These are as deterministic as you can get, which is why I chose them to illustrate free will. Let S be a system of interacting discrete finite automata such as that shown in Figure 1. Each box represents a subautomaton and each line represents a signal. The value of a particular signal at time t is determined by the state at time t of the automaton from which it comes. Signals without a source subautomaton represent inputs from the outside and signals without a destination represent outputs.
Finite automata are the simplest examples of systems that interact over time.
The automaton representation consists in regarding the world as a system of interacting subautomata. For example, we might regard each person in the room as a subautomaton and the environment as consisting of one or more additional subautomata. As we shall see, this representation has many of the qualitative properties of interactions among things and persons. The number of states required in the subautomata is very large, for example , if we try to represent a person's knowledge. Automata this large have to be represented by systems of equations or by computer programs, or in some other way that does not involve mentioning states individually.