Extracting Boolean rules from CA patterns

A multiobjective genetic algorithm (GA) is introduced to identify both the neighborhood and the rule set in the form of a parsimonious Boolean expression for both one- and two-dimensional cellular automata (CA). Simulation results illustrate that the new algorithm performs well even when the patterns are corrupted by static and dynamic nois

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

Pseudorandom number generation with self programmable cellular automata

In this paper, we propose a new class of cellular automata – self programming cellular automata (SPCA) with specific application to pseudorandom number generation. By changing a cell's state transition rules in relation to factors such as its neighboring cell's states, behavioral complexity can be increased and utilized. Interplay between the state transition neighborhood and rule selection neighborhood leads to a new composite neighborhood and state transition rule that is the linear combination of two different mappings with different temporal dependencies. It is proved that when the transitional matrices for both the state transition and rule selection neighborhood are non-singular, SPCA will not exhibit non-group behavior. Good performance can be obtained using simple neighborhoods with certain CA length, transition rules etc. Certain configurations of SPCA pass all DIEHARD and ENT tests with an implementation cost lower than current reported work. Output sampling methods are also suggested to improve output efficiency by sampling the outputs of the new rule selection neighborhoods

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 cellular automata based on incomplete observations with bounded time gaps

In this paper, the problem of identifying the cellular automata (CAs) is considered. We frame and solve this problem in the context of incomplete observations, i.e., prerecorded, incomplete configurations of the system at certain, and unknown time stamps. We consider 1-D, deterministic, two-state CAs only. An identification method based on a genetic algorithm with individuals of variable length is proposed. The experimental results show that the proposed method is highly effective. In addition, connections between the dynamical properties of CAs (Lyapunov exponents and behavioral classes) and the performance of the identification algorithm are established and analyzed

Neighborhood detection and rule selection from cellular automata patterns

Using genetic algorithms (GAs) to search for cellular automation (CA) rules from spatio-temporal patterns produced in CA evolution is usually complicated and time-consuming when both, the neighborhood structure and the local rule are searched simultaneously. The complexity of this problem motivates the development of a new search which separates the neighborhood detection from the GA search. In the paper, the neighborhood is determined by independently selecting terms from a large term set on the basis of the contribution each term makes to the next state of the cell to be updated. The GA search is then started with a considerably smaller set of candidate rules pre-defined by the detected neighhorhood. This approach is tested over a large set of one-dimensional (1-D) and two-dimensional (2-D) CA rules. Simulation results illustrate the efficiency of the new algorith

Identification of the neighborhood and CA rules from spatio-temporal CA patterns

Extracting the rules from spatio-temporal patterns generated by the evolution of cellular automata (CA) usually produces a CA rule table without providing a clear understanding of the structure of the neighborhood or the CA rule. In this paper, a new identification method based on using a modified orthogonal least squares or CA-OLS algorithm to detect the neighborhood structure and the underlying polynomial form of the CA rules is proposed. The Quine-McCluskey method is then applied to extract minimum Boolean expressions from the polynomials. Spatio-temporal patterns produced by the evolution of 1D, 2D, and higher dimensional binary CAs are used to illustrate the new algorithm, and simulation results show that the CA-OLS algorithm can quickly select both the correct neighborhood structure and the corresponding rule