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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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Confluence of Typed Attributed Graph Transformation Systems
 In: Proc. ICGT 2002. Volume 2505 of LNCS
, 2002
"... The issue of confluence is of major importance for the successful application of attributed graph transformation, such as automated translation of UML models into semantic domains. Whereas termination is undecidable in general and must be established by carefully designing the rules, local confl ..."
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Cited by 38 (6 self)
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The issue of confluence is of major importance for the successful application of attributed graph transformation, such as automated translation of UML models into semantic domains. Whereas termination is undecidable in general and must be established by carefully designing the rules, local confluence can be shown for term rewriting and graph rewriting using the concept of critical pairs. In this paper, we discuss typed attributed graph transformation using a new simplified notion of attribution. For this kind of attributed graph transformation systems we establish a definition of critical pairs and prove a critical pair lemma, stating that local confluence follows from confluence of all critical pairs.
Tutorial introduction to graph transformation: A software engineering perspective
 In Proc. of the First International Conference on Graph Transformation (ICGT 2002
, 2002
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Adhesive categories
, 2004
"... Abstract. We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are wellbehaved. Many types of graphical structures used in computer science are shown to be examples of adhesive categories. Doublepushout graph rewriting generalises well to ..."
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Cited by 35 (7 self)
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Abstract. We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are wellbehaved. Many types of graphical structures used in computer science are shown to be examples of adhesive categories. Doublepushout graph rewriting generalises well to rewriting on arbitrary adhesive categories.
ADHESIVE AND QUASIADHESIVE CATEGORIES
 THEORETICAL INFORMATICS AND APPLICATIONS
, 1999
"... We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are wellbehaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be ex ..."
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Cited by 35 (3 self)
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We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are wellbehaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Doublepushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.
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...
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 27 (14 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.
Detection of Conflicting Functional Requirements in a Use CaseDriven Approach  A static analysis technique based on graph transformation
 ICSE 2002
, 2002
"... In objectoriented software development, requirements of different stakeholders are often manifested in use case models which complement the static domain model by dynamic and functional requirements. In the course of development, these requirements are analyzed and integrated to produce a consisten ..."
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Cited by 21 (5 self)
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In objectoriented software development, requirements of different stakeholders are often manifested in use case models which complement the static domain model by dynamic and functional requirements. In the course of development, these requirements are analyzed and integrated to produce a consistent overall requirements specification. Iterations of the model may be triggered by conflicts between requirements of different parties. However, due to the...
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.