Probability Automaton

a system in which the transition from one state to another proceeds randomly. The probability of such a transition is determined by the sequence of states preceding it (a₁, a₂,…, a_i,…, a_n) and by the input signals (S_l, S₂,…, S_m) and is written in the form of the function P(a_i → a_j, S_k), where a_i → a_j denotes the transition from state a_i to state a_j.

The probability automaton is used in formal models of learning processes and in models of complex behavior when the automaton’s reaction is ambiguous.

An example of a probability automaton is a system for the automatic control of traffic at the intersection of two streets with different traffic flows. For simplicity, let us consider a probability automaton with two states: “open,” that is, passage along the main route (a street with heavy traffic) is open, and “closed,” that is, the main route is closed and cross traffic is permitted. There are also two input signals: S₁—“a vehicle is waiting at a cross street”—and S₂—“this street is empty.” The transition probabilities are determined as follows: P(closed → closed, S₂) = P(open → closed, S₂) = 0; P(open → open, S₂) = P(closed → open, S₂) = 1; P(open → open, S₁) = 0.7; P(open → closed, S₁) = 0.3; P(closed → closed, S₁) = 0.5; and P(closed → open, S₁) = 0.5.

Such an automaton, as required, lets cross traffic pass but does not close the main route upon the appearance of an individual vehicle in the cross direction. The numerical values of the transition probabilities and the duration of the basic operating cycle of the automaton have to be selected on the basis of a concrete traffic schedule.

A probability automaton can be represented in the form of a system consisting of a deterministic automaton and a random-number generator, which feeds independent signals with a preassigned probability distribution to one of the automaton’s inputs.