Software quality assessment, although acknowledged to be of the first importance, is today an art rather than a science. Program testing is the best defined and least subjective component of quality assurance, but even its methods are poorly related to measurable quality. Program testing has two purposes: (1) to expose software failures for repair, and (2) to establish confidence that future failures are unlikely. The foundational theory must be probabilistic, because any test is no more than a sample of program behavior. For any program P and test method M, (1) What is the probability that M will uncover a failure in P? (2) After M has been used without failure, what is the probability that in fact P cannot fail? The purpose of this project is to improve on previous theoretical answers to these questions. Prior theoretical work can be characterized first as being imprecise, in that characteristics of M and P do not enter the theory in a useful way; and second, as being overly pessimistic, in that under the best of circumstances the probabilities are very low. New theoretical work will be guided by experiments on existing and new test methods, using novel support tools.
