Restricted failure detectors: Definition and reduction protocols

This paper investigates unreliable failure detectors with restricted properties, in the context of asynchronous distributed systems made up of n processes where at most f may crash. “Restricted” means that the completeness and the accuracy properties defining a failure detector class are not required to involve all the correct processes but only k and k′ of them, respectively ( k are involved in the completeness property, and k′ in the accuracy property). These restricted properties define the classes R(k,k′) and ♢ R(k,k′) of unreliable failure detectors. A reduction protocol that transforms a restricted failure detector into its non-restricted counterpart is presented. It is shown that the reduction requires k+ k′> n (to be safe) and max( k, k′)≤ n− f (to be live). So, when these two conditions are satisfied, R(k,k′) and ♢ R(k,k′) are equivalent to the Chandra–Toueg's failure detector classes S and ♢ S , respectively. This theoretical transformation is also interesting from a practical point of view because the restricted properties are usually easier to satisfy than their non-restricted counterparts in asynchronous distributed systems.