ANALYSIS OF ADVANCED COMPUTER TECHNOLOGIES FOR CALCULATION OF EXACT APPROXIMATIONS OF STATISTICS PROBABILITY DISTRIBUTIONS

Abstract

The paper is devoted to the evaluation of the hardware resource of computer systems for
solving a computational-expensive problem such as calculation of the probability distributions of
statistics by the second multiplicity method based on Δ-exact approximations for samples with a
size of 320-1280 characters and an alphabet power of 128-256 characters, and with an accuracy
of Δ=10-5. The total solution time should not exceed 30 days or 2.592·106 seconds for 24/7 computing.
Owing to the use of the properties of the second multiplicity method, the computational complexity
of the calculations can be brought to the range of 9.68·1022-1.60·1052 operations with the
number of tested vectors of 6.50·1023-1.39·1050. The solution of this problem for the specified parameters
of samples during the given time requires the hardware resource which cannot be provided
by modern computer means such as processors, graphics accelerators, programmable logic
integrated circuits. Therefore, in the paper we analyze the possibilities of promising quantum and
photon technologies for solving the problem with the given parameters. The main advantage of
quantum computer systems is the high speed of calculations for all possible parameter values.
However, quantum acceleration will not be achieved to calculate the probability distributions of
statistics due to the need to check all the obtained solutions. Here, the number of obtained solutions
corresponds to the dimension of the problem. In addition, due to the current development
level of the quantum hardware components, it is impossible to create and use the 120-qubit quantum
computers for the solution of the considered problem. Photon computers can provide high
computation speed at low power consumption and require the smallest number of nodes to solve
the considered problem. However, unsolved problems with the physical implementation of efficient
memory elements and the lack of available hardware components make the use of photon computer
technologies impossible for calculation of the probability distributions of statistics in the near
future (5-7 years). Therefore, it is most reasonable to use hybrid computer systems containing
nodes of different architectures. To solve the problem on various hardware platforms (generalpurpose
processors, GPUs, FPGAs) and configurations of hybrid computer systems, we suggest to
use an architecture independent high-level programming language SET@L. The language combines
the representation of calculations as sets and collections (based on the alternative set theory
of P. Vopenka), the absolutely parallel form of the problem represented as an information graph,
and the paradigm of aspect-oriented programming.