On the equivalence of certain fault localization techniques

Software fault localization is an expensive component of program debugging, and thus, many different types of fault localization techniques have been proposed over the recent years. Such techniques aim to rank program components (such as statements, blocks, functions, etc.) in decreasing order of their likelihood of being faulty, such that programmers may then examine the ranking starting from the top, until a fault is found. However, comparisons between fault localization techniques (to see which one is more effective) have generally been based on case studies and empirical data. In this paper we propose an equivalence relation by virtue of which two or more fault localization techniques may be considered equivalent if they produce identical rankings of program components, and are therefore, equally as effective. We then make use of the proposed equivalence relation to prove that several similarity coefficient-based fault localization techniques are in fact equivalent to one another. Furthermore, no case studies and/or data were required for any of the proofs of equivalency provided in this paper.