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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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.

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.

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.

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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.

Abstract. We present a Mobile-Ambients-based process calculus to describe context-aware computing in an infrastructure-based Ubiquitous Computing setting. In our calculus, computing agents can provide and discover contextual information and are owners of security policies. Simple access control to contextual information is not sufficient to insure confidentiality in Global Computing, therefore our security policies regulate agents ’ rights to the provision and discovery of contextual information over distributed flows of actions. A type system enforcing security policies by a combination of static and dynamic checking of mobile agents is provided, together with its type soundness. Key words: Ubiquitous Computing, Mobile Ambients, context awareness, security, type system 1

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Informatics bridges Turing-computation and interactive behaviour; examples of the latter include ubiquitous/pervasive and biological systems. But how does a model of computation fit within a model of less disciplined informatic behaviour? This paper offers a precise treatment of that relationship, identifying a class of calculational bigraphical reactive systems. We show how such a system contain a confluent calculation sub-model, and how calculation only ever enables, never prevents, informatic behaviour of the larger model. We submit these results as a modest but essential beginning of a unified informatic theory.