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It is shown that the energy image spectrum can be described by a set of spectral moments used as an instrumental spectrum estimate in solving some problems of image analysis and classification. An analytical relationship between the power characteristics of signals in the space and frequency regions, which extends the Rayleigh theorem to moments of any arbitrary order of the function of two variables, is obtained. It is proved that a moment of any high order in the frequency domain is always in correspondence with the second-order moment in the space region. A spectral moment calculation algorithm is presented.

A block-structural representation of feedback systems allows one to separate motions of a complex object by the simplest procedure and thereby increase the efficiency of present-day CAD systems at stages of improving the equipment. It is shown that the most universal method for analyzing automatic control systems is the matrix-free simulation method. It is proposed to use a simulation method ensuring calculations with a variable balanced error and the minimum labor consumption, along with the motion separation principle.

Some problems arising in designing computer driving simulators (DS) based on PC are considered. Examples of possible DS applications are presented. Components of the typical DS are listed.

A method is proposed for constructing a probabilistic cellular automaton (CA) whose evolution simulates a spatially distributed diffusion-reaction process. In the method, both the diffusion and reaction process components, which are usually given as a Laplace operator and a nonlinear function, respectively, are represented by special operations on Boolean arrays. The kernel of the operations is a transformation  of a real spatial function into a Boolean array whose averaged form approximates the initial function. Transition rules of the resulting CA are a combination of the transition function of a CA-model of the diffusion component and a probabilistic threshold function depending on the reaction. Approximation errors are assessed and some simulation results are presented.

A parallel substitution algorithm (PSA) is developed. It models the process of structure self-replication in the cellular space in two directions (from bottom to top and from left to right); the structure having the shape of a tetragonal loop. The proposed PSA self-replication model is much more laconic compared with the classical cellular automaton model.

An associative version of the Lengauer-Tarjan algorithm on a model of a parallel vertical data processor is presented. The algorithm is implemented as a procedure in the STAR language. The time complexity is estimated and correctness of the procedure is substantiated.

Practically important results concerned with determination of percolation thresholds in homogeneous structures are proposed. Their usage allows one to estimate the bounds of reliability of homogeneous computing systems and the minimal requirements to reliability of processor elements.

Cellular automaton models applied to hydrodynamics problems and also an original 3D model of a viscous fluid flow with 12 neighbors are considered. A program package for 3D flow simulation using the proposed model and results of experimental simulation are presented.

Computational potentialities of the residue number system for simulation of a 1D diffusion process is investigated. The conventional finite-difference diffusion representation is modified in terms of the residue number system (RNS). Numerical simulation of the diffusion process was performed. The computational characteristics (stability, accuracy, and time complexity) are assessed and compared with similar ones obtained by the explicit method solution of partial differential equations.