On the completeness of a test suite reduction strategy

The problem of test suite reduction is to find a subset of test cases from the test suite that can still satisfy the same testing objective. Such a subset is referred to as a representative set of the test suite. We use a problem reduction technique, namely the 1-to-1 redundancy dividing strategy, to find the optimal representative sets, which are the representative sets of the smallest size. The l-to-l redundancy dividing strategy guarantees that an optimal representative set of the reduced test suite is still an optimal representative set of the original one. However, the converse is not necessarily true. This paper investigates how to find all optimal representative sets of the original test suite from the reduced one. Furthermore, for the minimal representative sets whose proper subsets are not representative sets, the same problem is addressed.