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29
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 62 (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, π-calculus 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
Axioms For Bigraphical Structure
- UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2005
"... This paper axiomatises the structure of bigraphs, and proves that the resulting theory is complete. Bigraphs are graphs with double structure, representing locality and connectivity. They have been shown to represent dynamic theories for the #-calculus, mobile ambients and Petri nets, in a way th ..."
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Cited by 41 (8 self)
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This paper axiomatises the structure of bigraphs, and proves that the resulting theory is complete. Bigraphs are graphs with double structure, representing locality and connectivity. They have been shown to represent dynamic theories for the #-calculus, mobile ambients and Petri nets, in a way that is faithful to each of those models of discrete behaviour. While the main purpose of bigraphs is to understand mobile systems, a prerequisite for this understanding is a well-behaved theory of the structure of states in such systems. The algebra of bigraph structure is surprisingly simple, as the paper demonstrates; this is because bigraphs treat locality and connectivity orthogonally
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, pi-calculus, 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 27 (3 self)
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Abstract. Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, 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 GT-VC 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 24 (12 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.
Typed polyadic pi-calculus 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 meta-model 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 20 (2 self)
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Bigraphs have been introduced with the aim to provide a topographical meta-model 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 π-calculus 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) π-calculus as sortings in the setting of bigraphs.
Representations of Petri net interactions
"... We introduce a novel compositional algebra of Petri nets, as well as a stateful extension of the calculus of connectors. These two formalisms are shown to have the same expressive power. ..."
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Cited by 11 (5 self)
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We introduce a novel compositional algebra of Petri nets, as well as a stateful extension of the calculus of connectors. These two formalisms are shown to have the same expressive power.
Axiomatizing Binding Bigraphs
- NORDIC JOURNAL OF COMPUTING
, 2006
"... We axiomatize the congruence relation for binding bigraphs and prove that the generated theory is complete. In doing so, we define a normal form for binding bigraphs, and prove that it is unique up to certain isomorphisms. Our work builds on Milner’s axioms for pure bigraphs. We have extended the ..."
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Cited by 6 (0 self)
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We axiomatize the congruence relation for binding bigraphs and prove that the generated theory is complete. In doing so, we define a normal form for binding bigraphs, and prove that it is unique up to certain isomorphisms. Our work builds on Milner’s axioms for pure bigraphs. We have extended the set of axioms with five new axioms concerned with binding, and we have altered some of Milner’s axioms for ions, because ions in binding bigraphs have names on both their inner and outer faces. The resulting theory is a conservative extension of Milner’s for pure bigraphs.
M.: Dbtk: A toolkit for directed bigraphs
, 2009
"... Abstract. We present DBtk, a toolkit for Directed Bigraphs. DBtk supports a textual language for directed bigraphs, the graphical visualization of bigraphs, the calculation of IPO labels, and the calculation of redex matchings. Therefore, this toolkit provides the main functions needed to implement ..."
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Cited by 3 (0 self)
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Abstract. We present DBtk, a toolkit for Directed Bigraphs. DBtk supports a textual language for directed bigraphs, the graphical visualization of bigraphs, the calculation of IPO labels, and the calculation of redex matchings. Therefore, this toolkit provides the main functions needed to implement simulators and verification tools. 1
Syntactic theory for bigraphs
, 2006
"... I investigate and develop theory for term languages for a variant of bigraphs with binding, thus building the formal foundation for a (term-based) tool for bigraphical reactive systems. I present two main results (developed with co-authors). First, I give an axiomatization of structural congruence ( ..."
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Cited by 2 (1 self)
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I investigate and develop theory for term languages for a variant of bigraphs with binding, thus building the formal foundation for a (term-based) tool for bigraphical reactive systems. I present two main results (developed with co-authors). First, I give an axiomatization of structural congruence (graph equivalence) for binding bigraphs. Along the way, I devise a term language for binding bigraphs and prove a series of normal form theorems for binding bigraphs. Second, using these results, I give a complete inductive characterization of matching in bigraphs — essentially, for describing when and where a bigraphical reaction rule can be applied. I include an introduction to the goals of my Ph.D. project and explain how it relates to the goals of the BPL project. Moreover, I outline a number of future challenges and include a litterature study for future work.