Synthesizing Self-Stabilizing Protocols under Average Recovery Time Constraints

A self-stabilizing system is one that converges to a legitimate state from any arbitrary state. Such an arbitrary state may be reachable due to wrong initialization or the occurrence of transient faults. Average recovery time of self-stabilizing systems is a key factor in evaluating their performance, especially in the domain of network and robotic protocols. This paper introduces a groundbreaking result on automated repair and synthesis of self-stabilizing protocols whose average recovery time is required to satisfy certain constraints. We show that synthesizing and repairing weak-stabilizing protocols under average recovery time constraints is NP-complete. To cope with the exponential complexity (unless P = NP), we propose a polynomial-time heuristic.