2021/09/30 by Jérôme Leroux, Leroux, Jérôme
Computer Science · #Cryptography and Data Security #Distributed systems and fault tolerance #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Privacy-Preserving Technologies in Data
paper · doi:10.48550/arxiv.2109.15171
openalex publication_date 2021/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Population protocols are a model of computation in which an arbitrary number of anonymous finite-memory agents are interacting in order to decide by stable consensus a predicate. In this paper, we focus on the counting predicates that asks, given an initial configuration, whether the number of agents in some initial state i is at least n. In 2018, Blondin, Esparza, and Jaax shown that with a fix number of leaders and interaction-width, there exists infinitely many n for which the counting predicate is stably computable by a protocol with at most O(loglog(n)) states. We provide in this paper a matching lower-bound (up to a square root) that improves the inverse-Ackermannian lower-bound presented at PODC in 2021.