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22
Pure bigraphs: structure and dynamics
, 2005
"... Bigraphs are graphs whose nodes may be nested, representing locality, independently of the edges connecting them. They may be equipped with reaction rules, forming a bigraphical reactive system (Brs) in which bigraphs can reconfigure themselves. Following an earlier paper describing link graphs, a c ..."
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Cited by 50 (5 self)
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Bigraphs are graphs whose nodes may be nested, representing locality, independently of the edges connecting them. They may be equipped with reaction rules, forming a bigraphical reactive system (Brs) in which bigraphs can reconfigure themselves. Following an earlier paper describing link graphs, a constituent of bigraphs, this paper is a devoted to pure bigraphs, which in turn underlie various more refined forms. Elsewhere it is shown that behavioural analysis for Petri nets, πcalculus and mobile ambients can all be recovered in the uniform framework of bigraphs. The paper first develops the dynamic theory of an abstract structure, a wide reactive system (Wrs), of which a Brs is an instance. In this context, labelled transitions are defined in such a way that the induced bisimilarity is a congruence. This work is then specialised to Brss, whose graphical structure allows many refinements of the theory. The latter part of the paper emphasizes bigraphical theory that is relevant to the treatment of dynamics via labelled transitions. As a running example, the theory is applied to finite pure CCS, whose resulting transition system and bisimilarity are analysed in detail. The paper also mentions briefly the use of bigraphs to model pervasive computing and
Transition systems, link graphs and Petri nets
, 2004
"... A framework is defined within which reactive systems can be studied formally. The framework is based upon scategories, a new variety of categories, within which reactive systems can be set up in such a way that labelled transition systems can be uniformly extracted. These lead in turn to behavi ..."
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Cited by 26 (5 self)
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A framework is defined within which reactive systems can be studied formally. The framework is based upon scategories, a new variety of categories, within which reactive systems can be set up in such a way that labelled transition systems can be uniformly extracted. These lead in turn to behavioural preorders and equivalences, such as the failures preorder (treated elsewhere) and bisimilarity, which are guaranteed to be congruential. The theory rests upon the notion of relative pushout previously introduced by the authors. The framework
Bigraphical Models of Contextaware Systems
, 2005
"... As part of ongoing work on evaluating Milner’s bigraphical reactive systems, we investigate bigraphical models of contextaware systems, a facet of ubiquitous computing. We find that naively encoding such systems in bigraphs is somewhat awkward; and we propose a more sophisticated modeling technique ..."
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Cited by 26 (14 self)
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As part of ongoing work on evaluating Milner’s bigraphical reactive systems, we investigate bigraphical models of contextaware systems, a facet of ubiquitous computing. We find that naively encoding such systems in bigraphs is somewhat awkward; and we propose a more sophisticated modeling technique, introducing Platographical models, alleviating this awkwardness. We argue that such models are useful for simulation and point out that for reasoning about such bigraphical models, the bisimilarity inherent to bigraphical reactive systems is not enough in itself; an equivalence between the bigraphical reactive systems themselves is also needed.
Spatial Logics for Bigraphs
 In Proceedings of ICALP’05, volume 3580 of LNCS
, 2005
"... Abstract. Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, picalculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper)graph for connections. With the aim of describing bigraphical structur ..."
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Cited by 22 (2 self)
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Abstract. Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, picalculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts. 1
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.
Static BiLog: a Unifying Language for Spatial Structures
 FUNDAMENTA INFORMATICAE??? (200?) 1–20
"... Aiming at a unified view of the logics describing spatial structures, we introduce a general framework, BiLog, whose formulae characterise monoidal categories. As a first instance of the framework we consider bigraphs, which are emerging as a an interesting (meta)model for spatial structures and d ..."
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Cited by 9 (0 self)
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Aiming at a unified view of the logics describing spatial structures, we introduce a general framework, BiLog, whose formulae characterise monoidal categories. As a first instance of the framework we consider bigraphs, which are emerging as a an interesting (meta)model for spatial structures and distributed calculi. Since bigraphs are built orthogonally on two structures, a hierarchical place graph for locations and a link (hyper)graph for connections, we obtain a logic that is a natural composition of other two instances of BiLog: a Place Graph Logic and a Link Graph Logic. We prove that these instances generalise the spatial logics for trees, for graphs and for tree contexts. We also explore the concepts of separation and sharing in these logics. We note that both the operator ∗ of Separation Logic and the operator  of spatial logics do not completely separate the underlying structures. These two different forms of separation can be naturally derived as instances of BiLog by using the complete separation induced by the tensor product of monoidal categories along with some form of sharing.
Bigraphical Logics for XML
, 2005
"... Bigraphs are emerging as an interesting model that can represent both the picalculus and the ambient calculus. Bigraphs are built orthogonally on two structures: a hierarchical `place' graph for locations and a `link' (hyper)graph for connections. ..."
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Cited by 7 (2 self)
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Bigraphs are emerging as an interesting model that can represent both the picalculus and the ambient calculus. Bigraphs are built orthogonally on two structures: a hierarchical `place' graph for locations and a `link' (hyper)graph for connections.
Distributed Reactive XML
, 2006
"... XMLcentric models of computation have been proposed as an answer to the demand for interoperability, heterogeneity and openness in coordination models. We present a prototype implementation of an open XMLcentric coordination middleware called Distributed Reactive XML. The middleware has as theoret ..."
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Cited by 4 (3 self)
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XMLcentric models of computation have been proposed as an answer to the demand for interoperability, heterogeneity and openness in coordination models. We present a prototype implementation of an open XMLcentric coordination middleware called Distributed Reactive XML. The middleware has as theoretical foundation a general distributed extensible process calculus inspired by the theory of Bigraphical Reactive Systems. The calculus is extensible just as XML is extensible, in that its signature and reaction rules are not fixed. It is distributed by allowing both the state of processesaswellasthesetofreaction rules to be distributed (or partly shared) between different clients. The calculus is implemented by representing process terms as XML documents stored in a valueoriented, peertopeer XML Store and reaction rules as XML transformations performed by the clients. The formalism does not require that only process terms are stored—inside process terms one may store application specific data as well. XML Store provides transparent sharing of process terms between all participating peers. Conflicts between concurrent reaction rules are handled by an optimistic concurrency control. The implementation thus provides an open XMLbased coordination middleware with a formal foundation that encompasses both the shared data, processes and reaction rules.