Let  P be an  n \times n stochastic matrix. It is well known that if P is aperiodic (or regular), then there exists a t < \infty such that p_{ij}^{t} > 0 for 1 \le i,j \le n, where P^{t} is the tth power of P. However, this result is not very useful for actually checking if P is aperiodic, since one can only be sure that P is periodic after performing an infinite number of multiplications. Is there a practical way to check whether  P is aperiodic or not?