Large Flocks of Small Birds: On the Minimal Size of Population Protocols

01/02/2018
by   Michael Blondin, et al.
0

Population protocols are a well established model of distributed computation by mobile finite-state agents with very limited storage. A classical result establishes that population protocols compute exactly predicates definable in Presburger arithmetic. We initiate the study of the minimal amount of memory required to compute a given predicate as a function of its size. We present results on the predicates x ≥ n for n ∈N, and more generally on the predicates corresponding to systems of linear inequalities. We show that they can be computed by protocols with O( n) states (or, more generally, logarithmic in the coefficients of the predicate), and that, surprisingly, some families of predicates can be computed by protocols with O( n) states. We give essentially matching lower bounds for the class of 1-aware protocols.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/23/2021

Lower Bounds on the State Complexity of Population Protocols

Population protocols are a model of computation in which an arbitrary nu...
research
02/05/2019

Expressive Power of Oblivious Consensus Protocols

Population protocols are a formal model of computation by identical, ano...
research
05/01/2023

Population Protocols with Unordered Data

Population protocols form a well-established model of computation of pas...
research
02/23/2022

Fast and Succinct Population Protocols for Presburger Arithmetic

In their 2006 seminal paper in Distributed Computing, Angluin et al. pre...
research
11/23/2021

Modular population protocols

Population protocols are a model of distributed computation intended for...
research
10/10/2019

Succinct Population Protocols for Presburger Arithmetic

Angluin et al. proved that population protocols compute exactly the pred...
research
05/15/2023

Selective Population Protocols

The model of population protocols provides a universal platform to study...

Please sign up or login with your details

Forgot password? Click here to reset