Identifying metamorphic relations: A data mutation directed approach

Metamorphic testing (MT) is an effective technique to alleviate the test oracle problem. The principle of MT is to detect failures by checking whether some necessary properties, commonly known as metamorphic relations (MRs), of software under test (SUT) hold among multiple executions of source and follow-up test cases. Since both the generation of follow-up test cases and test result verification depend on MRs, the identification of MRs plays a key role in MT, which is an important yet difficult task requiring deep domain knowledge of the SUT. Accordingly, techniques that can direct a tester to identify MRs effectively are desirable. In this paper, we propose mu$$ \mu $$MT, a data mutation directed approach to identifying MRs. mu$$ \mu $$MT guides a tester to identify MRs by providing a set of data mutation operators and template-style mapping rules, which not only alleviates the difficulties faced in the process of MR identification but also improves the identification effectiveness. We have further developed a tool to implement the proposed approach and conducted an empirical study to evaluate the MR identification effectiveness of mu$$ \mu $$MT and the performance of MRs identified by mu$$ \mu $$MT with respect to fault detection capability and statement coverage. The empirical results show that mu$$ \mu $$MT is able to identify MRs for numeric programs effectively, and the identified MRs have high fault detection capability and statement coverage. The work presented in this paper advances the field of MT by providing a simple yet practical approach to the MR identification problem.