An investigation into Event-B methodologies and timing constraint modelling

In the domain of formal modelling and verification of real-time safety-critical systems, our focus is on complex - i.e. nested, interdependent and cyclic - timing constraints. We strengthen the pallet of modelling tools and techniques to describe and verify timing properties in such real-time systems.Our contribution builds on Event-B - a formal language for systems modelling, based on set theory and predicate logic. The language has the advantage of mechanised proof and tackles system complexity through a stepwise refinement.The foundation of our scheme - a notion of a timing interval - is a higher level abstraction in terms of statemachine and formal timing interval specification. It can formally bind together several related timing requirements, expressed in delay, deadline and expiry concepts. To support the timing interval abstraction through the Event-B based refinement method, we present five compositional refinement transformations: Sub-Interval, Alternative, Abort-to-Response, Single-to-Multi and Retry. The timing interval and its refinement transformations use a template-based generative scheme for the transformation of timed models - specified with state machines and timing interval - to Event-B. We provide a workflow and a recommended convention for modelling and graphically representing a timing interval and its refinement transformations in state machine diagrams. The modelling of a timing interval and its refinement transformations process is automated with our tool - tiGen.Finally, we validate our approach and the recommended development workflow in three case studies. The results show that our timing interval can be developed through multiple levels of refinement. The process of modelling and proving is mostly automated