Brief Announcement: Why Extension-Based Proofs Fail

Abstract

We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve k-set agreement among n > k ≥ 2 processes in a wait-free manner. However, it was unknown whether proofs based on simpler techniques were possible. We explain why this impossibility result cannot be obtained by an extension-based proof and, hence, extension-based proofs are limited in power.