Discrete Modeling Using Stochastic Cellular Automata

New approach to low-level discrete simulation of natural (especially biological) systems using stochastic block cellular automata is considered. The notion of a Markov system, which is a special case of the string rewriting systems, is introduced. A key feature of Markov systems compared with other string rewriting systems are the stochastic procedure of the splitting the string into substrings and stochastic simultaneous application of the substitutions system to all obtained substrings. In such automata cellular space forms a matrix, and block decomposition into horizontal and vertical components occurs in probabilistic way. Based on a Markov system model the notion of two-dimensional Markov automata, which is a special case of block stochastic cellular automata, is constructed. The characteristics and expressive capabilities of such systems are considered. As an application, the problem of constructing neural network low-level model is considered. With this purpose a model of excitable medium, supporting the inhibition mechanism of excitation, is proposed. Based on this model an artificial neuron, including a system of communication (axons, dendrites, synapses) is constructed. Simple feedforward neural network, that implements the logical operation of exclusive disjunction, is considered and numerically investigated.

string rewriting systems, stochastic cellular automata, block cellular automata, excitable medium, neural networks