Paper 2025/2339 Original: eprint.iacr.org/2025/2339 ↗

SoK: Approximate Agreement

Abstract

Approximate Agreement (AA) is a relaxation of consensus that requires honest parties to output values that are close and within the honest inputs' range. Introduced as a relaxation of exact consensus, AA has become a versatile primitive with applications from blockchain oracles to cyber-physical systems. This paper provides a systematization of knowledge (SoK) on byzantine-resilient AA in complete networks. We mainly focus on the real-valued variant, and chart the feasibility frontiers in synchronous, asynchronous, and network-agnostic models. We compare protocols in terms of resilience, round complexity, and communication efficiency, while also clarifying overlooked details and gaps. Beyond standard requirements on the outputs, we discuss stronger conditions, such as having the outputs \emph{close} to the honest inputs' median. Moreover, we briefly situate the real-valued AA problem within the broader landscape of AA, where other input domains such as higher-dimensional spaces and graphs introduce further challenges.