A Framework for Certified Self-Stabilization

Karine Altisen (1) , Pierre Corbineau (1) , Stéphane Devismes (1)

1 VERIMAG - IMAG - VERIMAG

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.

Mots clés: Potential functions.; Silent algorithms; Self-stabilization; Proof assistant; Coq

Domaines: Informatique [cs]

Karine Altisen, Pierre Corbineau, Stéphane Devismes. A Framework for Certified Self-Stabilization. [Technical Report] VERIMAG UMR 5104, Université Grenoble Alpes, France. 2016. ⟨hal-01272158v2⟩