Automatic Analysis of Expected Termination Time for Population Protocols

TL;DR

This paper introduces an algorithm that automatically computes bounds on the expected time for population protocols to reach consensus, aiding in the analysis of their efficiency.

Contribution

It presents the first algorithm capable of automatically deriving parametric bounds on expected consensus time in population protocols.

Findings

Algorithm successfully computes bounds for many existing protocols.

The bounds are often tight and improve understanding of protocol efficiency.

Experimental results demonstrate the algorithm's termination and practical usefulness.

Abstract

Population protocols are a formal model of sensor networks consisting of identical mobile devices. Two devices can interact and thereby change their states. Computations are infinite sequences of interactions in which the interacting devices are chosen uniformly at random. In well designed population protocols, for every initial configuration of devices, and for every computation starting at this configuration, all devices eventually agree on a consensus value. We address the problem of automatically computing a parametric bound on the expected time the protocol needs to reach this consensus. We present the first algorithm that, when successful, outputs a function f(n) such that the expected time to consensus is bound by O(f(n)), where n is the number of devices executing the protocol. We experimentally show that our algorithm terminates and provides good bounds for many of the protocols found in the literature.