Bounding Random Test Set Size with Computational Learning Theory

Random testing approaches work by generating inputs at random, or by selecting inputs randomly from some pre-defined operational profile. One long-standing question that arises in this and other testing contexts is as follows: When can we stop testing? At what point can we be certain that executing further tests in this manner will not explore previously untested (and potentially buggy) software behaviors? This is analogous to the question in Machine Learning, of how many training examples are required in order to infer an accurate model. In this paper we show how probabilistic approaches to answer this question in Machine Learning (arising from Computational Learning Theory) can be applied in our testing context. This enables us to produce an upper bound on the number of tests that are required to achieve a given level of adequacy. We are the first to enable this from only knowing the number of coverage targets (e.g. lines of code) in the source code, without needing to observe a sample test executions. We validate this bound on a large set of Java units, and an autonomous driving system.