Fault coupling in finite bijective functions

Abstract Fault‐based testing attempts to show that particular faults cannot exist in software by using test sets that differentiate between the original program (hypothesized to be correct) and faulty alternate programs. The success of this approach depends on a number of assumptions, notably that programmers are competent insofar as they only commit relatively trivial faults, and that faults only couple infrequently. Fault coupling occurs when test sets are able to differentiate between the original program and faulty alternate programs when faults occur in isolation, but not when they occur in combination; it is a complicating factor in fault‐based testing. Fault coupling is studied here within the context of finite bijective functions. A complete mathematical solution of the problem is possible in this simplified case; the results indicate that fault coupling does indeed occur infrequently, and are thus in agreement with the empirical results obtained by others in the field. One surprising result is that certain kinds of test set are able to avoid fault coupling altogether.