LIMITING THE NUMBER OF DIFFERENT TEST VECTORS TO OBTAIN ALL SOLUTIONS OF A SYSTEM OF THE SECOND MULTIPLICITY LINEAR EQUATIONS ON MULTIPROCESSOR COMPUTER SYSTEM

Abstract

In the paper we consider calculation of all integer nonnegative solutions of a linear equation system (LES) of the second types order by a method of sequential vector testing. The method checks whether a vector is a solution of the LES. We consider different vectors and test if they belong to the set of the LES solutions. As a result, after such testing we obtain all solutions of the LES. The LES testing vector consists of the elements which are the numbers of some alphabet signs with the same number of occurrences in the sample. The LES unites the number of occurrences of the elements of all types into the considering sample, the power of the alphabet, the size of the sample, and the limitation for the maximum number of occurrences of the alphabet signs into the sample. The LES solution is the base for calculation of exact statistics probability distributions and their exact approximations by the method of the second types order. Here, the exact approximations are Δexact distributions. The difference between the Δexact distributions and the exact distributions does not exceed the predefined arbitrary small value Δ. The number of test vectors is one of those which defines algorithmic complexity of the method of second types order. Without it, it is impossible to define the parameters of samples, and to calculate exact distributions and their exact approximations for limited hardware resource. We consider various test vectors for the limited maximum number of occurrences of the alphabet signs in the sample, and for the unlimited one. We have obtained formulas to calculate the number of tests for various vectors. Here, the values of the power of the alphabet, the size of the sample, and the limitations for the maximum number of occurrences of the alphabet signs into the sample can be arbitrary. Using the obtained formulas, we can get all integer nonnegative solutions of the LES of the second types order. We can use the obtained formula for analysis of algorithmic complexity of calculations of exact distributions and their exact approximations with the predefined accuracy Δ.