A formal framework for modelling and analysing mobile systems

This paper presents a formal framework for modelling and analysing mobile systems. The framework comprises a collection of models of the dominant design paradigms which are readily extended to incorporate details of particular technologies, i.e., programming languages and their run-time support, and applications. The modelling language is Object-Z, an extension of the well-known Z specification language with explicit support for object-oriented concepts. Its support for object orientation makes Object-Z particularly suited to our task. The system structuring techniques offered by object-orientation are well suited to modelling mobile systems. In addition, inheritance and polymorphism allow us to exploit commonalities in mobile systems by defining more complex models in terms of simpler ones.

Linear temporal logic and z refinement

Since Z, being a state-based language, describes a system in terms of its state and potential state changes, it is natural to want to describe properties of a specified system also in terms of its state. One means of doing this is to use Linear Temporal Logic (LTL) in which properties about the state of a system over time can be captured. This, however, raises the question of whether these properties are preserved under refinement. Refinement is observation preserving and the state of a specified system is regarded as internal and, hence, non-observable. In this paper, we investigate this issue by addressing the following questions. Given that a Z specification A is refined by a Z specification C, and that P is a temporal logic property which holds for A, what temporal logic property Q can we deduce holds for C? Furthermore, under what circumstances does the property Q preserve the intended meaning of the property P? The paper answers these questions for LTL, but the approach could also be applied to other temporal logics over states such as CTL and the mgr-calculus.