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13
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 36 (2 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.
Bigraphs for Petri nets
, 2004
"... A simple example is given of the use of bigraphical reactive systems (BRSs). It provides a behavioural semantics for conditionevent Petri nets whose interfaces are named condition nodes, using a simple form of BRS equipped with a labelled transition system and its associated bisimilarity equivalenc ..."
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Cited by 33 (3 self)
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A simple example is given of the use of bigraphical reactive systems (BRSs). It provides a behavioural semantics for conditionevent Petri nets whose interfaces are named condition nodes, using a simple form of BRS equipped with a labelled transition system and its associated bisimilarity equivalence. Both of the latter are derived from the standard net firing rules by a uniform technique in bigraphs, which also ensures that the bisimilarity is a congruence. Furthermore, this bisimilarity is shown to coincide with one induced by a natural notion of experiment on conditionevent nets, defined independently of bigraphs. The paper
Adhesive highlevel replacement categories and systems
, 2004
"... Adhesive highlevel replacement (HLR) categories and systems are introduced as a new categorical framework for graph transformation in a broad sense, which combines the wellknown concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobociński. In this paper we s ..."
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Cited by 25 (6 self)
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Adhesive highlevel replacement (HLR) categories and systems are introduced as a new categorical framework for graph transformation in a broad sense, 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 ad hoc to generalize some basic results from the category of graphs to highlevel structures, are valid already in adhesive HLR categories. As a main new result in a categorical framework we show the Critical Pair Lemma for local confluence of transformations. Moreover we present a new version of embeddings and extensions for transformations in our framework of adhesive HLR systems.
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 23 (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.
Matching of Bigraphs
 PREPRINT OF GTVC 2006
, 2006
"... We analyze the matching problem for bigraphs. In particular, we present a sound and complete inductive characterization of matching of binding bigraphs. Our results pave the way for a provably correct matching algorithm, as needed for an implementation of bigraphical reactive systems. ..."
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Cited by 20 (11 self)
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We analyze the matching problem for bigraphs. In particular, we present a sound and complete inductive characterization of matching of binding bigraphs. Our results pave the way for a provably correct matching algorithm, as needed for an implementation of bigraphical reactive systems.
Locating Reaction with 2categories
, 2004
"... Groupoidal relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner's approach to deriving labelled bisimulation congruences from reduction systems. In this paper, we develop the theory of GRPOs further, proving that wellknown equivalences, othe ..."
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Cited by 11 (1 self)
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Groupoidal relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner's approach to deriving labelled bisimulation congruences from reduction systems. In this paper, we develop the theory of GRPOs further, proving that wellknown equivalences, other than bisimulation, are congruences. To demonstrate the type of category theoretic arguments which are inherent in the 2categorical approach, we construct GRPOs in a category of `bunches and wirings.' Finally, we prove that the 2categorical theory of GRPOs is a generalisation of the approaches based on Milner's precategories and Leifer's functorial reactive systems.
On the Construction of Sorted Reactive Systems
 IN PROCEEDINGS OF CONCUR’08, LNCS
, 2008
"... We develop a theory of sorted bigraphical reactive systems. Every application of bigraphs in the literature has required an extension, a sorting, of pure bigraphs. In turn, every such application has required a redevelopment of the theory of pure bigraphical reactive systems for the sorting at hand. ..."
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Cited by 8 (4 self)
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We develop a theory of sorted bigraphical reactive systems. Every application of bigraphs in the literature has required an extension, a sorting, of pure bigraphs. In turn, every such application has required a redevelopment of the theory of pure bigraphical reactive systems for the sorting at hand. Here we present a general construction of sortings. The constructed sortings always sustain the behavioural theory of pure bigraphs (in a precise sense), thus obviating the need to redevelop that theory for each new application. As an example, we recover Milner’s local bigraphs as a sorting on pure bigraphs. Technically, we give our construction for ordinary reactive systems, then lift it to bigraphical reactive systems. As such, we give also a construction of sortings for ordinary reactive systems. This construction is an improvement over previous attempts in that it produces smaller and much more natural sortings, as witnessed by our recovery of local bigraphs as a sorting.
Congruence for structural congruences
 In Proceedings of the 8th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2005, volume 3441 of LNCS
, 2005
"... Abstract. Structural congruences have been used to define the semantics and to capture inherent properties of language constructs. They have been used as an addendum to transition system specifications in Plotkin's style of Structural Operational Semantics (SOS). However, there has been little theor ..."
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Cited by 6 (3 self)
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Abstract. Structural congruences have been used to define the semantics and to capture inherent properties of language constructs. They have been used as an addendum to transition system specifications in Plotkin's style of Structural Operational Semantics (SOS). However, there has been little theoretical work on establishing a formal link between these two semantic specification frameworks. In this paper, we give an interpretation of structural congruences inside the transition system specification framework. This way, we extend a number of wellbehavedness metatheorems for SOS (such as welldefinedness of the semantics and congruence of bisimilarity) to the extended setting with structural congruences. 1 Introduction Structural congruences were introduced in [12,13] in the operational semanticsspecification of the sscalculus. There, structural congruences are a set of equationsdefining an equality and congruence relation on process terms. These equations
Congruences for Contextual GraphRewriting
, 2004
"... We introduce a comprehensive operational semantic theory of graphrewriting. Graphrewriting here is ..."
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Cited by 6 (3 self)
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We introduce a comprehensive operational semantic theory of graphrewriting. Graphrewriting here is