Graph Grammars and Computing by Graph Transformation, 1: Foundations, 1997.

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A. Corradini et al. Algebraic approaches to graph transformation, part I. In Handbook of Graph Grammars and Computing by Graph Transformation, volume 1. World Scientific, 1997.

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