Identification of Probabilistic Cellular Automata

The identification of Probabilistic Cellular Automata (PCA) is studied using a new two stage neighbourhood detection algorithm. It is shown that a Binary Probabilistic Cellular Automaton (BPCA) can be described by an integer-parameterised polynomial customised by noise. Searching for the correct neighbourhood of a BPCA is then equivalent to selecting the correct terms, which constitute the polynomial model of the BPCA from a large initial term set. It is proved that the contribution values for the correct terms can be calculated independently of the contribution values for noise terms. This allows the neighbourhood detection technique developed for deterministic rules in [16] to be applied with with a larger cutoff value to discard the majority of spurious terms and to produce an initial pre-search for the BPCA neighbourhood. A multi-objective GA search with integer constraints is then evolved to refine the reduced neighbourhood and to identify the polynomial rule, which is equivalent to the probabilistic rule with the largest probability. A probability table representing the BPCA can then be determined based on the identified neighbourhood and the deterministic rule. The new algorithm is tested over a large set of 1-D,2-D and 3-D BPCA rules. Simulation results demonstrate the efficiency of the new method.