Identification of probabilistic cellular automata

The identification of probabilistic cellular automata (PCA) is studied using a new two stage neighborhood detection algorithm. It is shown that a binary probabilistic cellular automaton (BPCA) can be described by an integer-parameterized polynomial corrupted by noise. Searching for the correct neighborhood 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 the noise terms. This allows the neighborhood detection technique developed for deterministic rules in to be applied with a larger cutoff value to discard the majority of spurious terms and to produce an initial presearch for the BPCA neighborhood. A multiobjective genetic algorithm (GA) search with integer constraints is then evolved to refine the reduced neighborhood 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 neighborhood and the deterministic rule. The new algorithm is tested over a large set of one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) BPCA rules. Simulation results demonstrate the efficiency of the new method

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

The identification of cellular automata

Although cellular automata have been widely studied as a class of the spatio temporal systems, very few investigators have studied how to identify the CA rules given observations of the patterns. A solution using a polynomial realization to describe the CA rule is reviewed in the present study based on the application of an orthogonal least squares algorithm. Three new neighbourhood detection methods are then reviewed as important preliminary analysis procedures to reduce the complexity of the estimation. The identification of excitable media is discussed using simulation examples and real data sets and a new method for the identification of hybrid CA is introduced

A New Class of Cellular Automata for Reaction-Diffusion Systems

We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion, and a probabilistic table-lookup for the reactive part. The applicability of the new CA is demonstrated using the Ginzburg-Landau equation.Comment: 4 pages, RevTeX 3.0 , 3 Figures 214972 bytes tar, compressed, uuencode

A Bibliography on Fuzzy Automata, Grammars and Lanuages

This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing

The dynamical origin of the universality classes of spatiotemporal intermittency

Studies of the phase diagram of the coupled sine circle map lattice have identified the presence of two distinct universality classes of spatiotemporal intermittency viz. spatiotemporal intermittency of the directed percolation class with a complete set of directed percolation exponents, and spatial intermittency which does not belong to this class. We show that these two types of behavior are special cases of a spreading regime where each site can infect its neighbors permitting an initial disturbance to spread, and a non-spreading regime where no infection is possible, with the two regimes being separated by a line, the infection line. The coupled map lattice can be mapped on to an equivalent cellular automaton which shows a transition from a probabilistic cellular automaton to a deterministic cellular automaton at the infection line. The origins of the spreading-non-spreading transition in the coupled map lattice, as well as the probabilistic to deterministic transition in the cellular automaton lie in a dynamical phenomenon, an attractor-widening crisis at the infection line. Indications of unstable dimension variability are seen in the neighborhood of the infection line. This may provide useful pointers to the spreading behavior seen in other extended systems.Comment: 20 pages, 9 figure