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Establishing Theoretical Minimal Sets of Mutants

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7th IEEE International Conference on Software Testing, Verification and Validation (ICST 2014),
March 2014, Cleveland Ohio, USA
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Paul Ammann, Marcio E. Delamaro, and Jeff Offutt

**Abstract**

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.

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