Counting-based impossibility proofs for renaming and set agreement

Abstract

Renaming and set agreement are two fundamental sub-consensus tasks. In the M-renaming task, processes start with names from a large domain and must decide on distinct names in a range of size M; in the k-set agreement task, processes must decide on at most k of their input values. Renaming and set agreement are representatives of the classes of colored and colorless tasks, respectively. This paper presents simple proofs for key impossibility results for wait-free computation using only read and write operations: n processes cannot solve (n - 1)-set agreement, and, if n is a prime power, n processes cannot solve (2n - 2)-renaming. Our proofs consider a restricted set of executions, and combine simple operational properties of these executions with elementary counting arguments, to show the existence of an execution violating the task's requirements. This makes the proofs easier to understand, verify, and hopefully, extend. © 2012 Springer-Verlag.