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

For a given finite set Σ of matrices with nonnegative integer entries we study the growth with t ofmax A1 ⋯ At norm of matrix : Ai ∈ Σ .We show how to determine in polynomial time whether this growth is bounded, polynomial, or exponential, and we characterize all possible behaviors. © 2007 Elsevier Inc. All rights reserved.