Lower bound on the step complexity of anonymous binary consensus

Abstract

Obstruction-free consensus, ensuring that a process running solo will eventually terminate, is at the core of practical ways to solve consensus, e.g., by using randomization or failure detectors. An obstructionfree consensus algorithm may not terminate in many executions, but it must terminate whenever a process runs solo. Such an algorithm can be evaluated by its solo step complexity, which bounds the worst case number of steps taken by a process running alone, from any configuration, until it decides. This paper presents a lower bound of Ω(log n) on the solo step complexity of obstruction-free binary anonymous consensus. The proof constructs a sequence of executions in which more and more distinct variables are about to be written to, and then uses the backtracking covering technique to obtain a single execution in which many variables are accessed.