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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 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.
On the Construction of Sorted Reactive Systems
 IN PROCEEDINGS OF CONCUR’08, LNCS
, 2008
"... 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. ..."
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Cited by 10 (5 self)
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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.
Static bilog: a unifying language for spatial structures
 Fundamenta Informaticae
, 2007
"... Abstract. 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 struct ..."
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Cited by 9 (0 self)
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Abstract. 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.
An implementation of bigraph matching
, 2008
"... We describe a provably sound and complete matching algorithm for bigraphical reactive systems. The algorithm has been implemented in our BPL Tool, a first implementation of bigraphical reactive systems. We describe the tool and present a concrete example of how it can be used to simulate a model of ..."
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We describe a provably sound and complete matching algorithm for bigraphical reactive systems. The algorithm has been implemented in our BPL Tool, a first implementation of bigraphical reactive systems. We describe the tool and present a concrete example of how it can be used to simulate a model of a mobile phone system in a bigraphical representation of the polyadic π calculus.
An algebraic approach to image schemas for geographic space. Spatial Information Theory
, 2009
"... Abstract. Formal models of geographic space should support reasoning about its static and dynamic properties, its objects, their behaviors, and the relationships between them. Image schemas, used to embody spatiotemporal experiential abstractions, capture highlevel perceptual concepts but do not ha ..."
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Cited by 3 (0 self)
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Abstract. Formal models of geographic space should support reasoning about its static and dynamic properties, its objects, their behaviors, and the relationships between them. Image schemas, used to embody spatiotemporal experiential abstractions, capture highlevel perceptual concepts but do not have generally accepted formalizations. This paper provides a method for formally representing topological and physical image schemas using Milner’s bigraphical models. Bigraphs, capable of independently representing mobile locality and connectivity, provide formal algebraic specifications of geographic environments enhanced by intuitive visual representations. Using examples from a built environment, we define topological schemas CONTAINER and LINK as static bigraph components, dynamic schemas INTO and LINKTO as rulebased changes in static components, and more complex schemas REMOVAL_OF_RESTRAINT and BLOCKAGE with sequences of rules. Finally, we demonstrate that bigraphs can be used to describe scenes with incomplete information, and that we can adjust the granularity of scenes by using bigraph composition to provide additional context.
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 (termbased) tool for bigraphical reactive systems. I present two main results (developed with coauthors). 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 (termbased) tool for bigraphical reactive systems. I present two main results (developed with coauthors). 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.
Computation in the Informatic Jungle
, 2010
"... Informatics bridges Turingcomputation 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, i ..."
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Cited by 2 (2 self)
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Informatics bridges Turingcomputation 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 submodel, 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.
On the decidability of bigraphical sorting
 Proc. CALCO Young Researchers Workshop, number 05/2010 in Technical Report
, 2009
"... Abstract. Bigraphical reactive systems are a general framework for mobile, concurrent, and communicating systems based on the notions of location and channel connection. Bigraphs have been shown to be suitable for representing several formalisms, but despite their expressive power, in many cases s ..."
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Abstract. Bigraphical reactive systems are a general framework for mobile, concurrent, and communicating systems based on the notions of location and channel connection. Bigraphs have been shown to be suitable for representing several formalisms, but despite their expressive power, in many cases some disciplines on the structure of bigraphs are needed to faithfully encode the computational model at hand. Sortings have been proposed as an abstract technique to discipline bigraphs. In this paper, we investigate the decidability problem of bigraphical sorting, that is, to decide whether a bigraph belongs to some sorted bigraphical category. While the problem is not decidable in general (and in particular in the case of Debois and coauthors ’ predicate sortings), we propose a decidable subclass of bigraphical sortings, match predicate sortings, which can be decided using the matching algorithm for bigraphs. The proposed subclass is shown to be expressive enough to capture several bigraphical sortings present in literature, e.g., homomorphic sortings and local bigraphs. 1