Probabilistic Induction of Cellular Automata Rules: I. A Reinforcement Scheme
Burton Voorhees, Rhyan Arthur and Todd Keller
A probabilistic reinforcement scheme is developed that provides an answer to the following question: Given an appropriately formatted time series and a specified modeling class, is it possible to choose a model from this class as the best guess estimate for the generator of the given time series. In this paper the reinforcement scheme is presented and considered for the case in which the modeling class is a set of cellular automata rules and the time sequence consists of m-digit binary strings. A number of theoretical results are obtained. Computer experiments show that if the sequence was generated by a cellular automaton, the reinforcement scheme yields, with high probability, an equivalence class of rules containing the generating rule. Even if the sequence is random, however, the usual result is prediction of a generating rule. While this illustrates the limits of the scheme, it also illustrates in a simple case the sort of type 1errors that the brain tends to make in causal attribution. This sort of error in response to a random sequence also provides a means of probing the internal structure of the modeling space.