Approximate Persistent Stochastic Non Interference

Abstract

In this thesis a security property for stochastic, cooperating processes expressed as terms of the Performance Evaluation Process Algebra (PEPA) is studied. It is expressed as the notion of Persistent Stochastic Non-Interference (PSNI). This work consists in the attempt of relaxing the strict condition of PSNI by introducing a novel equivalence relation over PEPA components, approximated strong equivalence, which induces a quasi-lumpable partition on the state-space of the underlying Markov process. Lumpability approach is a method to tackle the state space explosion problem by reducing the state space of a Markov chain. Equivalent states are aggregated into an unique partition, creating a new aggregated Markov chain that is smaller but its behaviour is the same as the original chain. However, the conditions for a partition on the original state space to be lumpable are quite strict. The introduction of quasi-lumpability is then an attempt to relax the conditions in order to aggregate the states of the considered Markov chain. In line with this thinking, also the property PSNI can be, in some sense, relaxed by adopting the approximated form of the concept of strong equivalence. For this purpose, this thesis can be divided in two main sections: one is the study about the concept of quasi-lumpability, the other is the application of quasi-lumpability to the property PSNI.