A tight space bound for consensus

Abstract

Existing n-process randomized wait-free (and obstruction-free) consensus protocols from registers all use at least n registers. In 1992, it was proved that such protocols must use Omega(sqrt(n)) registers. Recently, this was improved to Omega(n) registers in the anonymous setting, where processes do not have identifiers. Closing the gap in the general case, however, remained an open problem. We resolve this problem by proving that every randomized wait-free (or obstruction-free) consensus protocol for n processes must use at least n-1 registers.