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In the context of robustness testing, the boundary between the valid andinvalid regions of the input space can be an interesting source of erroneousinputs. Knowing where a specific software under test (SUT) has a boundary isessential for validation in relation to requirements. However, finding where aSUT actually implements the boundary is a non-trivial problem that has notgotten much attention. This paper proposes a method of finding the boundarybetween the valid and invalid regions of the input space. The proposed methodconsists of two steps. First, test data generators, directed by a searchalgorithm to maximise distance to known, valid test cases, generate valid testcases that are closer to the boundary. Second, these valid test cases undergomutations to try to push them over the boundary and into the invalid part ofthe input space. This results in a pair of test sets, one consisting of testcases on the valid side of the boundary and a matched set on the outer side,with only a small distance between the two sets. The method is evaluated on anumber of examples from the standard library of a modern programming language.We propose a method of determining the boundary between valid and invalidregions of the input space and apply it on a SUT that has a non-contiguousvalid region of the input space. From the small distance between the developedpairs of test sets, and the fact that one test set contains valid test casesand the other invalid test cases, we conclude that the pair of test setsdescribed the boundary between the valid and invalid regions of that inputspace. Differences of behaviour can be observed between different distances andsets of mutation operators, but all show that the method is able to identifythe boundary between the valid and invalid regions of the input space. This isan important step towards more automated robustness testing.

Finding a boundary between valid and invalid regions of the input space