Efficient algorithms for deciding the type of growth of products of integer matrices
<|reference_start|>Efficient algorithms for deciding the type of growth of products of integer matrices: For a given finite set $\Sigma$ of matrices with nonnegative integer entries we study the growth of $$ \max_t(\Sigma) = \max\{\|A_{1}... A_{t}\|: A_i \in \Sigma\}.$$ We show how to determine in polynomial time whether the growth with $t$ is bounded, polynomial, or exponential, and we characterize precisely all possible behaviors.<|reference_end|>
@article{jungers2006efficient,
    title={Efficient algorithms for deciding the type of growth of products of
  integer matrices},
    author={Rapha"el Jungers, Vladimir Protasov, Vincent D. Blondel},
    journal={arXiv preprint arXiv:cs/0604047},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0604047},
    primaryClass={cs.CC}
}