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Bigraphical Reactive Systems: Basic Theory
 PROCEEDINGS OF THE INTERNATIONAL CONFERENCE OF MATHEMATICIANS
, 2001
"... A notion of bigraph is proposed as the basis for a model of mobile interaction. A bigraph consists of two independent structures: a topograph representing locality and a monograph representing connectivity. Bigraphs are equipped with reaction rules to form bigraphical reactive systems (BRSs), which ..."
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Cited by 25 (6 self)
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A notion of bigraph is proposed as the basis for a model of mobile interaction. A bigraph consists of two independent structures: a topograph representing locality and a monograph representing connectivity. Bigraphs are equipped with reaction rules to form bigraphical reactive systems (BRSs), which include versions of the calculus and the ambient calculus. Bigraphs are shown to be a special case of a more abstract notion, wide reactive systems (WRSs), not assuming any particular graphical or other structure but equipped with a notion of width, which expresses that agents, contexts and reactions may all be widely distributed entities. A behavioural theory is established for WRSs using the categorical notion of relative pushout; it allows labelled transition systems to be derived uniformly, in such a way that familiar behavioural preorders and equivalences, in particular bisimilarity, are congruential under certain conditions. Then the theory of bigraphs is developed, and they are shown to meet these conditions. It is shown that, using certain functors, other WRSs which meet the conditions may also be derived; these may, for example, be forms of BRS with additional structure. Simple examples of bigraphical systems are discussed; the theory is developed in a number of ways in preparation for deeper application studies.
Deriving bisimulation congruences: 2categories vs. precategories
 In FOSSACS ’03, volume 2620 of LNCS
, 2003
"... Grelative 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. This paper develops the theory of GRPOs further, arguing that they provide a simple and powerful basis tow ..."
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Cited by 24 (7 self)
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Grelative 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. This paper develops the theory of GRPOs further, arguing that they provide a simple and powerful basis towards a comprehensive solution. As an example, we construct GRPOs in a category of ‘bunches and wirings. ’ We then examine the approach based on Milner’s precategories and Leifer’s functorial reactive systems, and show that it can be recast in a much simpler way into the 2categorical theory of GRPOs.
Towards a Theory of Bisimulation for Local Names
 In 14th Annual Symposium on Logic in Computer Science
, 1999
"... Pitts and Stark have proposed the ncalculus as a language for investigating the interaction of unique name generation and higherorder functions. They developed a sound model based on logical relations, but left completeness as an open problem. In this paper, we develop a complete model based on bis ..."
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Cited by 23 (1 self)
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Pitts and Stark have proposed the ncalculus as a language for investigating the interaction of unique name generation and higherorder functions. They developed a sound model based on logical relations, but left completeness as an open problem. In this paper, we develop a complete model based on bisimulation for a labelled transition system semantics. We show that bisimulation is complete, but not sound, for the ncalculus. We also show that by adding assignment to the ncalculus, bisimulation becomes sound and complete. The analysis used to obtain this result illuminates the difficulties involved in finding fully abstract models for ncalculus proper. Keywords: semantics, bisimulation, nominal calculi. 1 Introduction The use of localised information in computing is endemic. In a workplace, where the prevalence of networks and mobile agents is increasing, the concepts of private and public data are of great importance, and the question of how secrecy can be maintained is a significan...
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.
A theory of bisimulation for a fragment of concurrent ML with local names
, 2003
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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 18 (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.
Towards Abstractions for Distributed Systems
, 2004
"... For historical, sociological and technical reasons, calculi have been the dominant theoretical paradigm in the study of functional computation. Similarly, but to a lesser degree, calculi dominate advanced mathematical accounts of concurrency. Alas, and despite its ever increasing ubiquity, an equa ..."
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Cited by 18 (5 self)
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For historical, sociological and technical reasons, calculi have been the dominant theoretical paradigm in the study of functional computation. Similarly, but to a lesser degree, calculi dominate advanced mathematical accounts of concurrency. Alas, and despite its ever increasing ubiquity, an equally convincing formal foundation for distributed computing has not been forthcoming. This thesis seeks to contribute towards ameliorating that omission. To this end, guided by the assumption that distributed computing is concurrent computing with partial failures of various kinds, we extend the asynchronous calculus with a notion of sites, the possibility of site failure, a persistence mechanism to deal with site failures, the distinction between intersite and intrasite communication, the possibility of message loss in intersite communication and a timer construct, as is often used in distributed algorithms to deal with various failure scenarios.
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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Abstract. We consider open terms and parametric rules in the context of the systematic derivation of labelled transitions from reduction systems.
Deriving structural labelled transitions for mobile ambients
, 2008
"... Abstract. We present a new labelled transition system (lts) for the ambient calculus on which ordinary bisimilarity coincides with contextual equivalence. The key feature of this lts is that it is the fruit of ongoing work on developing a systematic procedure for deriving ltss in the structural styl ..."
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Abstract. We present a new labelled transition system (lts) for the ambient calculus on which ordinary bisimilarity coincides with contextual equivalence. The key feature of this lts is that it is the fruit of ongoing work on developing a systematic procedure for deriving ltss in the structural style from the underlying reduction semantics and observability. Notably, even though we have derived our lts for ambients systematically it compares very favourably with existing transition systems for the same calculus.