Reasoning about almost-certain convergence properties using Event-B

Highlights

• We present an approach for proving almost-certain convergence properties.

• The approach is based on Event-B and is supported by the Rodin platform.

• It makes use of refinement, probabilistic convergence, and deadlock-freedom reasoning.

• We formalise Herman’s probabilistic self-stabilisation, and Rabin’s choice coordination.

Abstract

We propose an approach for proving that a system guarantees to establish a given 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), deadlock-freedom and invariant techniques. We illustrate the approach by formalising some non-trivial algorithms, including the duelling cowboys, Herman’s probabilistic self-stabilisation and Rabin’s choice coordination. We extend the supporting Rodin Platform (Rodin) of Event-B to generate appropriate proof obligations for our reasoning, then subsequently (automatically/interactively) discharge the obligations using the built-in provers of Rodin.