| Summary: | <p>Most computing systems are shared between users of various kinds. This thesis treats such systems as mathematical objects, and investigates two of their properties: refinement and security. The first is the analysis of the conditions under which one shared system can be replaced by another, the second the determination of a measure of the information flow through a shared system.</p> <p>Under the heading of refinement we show what it means for one shared system to be a suitable replacement for another, both in an environment of co-operating users and in an environment of independent users. Both refine- ment relations are investigated, and a large example is given to demonstrate the relation for cooperating users.</p> <p>We show how to represent the security of a shared system as an 'inference function', and define several security properties in terms of such functions. A partial order is defined on systems, with the meaning 'at least as secure as'. We generalise inference functions to produce 'security specifications' which can be used to capture the desired degree of security in any shared system. We define what it means for a shared system to meet a security specification and indicate how implementations may be derived from their specifications in some cases.</p> <p>A summary of related work is given.</p>
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