1 - adaptivity

A 1-adaptive self-stabilizing system is a self-stabilizing system that can correct any memory corruption of a single process in one computation step. 1-adaptivity means that, if in a legitimate state the memory of a single process is corrupted, then the next system transition will lead to a legitimate state. Then, in one step the system recovers a correct behavior. Then 1-adaptive self-stabilizing algorithms guarantee that a single failure will not propagate and will be corrected immediately. This is not the case for most of the existing self-stabilizing algorithms. Our aim here is to study the possibility of designing such algorithms. More precisely we discuss necessary and sufficient conditions for a self-stabilizing algorithm to be 1-adaptive. Such conditions yield a simple way to verify whether or not a selfstabilizing algorithm is also 1-adaptive, as they only look at a small subset of the system states and as they can be verified locally. We also provide examples of self-stabilizing 1-adaptive algorithms.