Unreliable Failure Detectors with Limited Scope Accuracy and an Application to Consensus

Let the scope of the accuracy property of an unreliable failure detector be the minimum number (k) of processes that may not erroneously suspect a correct process to have crashed. Classical failure detectors implicitly consider a scope equal to n (the total number of processes). This paper investigates accuracy properties with limited scope, thereby giving rise to the Sk and ⋄Sk classes of failure detectors. A reduction protocol transforming any failure detector belonging to Sk (resp. ⋄Sk) into a failure detector (without limited scope) of the class S (resp. ⋄S) is given. This reduction protocol requires f k, where f is the maximum number of process crashes. (This leaves open the problem to prove/disprove that this condition is necessary.) Then, the paper studies the consensus problem in asynchronous distributed message-passing systems equipped with a failure detector of the class ⋄Sk. It presents a simple consensus protocol that is explicitly based on ⋄Sk. This protocol requires f < min(k, n/2).