As part of ongoing work on evaluating Milner’s bigraphical reactive systems, we investigate bigraphical models of context-aware 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 Plato-graphical 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.

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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We present local Hoare reasoning about data update, using Context Logic for analysing structured data. We apply our reasoning to tree update, heap update which is analogous to local Hoare reasoning using Separation Logic, and term rewriting.

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.

We discuss the tensions between intensionality and extensionality of spatial observations in distributed systems, showing that there are natural models where extensional observational equivalences may be characterized by spatial logics, including the composition and void operators. Our results support the claim that spatial observations do not need to be always considered intensional, even if expressive enough to talk about the structure of systems. For simplicity, our technical development is based on a minimalist process calculus, that already captures the main features of distributed systems, namely local synchronous communication, local computation, asynchronous remote communication, and partial failures.

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Separation Logic and Context Logic have been used to reason locally about heap update and simple tree update. We study local reasoning based on Context Logic for a more realistic, local tree-update language which combines update commands with queries. This combination results in updates at multiple locations, which significantly affects the complexity of the reasoning.

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.