Establishing Theoretical Minimal Sets of Mutants

Mutation analysis generates tests that distinguish variations, or mutants, of an artifact from the original. Mutation analysis is widely considered to be a powerful approach to testing, and hence is often used to evaluate other test criteria in terms of mutation score, which is the fraction of mutants that are killed by a test set. But mutation analysis is also known to provide large numbers of redundant mutants, and these mutants can inflate the mutation score. While mutation approaches broadly characterized as reduced mutation try to eliminate redundant mutants, the literature lacks a theoretical result that articulates just how many mutants are needed in any given situation. Hence, there is, at present, no way to characterize the contribution of, for example, a particular approach to reduced mutation with respect to any theoretical minimal set of mutants. This paper's contribution is to provide such a theoretical foundation for mutant set minimization. The central theoretical result of the paper shows how to minimize efficiently mutant sets with respect to a set of test cases. We evaluate our method with a widely-used benchmark.