Chaotic Evolution via Generalized Probabilistic Automata (Probabilistic Arrays)

briefly the conventional probabilistic model in automata theory; the main objective is to observe that the corresponding distributional transformations are linear and have simple asymptotics under iteration. For a time-sequential finite-state probabilistic machine which is autonomous (free of inputs, or with only a constant clocked-time input), the only significant quantities are the states, the state-to-state (conditional) transition probabilities, and the (unconditional) state-occupancy probabilities. In this setting, a machine with n states is defined by specifying its one-step transition probabilities a ij , i, j = 1, 2, . . . , n; the interpretation is that a ij is the numerical label on the directed edge from state #i to state #j in the state graph, or the ij entry 1 The contribution of the first author was sup