For a given finite set Σ of matrices with nonnegative integer entries
we study the growth of tmax(Σ)=max{∥A1...At∥:Ai∈Σ}. 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.Comment: 20 pages, 4 figures, submitted to LA