To locate multiple bugs in parallel, one common practice is to generate fault-focused clusters where failed test cases that are likely caused by the same bug are grouped together. With respect to the fault-focused clustering and fault localization, Spectrum-based fault localization (SBFL) technique and distance metric are two critical impact factors. This article proposes a method to evaluate the parallel fault localization performance of SBFL techniques and distance metrics where the fault-focused information for each failed test case is already given. Case studies are conducted using the proposed method to evaluate five SBFL techniques and five distance metrics on three programs with multiple bugs.

Model-based testing has been highlighted in the last few decades. Many improvements have been proposed for this testing method. One improvement is the use of extended regular expressions (EREs) for modeling software behavior, and then using the ERE model to generate test paths. To improve the theory of test generation based on the ERE model, this article presents an algebraic system, named transition algebra, by extending Kleene algebra. Eight operations and their corresponding operational properties, including basic and nonbasic operational properties, are designed for transition algebra, and all such properties are proven. Five examples are given to illustrate the use of ERE modeling and algebraic operations. To ensure the automatic generation of test paths from the ERE model, the article proves that any ERE model constructed by transition algebra can be converted to a set of transition sequences. Compared to Kleene algebra with tests, transition algebra has more operations to build a powerful ERE model and more operational properties to process the ERE model for the generation of test paths.