ANALYSIS OF ADVANCED COMPUTER TECHNOLOGIES FOR CALCULATION OF EXACT APPROXIMATIONS OF STATISTICS PROBABILITY DISTRIBUTIONS
In the paper we consider the solution of a computationally expensive problem such as calculation of statistics probability distribution with the help of modern computer technologies. To reduce computational complexity and to provide a sufficient level of criteria efficiency not less than the specified threshold, we suggest to use ∆-exact approximations. To calculate exact approximations, we use the method of second order, based on solution of a system of linear equations. Owing to this method, it is possible to calculate exact approximations for the maximum values of sample parameters for available computational resource. The most laborious part of the method of second order is the procedure of sequential detection of the vectors of possible solutions and test if the vectors belong to the set of solutions. The system solution set membership test for the vectors of possible solutions is data independent, so the algorithm can be data-parallelized. We give the algorithm complexity equation for calculation of exact approximations of statistics probability distributions. Using this equation, we calculated the complexity of modern practical problems for the samples with the parameters (N, n) of the alphabet power and the sample size: (256,1280), (128,640), (128, 320), and (192,3200) for the accuracy of calculations D=10<sup>-5</sup>. The computational complexity is 9.68·10<sup>22</sup>-1.60·10<sup>52</sup> operations, and its average value is about 4.55·10<sup>25</sup> operations, the number of tested vectors is 6.50·10<sup>23</sup>-1.39·10<sup>50</sup>, and the number of solutions is 4.67·10<sup>12</sup>-5.60·10<sup>25</sup>, respectively. The total solution time for clock-round duration of calculations cannot exceed 30 days or 2.592·10<sup>6 </sup>sec. For the obtained complexity evaluation, we analysed abilities of modern cluster computer systems based on general-purpose processors, graphic accelerators, and FPGA-based reconfigurable computer systems. For each technology, we determined the number of computational nodes needed for calculation of exact approximations with the specified parameters during the specified time. We proved that it is impossible to obtain a solution for the required parameters of exact approximations of statistics probability with the help of the reviewed modern computer technologies. In conclusion, we claim that it is necessary to analyse the abilities of advanced computer technologies based of quantum and photonic computers, and also hybrid computer systems for calculation of exact approximations of statistics probability distributions with the specified parameters during reasonable time.