There has been much discussion about the merits of various testing and integration strategies. Top-down, bottom-up, big-bang, and sandwich integration strategies are advocated by various authors. Also, some authors insist that modules be unit tested, while others believe that unit testing diverts resources from more effective verification processes. This article addresses the ability of the aforementioned integration strategies to detect defects, and produce reliable systems. It also explores the efficacy of spot unit testing, and compares phased and incremental versions of top-down and bottom-up integration strategies. Relatively large artificial software systems were constructed using a code generator with ten basic module templates. These systems were seeded with known defects and tested using the above testing and integration strategies. A number of experiments were then conducted using a simulator whose validity was established by comparing results against these artificial systems. The defect detection ability and resulting system reliability were measured for each strategy. Results indicated that top-down integration strategies are generally most effective in terms of defect correction. Top-down and big-bang strategies produced the most reliable systems. Results favored neither those strategies that incorporate spot unit testing nor those that do not; also, results favored neither phased nor incremental strategies.>

Several inequalities are derived for use in certifying function subroutines by means of black box testing. It is assumed that a function is approximated by means of a polynomial of limited degree on a closed interval. These inequalities give upper bounds on the error of the approximation over the entire interval based on the error measured over a finite sample and known properties of the function.

This investigation deals with the selection of test data for vector-valued sequences which can be generated by a linear first order system of difference equations with rational coefficients of limited degree. Let $\mathcal{F}(\nu,k,l,m)$ be the class of v-dimensional sequences y which satisfy an equation of the form $P(n)y(n + 1) = A(n)y(n) + R(n)$ where $A,P$, and R are polynomial matrices of degree $ \leqq k,\, l$, and m, respectively, and P is diagonal. It is shown that there is a finite sample which uniquely identifies members of $\mathcal{F}(\nu,k,l,m)$. A finite sample also exists for the case where y is considered to be a function of its initial value. If y satisfies two distinct equations of the above type, then there is a transformation under which certain coordinates must eventually be rational functions, or even polynomials if P is the identity.

The element z is called a transcendental for the class F if functions in F can be uniquely identified by their values at z. Conditions for the existence of transcendentals are discussed for certain classes of polynomials, multinomials, and rational functions.Of particular interest are those transcendentals having an exact representation in computer arithmetic.Algorithms are presented for reconstruction of the coefficients of a polynomial from its value at a transcendental.The theory is illustrated by application to polynomials, quadratic forms, and quadrature formulas.

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.