Fault Coupling in Finite Functions

This thesis presents a theoretical investigation of fault coupling in finite functions. The results indicate that fault coupling occurs so infrequently that it can be ignored in practice, thus vindicating current approaches to fault-based testing. Fault-based testing aims to show that particular faults cannot exist in software by designing tests specifically to detect them. The phenomenon of fault coupling arises when test sets are able to detect faults when they occur in isolation, but not when they occur in combination; it is clearly a complicating factor in practical fault-based testing, which is geared towards the detection of single faults. An idealised model of fault-based testing is proposed and developed as the basis of the investigation; the model makes use of finite functions. It is argued that a thoroughgoing functional approach is likely to pay dividends in a theoretical investigation; in addition, requiring functions to be finite ensures that the problem of fault coupling becomes solvable. Since real computers have finite resources, the latter requirement is not much of a restriction, and the results obtained here are expected to be generally applicable. It is shown in detail how to arrive at the solution of the idealised problem of fault coupling for test sets of order 1 and test sets of order 2; in the case of the latter, a number of quite different types are recognised, which exhibit characteristic behaviour with respect to fault coupling. In particular, some kinds of test set are able to avoid fault coupling altogether in the case that the functions are further restricted to be bijective. An important by-product of the present investigation is the development of a powerful technique that can hopefully be applied to other problems in software testing and analysis. The basic idea is to regard (idealise) programs as finite functions; one can then make use of the powerful machinery of mathematics to investigate the particular problem of interest.