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25
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.
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.
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.
Process Bisimulation via a Graphical Encoding
 IN: ICGT ‘06. VOLUME 4178 OF LNCS
, 2006
"... The paper presents a case study on the synthesis of labelled transition systems (ltss) for process calculi, choosing as testbed Milner’s Calculus of Communicating System (ccs). The proposal is based on a graphical encoding: each ccs process is mapped into a graph equipped with suitable interfaces, s ..."
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Cited by 17 (11 self)
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The paper presents a case study on the synthesis of labelled transition systems (ltss) for process calculi, choosing as testbed Milner’s Calculus of Communicating System (ccs). The proposal is based on a graphical encoding: each ccs process is mapped into a graph equipped with suitable interfaces, such that the denotation is fully abstract with respect to the usual structural congruence. Graphs with interfaces are amenable to the synthesis mechanism based on borrowed contexts (bcs), proposed by Ehrig and König (which are an instance of relative pushouts, originally introduced by Milner and Leifer). The bc mechanism allows the effective construction of an lts that has graphs with interfaces as both states and labels, and such that the associated bisimilarity is automatically a congruence. Our paper focuses on the analysis of the lts distilled by exploiting the encoding of ccs processes: besides offering some technical contributions towards the simplification of the bc mechanism, the key result of our work is the proof that the bisimilarity on processes obtained via bcs coincides with the standard strong bisimilarity for ccs.
Algebra and Logic for Resourcebased Systems Modelling
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2009
"... ... often, models are required to be executable, as a simulation, on a computer. In this paper, we present some contributions to the processtheoretic and logical foundations of discreteevent modelling with resources and processes. We present a process calculus with an explicit representation of re ..."
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Cited by 17 (10 self)
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... often, models are required to be executable, as a simulation, on a computer. In this paper, we present some contributions to the processtheoretic and logical foundations of discreteevent modelling with resources and processes. We present a process calculus with an explicit representation of resources in which processes and resources coevolve. The calculus is closely connected to a logic that may be used as a specification language for properties of models. The logic is strong enough to allow requirements that a system has certain structure; for example, that it is a parallel composite of subsystems. This work consolidates, extends, and improves upon aspects of earlier work of ours in this area. An extended example, consisting of a semantics for a simple parallel programming language, indicates a connection with separating logics for concurrency.
Labels from Reductions: Towards a General Theory
 In Algebra and Coalgebra in Computer Science, Calco ’05, volume 3629 of LNCS
, 2005
"... Abstract. We consider open terms and parametric rules in the context of the systematic derivation of labelled transitions from reduction systems. ..."
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Cited by 14 (3 self)
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Abstract. We consider open terms and parametric rules in the context of the systematic derivation of labelled transitions from reduction systems.
Typed polyadic picalculus in bigraphs
 Proceedings of the 8th International Symposium on Principles and Practice of Declarative Programming (PPDP'06)
, 2006
"... Bigraphs have been introduced with the aim to provide a topographical metamodel for mobile, distributed agents that can manipulate their own communication links and nested locations. In this paper we examine a presentation of type systems on bigraphical systems using the notion of sorting. We focus ..."
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Cited by 14 (2 self)
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Bigraphs have been introduced with the aim to provide a topographical metamodel for mobile, distributed agents that can manipulate their own communication links and nested locations. In this paper we examine a presentation of type systems on bigraphical systems using the notion of sorting. We focus our attention on the typed polyadic πcalculus with capability types à la Pierce and Sangiorgi, which we represent using a novel kind of link sorting called subsorting. Using the theory of relative pushouts we derive a labelled transition system which yield a coinductive characterisation of a behavioural congruence for the calculus. The results obtained in this paper constitute a promising foundation for the presentation of various type systems for the (polyadic) πcalculus as sortings in the setting of bigraphs.
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.
Observing reductions in nominal calculi via a graphical encoding of processes
 Processes, terms and cycles (Klop Festschrift), volume 3838 of LNCS
"... Abstract. The paper introduces a novel approach to the synthesis of labelled transition systems for calculi with name mobility. The proposal is based on a graphical encoding: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural ..."
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Cited by 7 (3 self)
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Abstract. The paper introduces a novel approach to the synthesis of labelled transition systems for calculi with name mobility. The proposal is based on a graphical encoding: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Ranked graphs are naturally equipped with a few algebraic operations, and they are proved to form a suitable (bi)category of cospans. Then, as proved by Sassone and Sobocinski, the synthesis mechanism based on relative pushout, originally proposed by Milner and Leifer, can be applied. The resulting labelled transition system has ranked graphs as both states and labels, and it induces on (encodings of) processes an observational equivalence that is reminiscent of early bisimilarity.
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