N-Consensus is the Second Strongest Object for N + 1 Processes

Abstract

Objects like queue, swap, and test-and-set allow two processes to reach consensus, and are consequently “universal” for a system of two processes. But are there deterministic objects that do not solve 2-process consensus, and nevertheless allow two processes to solve a task that is not otherwise wait-free solvable in read-write shared memory?

The answer “no” is a simple corollary of the main result of this paper: Let A be a deterministic object such that no protocol solves consensus among n + 1 processes using copies of A and read-write registers. If a task T is wait-free solvable by n + 1 processes using read-write shared-memory and copies of A, then T is also wait-free solvable when copies of A are replaced with n-consensus objects. Thus, from the task-solvability perspective, n-consensus is the second strongest object (after (n + 1)-consensus) in deterministic shared memory systems of n + 1 processes, i.e., there is a distinct gap between n- and (n + 1)-consensus.

We derive this result by showing that any (n + 1)-process protocol P that uses objects A can be emulated using only n-consensus objects. The resulting emulation is non-blocking and relies on an a priori knowledge of P. The emulation technique is another important contribution of this paper.