The impossibility of boosting distributed service resilience

We prove two theorems saying that no distributed system in which processes coordinate using reliable registers and f-resilient services can solve the consensus problem in the presence of f + 1 undetectable process stopping failures. (A service is f-resilient if it is guaranteed to operate as long as no more than f of the processes connected to it fail.) Our first theorem assumes that the given services are atomic objects, and allows any connection pattern between processes and services. In contrast, we show that it is possible to boost the resilience of systems solving problems easier than consensus: the k-set consensus problem is solvable for 2k - 1 failures using 1-resilient consensus services. The first theorem and its proof generalize to the larger class of failure-oblivious services. Our second theorem allows the system to contain failureaware services, such as failure detectors, in addition to failure-oblivious services; however, it requires that each failure-aware service be connected to all processes. Thus, f + 1 process failures overall can disable all the failure-aware services. In contrast, it is possible to boost the resilience of a system solving consensus if arbitrary patterns of connectivity are allowed between processes and failure-aware services: consensus is solvable for any number of failures using only 1-resilient 2-process perfect failure detectors.