Bounding Random Test Set Size with Computational Learning Theory

TL;DR

This paper applies probabilistic methods from Computational Learning Theory to determine an upper bound on the number of random tests needed to confidently cover software behaviors, without requiring prior test execution data.

Contribution

It introduces a novel approach to estimate testing bounds using only coverage targets, without observing test samples, validated on Java units and autonomous systems.

Findings

Provides a theoretical upper bound on test set size

First to estimate testing bounds solely from coverage targets

Validated bounds on real-world Java and autonomous systems

Abstract

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.