Numerical evaluation of stochastic automata networks

This paper examines some numerical issues in computing solutions to networks of stochastic automata. It is well-known that when the automata are completely independent, the cost of performing the operation basic to all iterative solution methods, that of matrix-vector multiply, is given by ρ_N=Π_i=1^Nn _i×Σ_i=1^Nn_i, where n_i is the number of states in the i^th automaton and N is the number of automata in the network. We provide a number of lemmas that show that this relatively small number of operations is sufficient in many other cases in which the automata are not independent and we show how the automata should be ordered to achieve this