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

Extracting Boolean Rules From CA Patterns

A multi-objective GA algorithm is introduced to identify both the neighbourhood and the rule set in the form of a parsimonious Boolean expression for both one-and-two-dimensional cellular automata. Simulation results illustrate that the new algorithm performs well even when the patterns are corrupted by static and dynamic noise

Identification of N-state spatio-temporal dynamical systems using a polynomial model

A multivariable polynomial model is introduced to describe n-state spatio-temporal systems. Based on this model, a new neighbourhood detection and transition rules determination method is proposed. Simulation results illustrate that the new method performs well even when the patterns are corrupted by static and dynamical noise

Identification of binary cellular automata from spatiotemporal binary patterns using a fourier representation

The identification of binary cellular automata from spatio-temporal binary patterns is investigated in this paper. Instead of using the usual Boolean or multilinear polynomial representation, the Fourier transform representation of Boolean functions is employed in terms of a Fourier basis. In this way, the orthogonal forward regression least-squares algorithm can be applied directly to detect the significant terms and to estimate the associated parameters. Compared with conventional methods, the new approach is much more robust to noise. Examples are provided to illustrate the effectiveness of the proposed approach

An evolutionary approach to the identification of Cellular Automata based on partial observations

In this paper we consider the identification problem of Cellular Automata (CAs). The problem is defined and solved in the context of partial observations with time gaps of unknown length, i.e. pre-recorded, partial configurations of the system at certain, unknown time steps. A solution method based on a modified variant of a Genetic Algorithm (GA) is proposed and illustrated with brief experimental results.Comment: IEEE CEC 201

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

The elementary cellular automata a journey into the computational world

“It's always seemed like a big mystery how nature, seemingly so effortlessly, manages to produce so much that seems to us so complex.” – Stephan Wolfram The topic of cellular automata has many interesting and wide-ranging applications to real life problems emerging from areas such as image processing, cryptography, neural networks, developing electronic devices to modelling biological systems

Evolutionary Computation in System Identification: Review and Recommendations

Two of the steps in system identification are model structure selection and parameter estimation. In model structure selection, several model structures are evaluated and selected. Because the evaluation of all possible model structures during selection and estimation of the parameters requires a lot of time, a rigorous method in which these tasks can be simplified is usually preferred. This paper reviews cumulatively some of the methods that have been tried since the past 40 years. Among the methods, evolutionary computation is known to be the most recent one and hereby being reviewed in more detail, including what advantages the method contains and how it is specifically implemented. At the end of the paper, some recommendations are provided on how evolutionary computation can be utilized in a more effective way. In short, these are by modifying the search strategy and simplifying the procedure based on problem a priori knowledge

A statistical approach to the identification of diploid cellular automata based on incomplete observations

In this paper, the identification problem of diploid cellular automata is considered, in which, based on a series of incomplete observations, the underlying cellular automaton rules and the states of missing cell states are to be uncovered. An algorithm for identifying the rule, based on a statistical parameter estimation method using a normal distribution approximation, is presented. In addition, an algorithm for filling the missing cell states is formulated. The accuracy of these methods is examined in a series of computational experiments

One dimensional cellular automata-The totalistic approach

The topic of cellular automata has many interesting and wide ranging applications to real life problems emerging from areas such as image processing, cryptography, neural networks, developing electronic devices and modelling biological systems. In fact cellular automata can be a powerful tool for modelling many kinds of systems. In the March 2018 issue of At Right Angles we had introduced the basic ideas which form the foundation of the Elementary Cellular Automata (ECA) as defined by Stephen Wolfram. The reader is urged to go through the article before reading this. The topic of Cellular Automata lends itself to interesting investigations which are well within the reach of high school students. We had illustrated the simple and yet powerful ideas in the previous article where we had described and analysed the behaviour of the 256 ECAs. In this article we shall provide a brief recap for the first time reader before moving on to the concept of Totalistic Cellular Automata