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59
Fundamental Theory for Typed Attributed Graph Transformation: Long Version.
, 2004
"... Abstract. The concept of typed attributed graph transformation is most significant for modeling and meta modeling in software engineering and visual languages, but up to now there is no adequate theory for this important branch of graph transformation. In this paper we give a new formalization of t ..."
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Cited by 83 (20 self)
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Abstract. The concept of typed attributed graph transformation is most significant for modeling and meta modeling in software engineering and visual languages, but up to now there is no adequate theory for this important branch of graph transformation. In this paper we give a new formalization of typed attributed graphs, which allows node and edge attribution. The first main result shows that the corresponding category is isomorphic to the category of algebras over a specific kind of attributed graph structure signature. This allows to prove the second main result showing that the category of typed attributed graphs is an instance of "adhesive HLR categories". This new concept combines adhesive categories introduced by Lack and Sobociński with the wellknown approach of highlevel replacement (HLR) systems using a new simplified version of HLR conditions. As a consequence we obtain a rigorous approach to typed attributed graph transformation providing as fundamental results the Local ChurchRosser, Parallelism, Concurrency, Embedding and Extension Theorem and a Local Confluence Theorem known as Critical Pair Lemma in the literature.
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 55 (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.
Reactive Systems over Cospans
, 2005
"... The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of wellbehaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimi ..."
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Cited by 47 (3 self)
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The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of wellbehaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimits (or, more usually and generally, bicolimits) which need to be constructed separately within each model. In this paper, we o#er a general construction of such bicolimits in a class of bicategories of cospans. The construction sheds light on as well as extends Ehrig and Konig's rewriting via borrowed contexts and opens the way to a unified treatment of several applications.
Weak Adhesive HighLevel Replacement Categories and Systems: A Unifying . . .
, 2006
"... Adhesive highlevel replacement (HLR) systems have been recently introduced as a new categorical framework for graph tranformation in the double pushout (DPO) approach. They combine the wellknown concept of HLR systems with the concept of adhesive categories introduced by Lack and Sobociński. Wh ..."
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Cited by 33 (10 self)
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Adhesive highlevel replacement (HLR) systems have been recently introduced as a new categorical framework for graph tranformation in the double pushout (DPO) approach. They combine the wellknown concept of HLR systems with the concept of adhesive categories introduced by Lack and Sobociński. While graphs, typed graphs, attributed graphs and several other variants of graphs together with corresponding morphisms are adhesive HLR categories, such that the categorical framework of adhesive HLR systems can be applied, this has been claimed also for Petri nets. In this paper we show that this claim is wrong for place/transition nets and algebraic highlevel nets, although several results of the theory for adhesive HLR systems are known to be true for the corresponding Petri net transformation systems. In fact, we are able to define a weaker version of adhesive HLR categories, called weak adhesive HLR categories, which is still sufficient to show all the results known for adhesive HLR systems. This concept includes not only all kinds of graphs mentioned above, but also place/transition nets, algebraic highlevel nets and several other kinds of Petri nets. For this reason weak adhesive HLR systems can be seen as a unifying framework for graph and Petri net transformations.
A congruence for Petri Nets
 PNGT’04
, 2004
"... We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our resul ..."
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Cited by 24 (10 self)
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We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our results are similar to the recent work by Milner on applying the theory of bigraphs to Petri Nets. The two main differences are that we treat p/t nets instead of c/e nets and we deal directly with a category of nets instead of encoding them into bigraphs.
Abstracting the differential semantics of rulebased models: exact and automated model reduction (revised version)
, 2010
"... ..."
Adhesive HighLevel Replacement Systems: A New Categorical Framework for Graph Transformation
, 2006
"... Adhesive highlevel replacement (HLR) systems are introduced as a new categorical framework for graph transformation in the double pushout (DPO) approach, which combines the wellknown concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobociński. In this pa ..."
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Cited by 21 (12 self)
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Adhesive highlevel replacement (HLR) systems are introduced as a new categorical framework for graph transformation in the double pushout (DPO) approach, which combines the wellknown concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobociński. In this paper we show that most of the HLR properties, which had been introduced to generalize some basic results from the category of graphs to highlevel structures, are valid already in adhesive HLR categories. This leads to a smooth categorical theory of HLR systems which can be applied to a large variety of graphs and other visual models. As a main new result in a categorical framework we show the Critical Pair Lemma for the local confluence of transformations. Moreover we present a new version of embeddings and extensions for transformations in our framework of adhesive HLR systems.
A Behavioural Congruence for Web services
 In Arbab, F., Sarjani, M., eds.: Fundamentals of Software Engineering, LNCS (To appear
, 2007
"... Abstract. Web services are emerging as a promising technology for the development of next generation distributed heterogeneous software systems. We define a new behavioural equivalence for Web services, based on bisimilarity and inspired by recent advances in the theory of reactive systems. The prop ..."
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Cited by 13 (6 self)
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Abstract. Web services are emerging as a promising technology for the development of next generation distributed heterogeneous software systems. We define a new behavioural equivalence for Web services, based on bisimilarity and inspired by recent advances in the theory of reactive systems. The proposed equivalence is compositional and decidable, and it provides a firm ground for enhanced behaviouraware discovery and for a sound incremental development of services and service compositions. 1
Categorical Frameworks for Graph Transformation and
 HLR Systems based on the DPO Approach, Bulletin of the EATCS 102
, 2010
"... Several variants of highlevel replacement (HLR) and adhesive categories have been introduced in the literature as categorical frameworks for graph transformation and HLR systems based on the double pushout (DPO) approach. In addition to HLR, adhesive, and adhesive HLR categories several weak vari ..."
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Cited by 13 (4 self)
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Several variants of highlevel replacement (HLR) and adhesive categories have been introduced in the literature as categorical frameworks for graph transformation and HLR systems based on the double pushout (DPO) approach. In addition to HLR, adhesive, and adhesive HLR categories several weak variants, especially weak adhesive HLR with horizontal and vertical variants, as well as partial variants, including partial map adhesive and partial VK square adhesive categories are reviewed and related to each other. We propose as weakest version the class of vertical weak adhesive HLR categories, shortMadhesive categories, which are still sufficient to obtain most of the main results for graph transformation and HLR systems. The results in this paper are summarized in Fig. 1 showing a hierarchy of all these variants of adhesive, adhesive HLR, andMadhesive categories, which can be considered as different categorical frameworks for graph transformation and HLR systems.
Model checking for nominal calculi
 IN FOSSACS, VOLUME 3441 OF LNCS
, 2005
"... Nominal calculi have been shown very effective to formally model a variety of computational phenomena. The models of nominal calculi have often infinite states, thus making model checking a difficult task. In this note we survey some of the approaches for model checking nominal calculi. Then, we f ..."
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Cited by 11 (4 self)
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Nominal calculi have been shown very effective to formally model a variety of computational phenomena. The models of nominal calculi have often infinite states, thus making model checking a difficult task. In this note we survey some of the approaches for model checking nominal calculi. Then, we focus on HistoryDependent automata, a syntaxfree automatonbased model of mobility. HistoryDependent automata have provided the formal basis to design and implement some existing verification toolkits. We then introduce a novel syntaxfree setting to model the symbolic semantics of a nominal calculus. Our approach relies on the notions of reactive systems and observed borrowed contexts introduced by Leifer and Milner, and further developed by Sassone, Lack and Sobocinski. We argue that the symbolic semantics model based on borrowed contexts can be conveniently applied to web service discovery and binding.