Efficient algorithms for deciding the type of growth of products of integer matrices Original Research Article

For a given finite set Σ of matrices with nonnegative integer entries we study the growth with t ofmax{double vertical barA1cdots, three dots, centeredAtdouble vertical bar:Aiset membership, variantΣ}.We show how to determine in polynomial time whether this growth is bounded, polynomial, or exponential, and we characterize all possible behaviors.