Reasoning about systems with evolving structure

This thesis is concerned with the specification and verification of mobile systems, i.e. systems with dynamically-evolving communication topologies. The expressiveness and applicability of the πυ-calculus, an extension of the π-calculus with first-order data, is investigated for describing and reasoning about mobile systems. The theory of confluence and determinacy in the πυ-calculus is studied, with emphasis on results and techniques which facilitate process verification. The utility of the calculus for giving descriptions which are precise, natural and amenable to rigorous analysis is illustrated in three applications. First, the behaviour of a distributed protocol is analysed. The use of a mobile calculus makes it possible to capture important intuitions concerning the behaviour of the algorithm; the theory of confluence plays a central role in its correctness proof. Secondly, an analysis of concurrent operations on a dynamic search structure, the B-tree, is carried out. This exploits results obtained concerning a notion of partial confluence by whose use classes of systems in which interaction between components is of a certain disciplined kind may be analysed. Finally, the πυ-calculus is used to give a semantic definition for a concurrent-object programming language and it is shown how this definition can be used as a basis for reasoning about systems prescribed by programs. Syntactic conditions on programs are isolated and shown to guarantee determinacy. Transformation rules which increase the scope for concurrent activity within programs without changing their observable behaviour are given and their soundness proved

A rigorous analysis of concurrent operations on B-trees

An account is given of a rigorous study of concurrent operations on a variant of the B-tree in the framework of a general theory of concurrent systems, an extension of the pi-calculus. The assertion of correctness of the algorithms is that the agent representing the system is behaviourally equivalent to an agent whose observable behaviour describes simply the expected interactions of the system with its environment. An outline of the proofs of correctness of algorithms for insertion and search is given. Algorithms for deletion and compression are considered briefly. The main theoretical contribution is an extension of the theory,of partial confluence of agents