Proving Distributed Coloring of Forests in Dynamic Networks

Abstract

The design and the proof of correctness of distributed algorithms in dynamic networks are difficult tasks. These networks are characterized by frequent topology changes due to unpredictable appearance and disappearance of mobile devices and/or communication links. In this paper, we propose a correct-by-construction approach for specifying and proving distributed algorithms in a forest topology. In the first stage, we specify a formal pattern using the Event-B method, based on the refinement technique. The proposed pattern relies on the Dynamicity Aware-Graph Relabeling Systems (DA-GRS) which is an existing model for building and maintaining a forest of spanning treesindynamicnetworks. It is based one volving graphs as a powerful model to record the evolution of a network topology. In the second stage, we deal with distributed algorithms which can be applied to spanning trees of the forest. In fact, we use the proposed pattern to specify a tree-coloring algorithm. The proof statistics comparing the development of this algorithm with and without using the pattern show the efficiency of our solution in terms of proofs reduction.