No matter how through, testing simply exposes the presence of flaws in a program; it cannot be used to verify the absence of flaws. It can increase your confidence that a program is correct, but it cannot prove correctness. To gain true correctness, one must use completely different processes, that is, correctness proofs.
Reference:
Dijkstra, E., "Notes on Structured Programming," in Structured Programming, Dahl, O., et al., Academic Press, 1972.
