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Angelic Processes
In the formal modelling of systems, demonic and angelic nondeterminism play
fundamental roles as abstraction mechanisms. The angelic nature of a choice
pertains to the property of avoiding failure whenever possible. As a concept,
angelic choice first appeared in automata theory and Turing machines, where it
can be implemented via backtracking. It has traditionally been studied in the
refinement calculus, and has proved to be useful in a variety of applications
and refinement techniques. Recently it has been studied within relational,
multirelational and higher-order models. It has been employed for modelling
user interactions, game-like scenarios, theorem proving tactics, constraint
satisfaction problems and control systems.
When the formal modelling of state-rich reactive systems is considered, it
only seems natural that both types of nondeterministic choice should be
considered. However, despite several treatments of angelic nondeterminism in
the context of process algebras, namely Communicating Sequential Processes, the
counterpart to the angelic choice of the refinement calculus has been elusive.
In this thesis, we develop a semantics in the relational setting of Hoare and
He's Unifying Theories of Programming that enables the characterisation of
angelic nondeterminism in CSP. Since CSP processes are given semantics in the
UTP via designs, that is, pre and postcondition pairs, we first introduce a
theory of angelic designs, and an isomorphic multirelational model, that is
suitable for characterising processes. We then develop a theory of reactive
angelic designs by enforcing the healthiness conditions of CSP. Finally, by
introducing a notion of divergence that can undo the history of events, we
obtain a model where angelic choice avoids divergence.Comment: Extended version of PhD thesis submitted to the University of York,
UK, 868 pages, 10 figures, 7 tables (revised to match print version deposited
in the White Rose eTheses Online), http://etheses.whiterose.ac.uk/9020