Pugh, WilliamWonnacott, DavidArray data dependence analysis methods currently in use generate false dependences that can prevent useful program transformations. These false dependences arise because the questions asked are conservative approximations to the questions we really should be asking. Unfortunately, the questions we really should be asking go beyond integer programming and require decision procedures for a subclass of Presburger formulas. In this paper, we describe how to extend the Omega test so that it can answer these queries and allow us to eliminate these false data dependences. We have implemented the techniques described here and believe they are suitable for use in production compilers. (An earlier version of this paper appeared at the ACM SIGPLAN PLDI'92 conference). (Also cross-referenced as UMIACS-TR-93-132)en-USTechnical Report