The internal mechanism used for a dependence test constrains its accuracy and determines its speed. The internal mechanism used for our Access Region Test (ART) is fundamentally different from that used in any other dependence test, and therefore its constraints and characteristics are likewise different. In this paper, we briefly describe our novel descriptor for representing memory accesses, the Access Region Descriptor (ARD) and the ART. We then describe the ARD intersection algorithm in some detail. Finally, we compare and contrast the mechanisms of the ARD intersection algorithm with the internal mechanisms for a number of popular prior dependence tests.