2021/01/11 by Czerner, Philipp, Jaax, Stefan
#Distributed #FOS: Computer and information sciences #Parallel #and Cluster Computing (cs.DC)
paper · doi:10.48550/arxiv.2101.03780
Broadcast consensus protocols (BCPs) are a model of computation, in which anonymous, identical, finite-state agents compute by sending/receiving global broadcasts. BCPs are known to compute all number predicates in NL=NSPACE(log n) where n is the number of agents. They can be considered an extension of the well-established model of population protocols. This paper investigates execution time characteristics of BCPs. We show that every predicate computable by population protocols is computable by a BCP with expected O(n log n) interactions, which is asymptotically optimal. We further show that every log-space, randomized Turing machine can be simulated by a BCP with O(n log n ⋅ T) interactions in expectation, where T is the expected runtime of the Turing machine. This allows us to characterise polynomial-time BCPs as computing exactly the number predicates in ZPL, i.e. predicates decidable by log-space bounded randomised Turing machine with zero-error in expected polynomial time where the input is encoded as unary.