To improve the performances of parallelizing compilers, one must detect recurrences in scientiic programs and subject them to special parallelization methods. We present a method for detecting recurrences which is based on the analysis of Systems of Recurrence Equations. This method identiies recurrences on arrays, recurrences of arbitrary order and multi-equations recurrences. We explain how t...

The paper is devoted to the methods of solving simultaneous recurrences. Specifically, we discuss transformation of matrix recurrences to regular recurrences and propose a way of solving special matrix recurrences of order three by their decomposition to matrix recurrences of order two.

with initial terms u0 ux = ••• = ur_2 = 0, ur_1 1. Then (u) is called a unit sequence with coefficients al5 a25 -.., ar. For a positive integer AT, the primitive period of (u) modulo AT, denoted by K(M), is the least positive integer m such that un + m = un (mod AT) for all nonnegative integers n greater than or equal to some fixed integer n0. It is known that the primitive period modulo M of a...