Economics

Topics to be investigated include:

• Resource Consumption: Here we aim to develop methods for describing and analysing how resources are used in computational processes. For example in long-run averages: determination of average resource consumption, or worst case scenarios. We have recently started work on an analysis of the heap utilisation in JVM programs. We are considering a small subset of the JVM extended with an input command. We assume some knowledge of the distributions of possible input values. We work from a SOS-style semantics for JVM where transitions are labelled with information about heap utilisation (cf [46]). Our intention is to use probabilistic abstract interpretation to approximate computations and gather information about average heap utilisation. This provides an interesting contrast with classical analyses where the emphasis is normally on worst-case behaviour.

• Resource Coordination: i.e. cooperative and competitive resource sharing in distributed systems. As illustrated in the examples presented before in Section 1, quantitative resources have an influence not only on the quantitative behaviour of a computational process (e.g. with more memory the process might run faster) but also on the qualitative behaviour (in the examples above: termination). In other words, it is necessary to understand and analyse the coordination of distributed and parallel processes not just in the traditional qualitative setting (e.g. signal exchange and synchronisation) but via analysing their dependency on resources. This is of course strongly related to security issues (which will be studied under the heading ``Distributed Security'').

• Information Costing and Optimisation: We argued that information is an important quantitative resource. Besides a quantitative description of information flow (in the sense of Shannon's theory), and a quantitative analysis of programs with respect to the resource information, we will also look at the problem of optimising information flow. This research has two different aspects to it: (i) Mainly in a security context we are interested in developing methods (e.g. program transformation techniques) which minimise the leaked amount of information. This also can to be put into relation with the average or worst damage some leaked information can cause, which leads to a kind of analysis typical in insurance mathematics; (ii) in a general context we are also interested in maximising the information flow: For example in a Grid-based context with certain fees levied by service providers it is economically essential to ``get the most out of the provider''. Obviously, any cost optimisation has to be based on a formal quantitative analysis of the situation. Initial ideas in this direction can be found in our work on Approximate Confinement [27] where one of the problems was to construct a ``most effective spy'', i.e. a process which is able to extract a maximum amount of information about (the identity) of some unknown processes.