Summary: Randomized Consensus in Expected O(n2
Total Work Using Single-Writer Registers
Abstract. A new weak shared coin protocol yields a randomized wait-
free shared-memory consensus protocol that uses an optimal O(n2
pected total work with single-writer registers despite asynchrony and
process crashes. Previously, no protocol was known that achieved this
bound without using multi-writer registers.
The consensus problem is to get a group of n processes to agree on a bit. In a
wait-free randomized consensus protocol, each process starts with an input
bit and produces a decision bit; the protocol is correct if it satisfies agreement,
where all processes that finish the protocol choose the same decision bit; valid-
ity, where every decision bit is equal to some process's input; and probabilistic
termination, where every non-faulty process completes the protocol after a fi-
nite number of its own steps with probability 1. These conditions are required
to hold despite asynchrony and up to n - 1 crash failures.