Formalising the Continuous/Discrete Modeling Step

Abstract

Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.

Evaluating the suitability of state‐based formal methods for industrial deployment

“…However, there are several proposals (see, eg, the works of Abrial and Mussat and Rehm) to express such properties in Event‐B specifications. Regarding special concepts , there exist proposals regarding hybrid and continuous systems (see, in particular, the work of Banach et al). Regarding the easy expression of rich concepts , Event‐B provides a rich language for set theory and, in particular, relation (and function) theory.…”

Refinement and Proof Based Development of Systems Characterized by Continuous Functions

“…However, there is no tool currently supporting this extension whereas our approach enabled us to develop and prove the models using available tools. Banach also worked on similar topics with ASM [9,10]. In our development we use reals defined by a minimal set of axioms.…”