Methods and means for optimizing the operational basis of specialized Grid-oriented computing structures

The methods for implementation the group operations for finite groups of arbitrary order and operations in finite fields with given characteristic in linear logic networks, which implementation oriented on programmable logic integrated circuits (FPGAs) are proposed and investigated. A list and the basic properties of group operations for groups of order 2n, which are implemented by regular logic networks of linear complexity for all values of n are defined. The methods of implementation for the operations of addition with remains, which is based on operations in any given finite fields with characteristic p> 2 are obtained further development. The method of substitutions on regular ordinary logic networks linear complexity of bilateral ties is developed. Quantitative characteristics and properties of these substitutions are defined. The technique of forming structures for design of logical network modules with linear complexity for implementation like forward and backward substitutions is developed. The method for non-distributing decomposition of systems of Boolean functions, including not fully defined Boolean functions is developed. The criterion to achieve significantly lower use of FPGA slices using forward and backward substitutions are designed. The methods for the use of the direct and reverse lookup for further data compression using any available means for sealing and non-algorithmic implementation of encoders and decoders for error-correcting coding are proposed. The method for significantly increasing the speed of reliability parameters calculation of logical networks in non-deterministic input distortion is developed. The technology of adaptive hierarchical comparison of information objects is further developed by way of hardware-software structures speed-optimizing for fuzzy comparisons.