  Higher-order mutation has the potential for improving major drawbacks of
traditional first-order mutation, such as by simulating more realistic faults
or improving test optimization techniques. Despite interest in studying
promising higher-order mutants, such mutants are difficult to find due to the
exponential search space of mutation combinations. State-of-the-art approaches
rely on genetic search, which is often incomplete and expensive due to its
stochastic nature. First, we propose a novel way of finding a complete set of
higher-order mutants by using variational execution, a technique that can, in
many cases, explore large search spaces completely and often efficiently.
Second, we use the identified complete set of higher-order mutants to study
their characteristics. Finally, we use the identified characteristics to design
and evaluate a new search strategy, independent of variational execution, that
is highly effective at finding higher-order mutants even in large code bases.
