A Framework for Certified Self-Stabilization

We propose a general framework to build certified proofs of distributed self-stabilizing algorithms with the proof assistant Coq. We first define in Coq the locally shared memory model with composite atomicity, the most commonly used model in the self-stabilizing area. We then validate our framework by certifying a non trivial part of an existing silent self-stabilizing algorithm which builds a $k$-hop dominating set of the network. We also certified a quantitative property related to the output of this algorithm. Precisely, we show that the computed $k$-hop dominating set contains at most $\lfloor \frac{n-1}{k+1} \rfloor + 1$ nodes, where $n$ is the number of nodes in the network. To obtain these results, we also developed a library which contains general tools related to potential functions and cardinality of sets

Formal Verification of Netlog Protocols

Abstract—Data centric languages, such as recursive rule based languages, have been proposed to program distributed applications over networks. They greatly simplify the code, while still admitting efficient distributed execution, including on sensor networks. From previous work [1], we know that they also provide a promising approach to another tough issue about distributed protocols: their formal verification. Indeed, we can take advantage of their data centric orientation, which allows us to explicitly handle global structures such as the topology of the network. We illustrate here our approach on two non-trivial protocols and discuss its Coq implementation. Keywords-formal verification; Coq; distributed algorithms; I