Behavioural Preorders on Stochastic Systems - Logical, Topological, and Computational Aspects

Computer systems can be found everywhere: in space, in our homes, in our cars, in our pockets, and sometimes even in our own bodies. For concerns of safety, economy, and convenience, it is important that such systems work correctly. However, it is a notoriously difficult task to ensure that the software running on computers behaves correctly. One approach to ease this task is that of model checking, where a model of the system is made using some mathematical formalism. Requirements expressed in a formal language can then be verified against the model in order to give guarantees that the model satisfies the requirements. For many computer systems, time is an important factor. As such, we need our formalisms and requirement languages to be able to incorporate real time. We therefore develop formalisms and algorithms that allow us to compare and express properties about real-time systems. We first introduce a logical formalism for reasoning about upper and lower bounds on time, and study the properties of this formalism, including axiomatisation and algorithms for checking when a formula is satisfied. We then consider the question of when a system is faster than another system. We show that this is a difficult question which can not be answered in general, but we identify special cases where this question can be answered. We also show that under this notion of faster-than, a local increase in speed may lead to a global decrease in speed, and we take step towards avoiding this. Finally, we consider how to compare the real-time behaviour of systems not just qualitatively, but also quantitatively. Thus, we are interested in knowing how much one system is faster or slower than another system. This is done by introducing a distance between systems. We show how to compute this distance and that it behaves well with respect to certain properties.Comment: PhD dissertation from Aalborg Universit

On the Additive Capacity Problem for Quantitative Information Flow

International audiencePreventing information leakage is a fundamental goal in achieving confidentiality. In many practical scenarios, however, eliminating such leaks is impossible. It becomes then desirable to quantify the severity of such leaks and establish bounds on the threat they impose. Aiming at developing measures that are robust wrt a variety of operational conditions, a theory of channel capacity for the g-leakage model was developed in [1], providing solutions for several scenarios in both the multiplicative and the additive setting. This paper continuous this line of work by providing substantial improvements over the results of [1] for additive leakage. The main idea of employing the Kan-torovich distance remains, but it is now applied to quasimetrics, and in particular the novel " convex-separation " quasimetric. The benefits are threefold: first, it allows to maximize leakage over a larger class of gain functions, most notably including the one of Shannon. Second, a solution is obtained to the problem of maximizing leakage over both priors and gain functions, left open in [1]. Third, it allows to establish an additive variant of the " Miracle " theorem from [3]