Complexity of testing iterated borders for structured programs

Abstract

One of the serious limitations of domain testing is the potentially infinite number of domains to be examined in the presence of iteration loops in the computer program. The authors show that only a small number of domain needs to be examined, and that one can concentrate on testing certain borders of those domains. It is first shown that for definite loops, where the number of iterations is known on entry, iteration loops can be represented by a primitive recursive schema. This involves the identification of simple loop patterns, and it is proved that these simple loop patterns can be used as basic building blocks to form arbitrarily complex loop patterns. It is further shown that domain testing can be adapted to test these simple loop patterns, precluding the necessity of testing any of the complex patterns. A bound is obtained on the number of loop patterns that have to be tested and worst cases identified for the corresponding control-flow graphs.<>