Better Sooner Rather Than Later

This article unifies and generalizes fundamental results related to n-process asynchronous crash-prone distributed computing. More precisely, it proves that for every 0≤k≤n, assuming that process failures occur only before the number of participating processes bypasses a predefined threshold that equals n-k (a participating process is a process that has executed at least one statement of its code), an asynchronous algorithm exists that solves consensus for n processes in the presence of f crash failures if and only iff≤k. In a very simple and interesting way, the “extreme” case k=0 boils down to the celebrated FLP impossibility result (1985, 1987). Moreover, the second extreme case, namely k=n, captures the celebrated mutual exclusion result by E.W. Dijkstra (1965) that states that mutual exclusion can be solved for n processes in an asynchronous read/write shared memory system where any number of processes may crash (but only) before starting to participate in the algorithm (that is, participation is not required, but once a process starts participating it may not fail). More generally, the possibility/impossibility stated above demonstrates that more failures can be tolerated when they occur earlier in the computation (hence the title).