Safe and Eventually Safe: Comparing Self-stabilizing and Non-stabilizing Algorithms on a Common Ground

Abstract

Self-stabilizing systems can be started in any arbitrary state and converge to exhibit the desired behavior. However, self-stabilizing systems can be started in predefined initial states, in the same way as non-stabilizing systems. In this case, a self-stabilizing system can mask faults just like any other distributed system. Moreover, whenever faults overwhelm the systems beyond their capabilities to mask faults, the stabilizing system recovers to exhibit eventual safety and liveness, while the behavior of non-stabilizing systems is undefined and may well remain totally and permanently undesired. We demonstrate the importance of defining the initial state of a self-stabilizing system in a specific case of distributed reset over a system composed of several layers of self-stabilizing algorithms. A self-stabilizing stabilization detector ensures that, at first, only the very first layer(s) takes action, and that then higher levels are activated, ensuring smooth restarts, while preserving the stabilization property. The safety of initialized self-stabilizing systems, combined with their better ability to regain safety and liveness following severe conditions, is then demonstrated over the classical fault masking modular redundancy architecture.