The Combined Power of Conditions and Information on Failures to Solve Asynchronous Set Agreement

To cope with the impossibility of solving agreement problems in asynchronous systems made up of n processes and prone to t process crashes, system designers tailor their algorithms to run fast in “normal” circumstances. Two orthogonal notions of “normality” have been studied in the past through failure detectors that give processes information about process crashes, and through conditions that restrict the inputs to an agreement problem. This paper investigates how the two approaches can benefit from each other to solve the k-set agreement problem, where processes must agree on at most k of their input values (when k = 1 we have the famous consensus problem). It proposes novel failure detectors for solving k-set agreement, and a protocol that combines them with conditions, establishing a new bridge among asynchronous, synchronous and partially synchronous systems with respect to agreement problems. Th