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arXiv · 1505.00144

Reachability of Consensus and Synchronizing Automata

Pierre-Yves Chevalier·Julien M. Hendrickx·Raphaël M. Jungers
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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.

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Pierre-Yves Chevalier, Julien M. Hendrickx, Raphaël M. Jungers. 2015-05-01. Reachability of Consensus and Synchronizing Automata. https://arxiv.org/abs/1505.00144

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