Efficient algorithms for deciding the type of growth of products of integer matrices

Details Efficient algorithms for deciding the type of growth of products of integer matrices Efficient algorithms for deciding the type of growth of products of integer matrices

2006-04-11

arxiv.org/abs/cs/0604047v1

Computer Science

Computational Complexity

20 pages, 4 figures, submitted to LAA

Scientific paper

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.

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