## Section: New Results

### Extensions of Self-stabilization

Participant : Sébastien Tixeuil.

We tackled the open problem of snap-stabilization in message-passing systems [35] . Snap-stabilization is a nice approach to design protocols that withstand transient faults. Compared to the well-known self-stabilizing approach, snap-stabilization guarantees that the effect of faults is contained immediately after faults cease to occur. Our contribution is twofold: we show that (1) snap-stabilization is impossible for a wide class of problems if we consider networks with finite yet unbounded channel capacity; (2) snap-stabilization becomes possible in the same setting if we assume bounded-capacity channels. We propose three snap-stabilizing protocols working in fully-connected networks. Our work opens exciting new research perspectives, as it enables the snap-stabilizing paradigm to be implemented in actual networks.

The loop-free property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol. The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. We presented [29] a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Second, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date.

Distributed fault-tolerance can mask the effect of a limited number of per- manent faults, while self-stabilization provides forward recovery after an arbitrary number of transient fault hit the system. FTSS protocols combine the best of both worlds since they are simultaneously fault-tolerant and self-stabilizing. To date, FTSS solutions either consider static (i.e. fixed point) tasks, or assume synchronous scheduling of the system components. We presented [39] the first study of dynamic tasks in asynchronous systems, considering the unison problem as a benchmark. Unison can be seen as a local clock synchronisation problem as neighbors must maintain digital clocks at most one time unit away from each other, and increment their own clock value infinitely often. We present many im- possiblity results for this difficult problem and propose a FTSS solution when the problem is solvable that exhibits optimal fault containment.