A Formal Analysis of the Subsume Relation Between Software Test Adequacy Criteria

Software test adequacy criteria are rules to determine whether a software system has been adequately tested. A central question in the study of test adequacy criteria is how they relate to fault detecting ability. We identify two idealized software testing scenarios. In the first scenario, which we call prior testing scenario, software testers are provided with an adequacy criterion in addition to the software under test. The knowledge of the adequacy criterion is used to generate test cases. In the second scenario, which we call posterior testing scenario, software testers are not provided with the knowledge of adequacy criterion. The criterion is only used to decide when to stop the generation of test cases. In 1993, Frankl and Weyuker proved that the subsume relation between software test adequacy criteria does not guarantee better fault detecting ability in the prior testing scenario. We investigate the posterior testing scenario and prove that in this scenario the subsume relation does guarantee a better fault detecting ability. Two measures of fault detecting ability will be used, the probability of detecting faults and the expected number of exposed errors.