K-DT: a formal system for the evaluation of linear data dependence testing techniques

The power of data dependence testing techniques of a parallelizing compiler is its essence to transform and optimize programs. Numerous techniques were proposed in the past, and it is, however, still a challenging problem to evaluate the relative power of these techniques to better understand the data dependence testing problem. In the past, either empirical studies or experimental evaluation results are published to compare these data dependence testing techniques, being not able to convince the research community completely. In this paper, we show a theoretical study on this issue, comparing the power on disproving dependences of existing techniques by proving theorems in a proposed formal system K-DT. Besides, we also present the upper bounds of these techniques and introduce their minimum complete sets. To the best of our knowledge, K-DT is the first formal system used to compare the power of data dependence testing techniques, and this paper is the first work to show the upper bounds and minimum complete sets of data dependence testing techniques.