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Programmed Graph Replacement Systems
 In Rozenberg, G. (Ed.), Handbook on Graph Grammars: Foundations
, 1997
"... Various forms of programmed graph replacement systems as extensions of contextsensitive graph replacement systems have been proposed until today. They differ considerably with respect to their underlying graph models, the supported forms of graph replacement rules, and offered rule regulation mechan ..."
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Cited by 37 (5 self)
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Various forms of programmed graph replacement systems as extensions of contextsensitive graph replacement systems have been proposed until today. They differ considerably with respect to their underlying graph models, the supported forms of graph replacement rules, and offered rule regulation mechanisms. Some of them have additional constructs for the definition of graph schemata, derived graph properties, and so forth. It is rather difficult to develop precise and compact descriptions of programmed graph replacement systems, a necessary prerequisite for any attempt to compare their properties in detail. Programmed Logicbased Structure Replacement (PLSR) systems are a kind of intermediate definition language for this purpose. They treat specific graph classes as sets of predicate logic formulas with certain properties, socalled structures. Their rules preserve the consistency of manipulated structures and use nonmonotonic reasoning for checking needed preand postconditions. Socalled Basic Control Flow (BCF) expressions together with an underlying fixpoint theory provide needed means for programming with rules. This chapter introduces first the basic framework of PLSR systems and studies afterwards the essential properties of contextsensitive graph replacement approaches themselves as well as popular rule regulation mechanisms.
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 28 (15 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.
Computing by Graph Transformation  A Survey and Annotated Bibliography
, 1996
"... this paper as candidates to represent the processes in a concurrent system or, more exactly, as representatives of equivalent views on the processes. The main results give sufficient conditions for existence and uniqueness of canonical derivations. ..."
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Cited by 13 (0 self)
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this paper as candidates to represent the processes in a concurrent system or, more exactly, as representatives of equivalent views on the processes. The main results give sufficient conditions for existence and uniqueness of canonical derivations.
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...
Spatial and Temporal Refinement of Typed Graph Transformation Systems
 In Proc. Mathematical Foundations of Computer Science (MFCS'98), LNCS 1450
, 1998
"... Graph transformation systems support the formal modeling of dynamic, concurrent, and distributed systems. States are given by their graphical structure, and transitions are modeled by graph transformation rules. In this paper we investigate two kinds of refinement relations for graph transformat ..."
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Cited by 7 (0 self)
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Graph transformation systems support the formal modeling of dynamic, concurrent, and distributed systems. States are given by their graphical structure, and transitions are modeled by graph transformation rules. In this paper we investigate two kinds of refinement relations for graph transformation systems in order to support the development of a module concept for graph transformation systems. In a spatial refinement each rule is refined by an amalgamation of rules, in a temporal refinement it is refined by a sequence of rules.
Concrete Spatial Refinement Construction for Graph Transformation Systems
, 1997
"... Graph Transformation Systems (GTS) are a widely accepted formal specification framework for various kind of systems. Recently, types have been introduced for GTS both for structuring and information hiding purposes. In order to develop a module concept for Typed GTS (TGTS), refinement morphisms are ..."
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Cited by 2 (1 self)
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Graph Transformation Systems (GTS) are a widely accepted formal specification framework for various kind of systems. Recently, types have been introduced for GTS both for structuring and information hiding purposes. In order to develop a module concept for Typed GTS (TGTS), refinement morphisms are required: intuitively, a TGTS is "more refined " than another TGTS if it has more atomic productions which can be combined to obtain the productions of the "less refined" systems. In this paper, we propose a concrete construction for the spatial refinement morphism of TGTS defined here and based only on the concrete notion of the set theoretic union and renaming of rules. We also show that the notion of subproduction can be simulated by an appropriate extension of the typing system. 1 Introduction The classical approach to graph rewriting of [3] based on double pushouts and sets of labels for edges and nodes has been extended to typed graph grammars in [2], where a graph morphism into a ty...
