On the Selection of Test Data for Recursive Mathematical Subroutines

Abstract

Let Y be a family of sequences defined by linear difference equations of the form $y(n + 1) = P(n)y(n) + Q(n)$, where P and Q are restricted to be polynomials of limited degree, constant matrices, multinomials, and so forth. The central problem is to find a finite sample which uniquely identifies members of Y. It is shown that such a sample exists when P and Q are polynomials of limited degree. The sample size depends linearly on the degree limits. A similar result holds for systems of difference equations with P a constant matrix and Q a column vector with polynomial components. Testing procedures are also derived for the case where the coefficients of P and Q are multinomials in a vector parameter x, and y is considered to be a function of its initial value.