Bigraphs: Modelling, Simulation, and Type Systems On Bigraphs for Ubiquitous Computing and on Bigraphical Type Systems

We study how bigraphical reactive systems may be used for modelling and simulating — in a manner controlled by sorts and types — global ubiquitous computing. Ubiquitous computing was in the early 1990s envisioned by Mark Weiser to be the third wave of computing (after mainframes, and then personal computers), in which each person has many computers, receding into the background, at his or her disposal. Global ubiquitous computing has been identified internationally, indeed it is a UK Grand Challenge, as one of the most important challenges for computing in the 21st century. In mathematical modelling of real-life systems, we aim to gain a deeper understanding of their behaviour by studying their essence. Concurrent and mobile systems are notoriously hard to understand in their entirety and thus to give guarantees about. The complexity increases when global ubiquitous computing is considered, especially as systems become larger. A key observation is the importance of understanding this new paradigm before it is realised by technological advances, because trustworthiness will be paramount, and theory is an important factor in achieving this. To this end, computer simulations complement well mathematical methods. In this dissertation we focus on context-aware computing — in particular location-aware computing — which is at the core of ubiquitous computing. Our point of origin is the theory of Bigraphs by Milner and co-workers. Up until now it has been an open question whether Bigraphs is a suitable model for ubiquitous computing, for which we provide a partial answer. The relevant literature is surveyed and Bigraphs challenged by modelling and simulation of location systems. Plato-graphical models are developed as a more advanced modelling technique. Finally, exploiting Bigraphs as a meta-model not just for (process) calculi but for type systems, and to control models, we show how to develop inductive type systems for Bigraphs. We thus expand the knowledge of what may be achieved with Bigraphs.

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