Refinements and Modules for Typed Graph Transformation Systems
"... Spatial and temporal refinement relations between typed graph transformation systems have been introduced in [6, 7]. In a spatial refinement each rule is refined by an amalgamation of rules while in a temporal refinement it is refined by a sequence of rules: in both cases, the refinement relation su ..."
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Cited by 2 (0 self)
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Spatial and temporal refinement relations between typed graph transformation systems have been introduced in [6, 7]. In a spatial refinement each rule is refined by an amalgamation of rules while in a temporal refinement it is refined by a sequence of rules: in both cases, the refinement relation supports the modeling of implementation. In the first part of this paper, we further investigate the properties of spatial and temporal refinements while, in the second part, we employ them for the development of a module concept for Typed Graph Transformation Systems (TGTS). Finally, as a first step towards an algebra of modules of TGTS, we introduce the operations of union and composition of modules. 1
Definition of an Encapsulated Hierarchical Graph Data Model Static Aspects, Part 1
, 1996
"... Graph grammars have been successfully used as a formalism for the specification of realistic problems but, as far as specificationinthelarge activities are concerned, they still have some deficiencies. In particular, most of them only support the use of flat graphs, whereas for certain applicatio ..."
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Graph grammars have been successfully used as a formalism for the specification of realistic problems but, as far as specificationinthelarge activities are concerned, they still have some deficiencies. In particular, most of them only support the use of flat graphs, whereas for certain applications hierarchical graphs would be a more suitable modelling tool. Furthermore, there is still the need for a graph grammar module concept that allows to split large specifications into smaller subspecifications. We want to address this problem by applying objectoriented concepts to develop a hierarchical graph data model that supports a suitable module concept for graph grammars. In this paper, we present the first step in the definition of our encapsulated hierarchical graph (EHG) data model. We introduce the notion of EHG that supports complex nodes (i.e. nodes with an encapsulated graph as their content), edges, encapsulated graphs (i.e. graphs that support importing and exporting of node...
Computing by Graph Transformation II (COMPUGRAPH II)
"... This report gives an overview over the ongoing activities of the ESPRIT Basic Research Working Group "Computing by Graph Transformation" started on March 1st, 1989. Its second phase COMPUGRAPH II began on October 1st, 1992 and lasts to March 31st, 1996. The main aim of the COMPUGRAPH ..."
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This report gives an overview over the ongoing activities of the ESPRIT Basic Research Working Group "Computing by Graph Transformation" started on March 1st, 1989. Its second phase COMPUGRAPH II began on October 1st, 1992 and lasts to March 31st, 1996. The main aim of the COMPUGRAPH project is to demonstrate the potential of graph transformation as a uniform framework for the development of modern software systems. The research activities therefore cover the whole spectrum from theoretical investigations to practical software engineering applications. This is reflected in the following research areas according to which the work in the COMPUGRAPH project has been organized:
Sequential and Parallel Algebra Transformation Systems and Their Composition
, 1997
"... Algebra transformation systems are introduced as formal models of components in an open distributed environment. Their interconnection and composition is defined using the categorical technique of diagrams and colimits. The diagrams represent the components that are put together and their correspond ..."
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Algebra transformation systems are introduced as formal models of components in an open distributed environment. Their interconnection and composition is defined using the categorical technique of diagrams and colimits. The diagrams represent the components that are put together and their correspondences, given via connecting subcomponents and morphisms. The colimit models the global behaviour of the composed system. Different kinds of compositions for sequential and parallel systems are discussed, all defined formally by the same technique. The formal models, algebra transformation systems, are two layered structures, given by a transition graph that models the control flow of the component, and partial algebras that model the data states corresponding to the control states. Thus temporal ordering of actions as well as rule based state transformation as specification paradigms are coverd. The main technical result of the paper is that the categories of algebra transformation sytems ha...