A Refinement-Based Approach for Proving Distributed Algorithms on Evolving Graphs

Proving the correctness of distributed algorithms in dynamic networks is a hard task due to the time complexity and the highly dynamic behavior. In the literature, the existing solutions lack a consensus about their developments and their proofs. Moreover, the proofs which have been presented are done manually. In this paper, we propose a reuse based approach for specifying and proving distributed algorithms in dynamic networks. It consists in developing a formal pattern using Event-B method, based on refinement techniques. The proposed pattern allows to handle topological events in dynamic networks and to characterize the concept of time. Our solution relies on evolving graphs as a powerful model to record the evolution of a network topology. To illustrate it, we present an example of a distributed counting algorithm. The proof statistics related to the development of the pattern and the algorithm show the efficiency of our solution.