Resilient Consensus for Infinitely Many Processes

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Abstract

We provide results for implementing resilient consensus for a (countably) infinite collection of processes.

  • For a known number of faults, we prove the following equivalence result: For every t≥ 1, there is a t-resilient consensus object for infinitely many processes if and only if there is a t-resilient consensus object for t+1 processes.

  • For an unknown or infinite number of faults, we consider whether an infinite set of wait-free consensus objects, capable of solving consensus for any finite collection of processes, suffice to solve wait-free consensus for infinitely many processes. We show that this implication holds under an assumption precluding runs in which the number of simultaneously active processes is not bounded, leaving the general question open.

All the proofs are constructive and several of the constructions have adaptive time complexity. (Reduced to the finite domain, some improve on the time complexity of known results.) Furthermore, we prove that the constructions are optimal in some space parameters by providing tight simultaneous-access and space lower bounds. Finally, using known techniques, we draw new conclusions on the universality of resilient consensus objects in the infinite domain.