Proving almost-certain convergence properties using event-B

Abstract

We propose a methodological approach to prove that a system guarantees to establish a property eventually with probability one. Using Event-B as our modelling language, our correctness reasoning is a combination of termination proofs in terms of probabilistic convergence and standard invariant techniques. We illustrate our approach by formalising some non-trivial algorithms, including the Duelling Cowboys, Herman’s Probabilistic Self-Stabilization and Rabin’s Choice Coordination. We extend the supporting Rodin platform of Event-B to generate appropriate proof obligations for our reasoning, then subsequently (automatically/ interactively) discharge the obligations using the built-in provers of the Rodin platform.