Reachability of Consensus and Synchronizing Automata
Distributed, Parallel, and Cluster Computing
2015-10-05 v2 Discrete Mathematics
Systems and Control
Abstract
We consider the problem of determining the existence of a sequence of matrices driving a discrete-time consensus system to consensus. We transform this problem into one of the existence of a product of the transition (stochastic) matrices that has a positive column. We then generalize some results from automata theory to sets of stochastic matrices. We obtain as a main result a polynomial-time algorithm to decide the existence of a sequence of matrices achieving consensus.
Cite
@article{arxiv.1505.00144,
title = {Reachability of Consensus and Synchronizing Automata},
author = {Pierre-Yves Chevalier and Julien M. Hendrickx and Raphaël M. Jungers},
journal= {arXiv preprint arXiv:1505.00144},
year = {2015}
}
Comments
Update after review