A new method for constructing metamorphic relations

A fundamental problem for software testing is the oracle problem, which means that in many practical situations, it is extremely expensive, if not impossible, to verify the test result given any possible program input. Metamorphic testing is an approach to alleviating the oracle problem. The key part of metamorphic testing is a set of necessary properties of the software under test, namely metamorphic relations. Metamorphic relations not only help generate test cases, but also provide a mechanism to partially verify the test results without the need of oracle. In most previous studies, metamorphic relations were identified manually by testers in an ad hoc way. There is no systematic methodology that helps us identify metamorphic relations. In this paper, we propose a simple method, namely, the composition of metamorphic relations, for systematically constructing new metamorphic relations based on the already identified metamorphic relations. We conduct a case study and show that new metamorphic relations can be easily constructed by compositing some existing metamorphic relations. It is also observed that the new metamorphic relations are very likely to deliver a higher cost-effectiveness of metamorphic testing than the original metamorphic relations.