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We introduce a framework for the analysis of memory reference sets addressed by induction variables without closed forms. This framework relies on a new data structure, the value evolution graph (VEG), which models the global flow of values taken by induction variable with and without closed forms. We describe the application of our framework to array data-flow analysis, privatization, and dependence analysis. This results in the automatic parallelization of loops that contain arrays addressed by induction variables without closed forms. We implemented this framework in the Polaris research compiler. We present experimental results on a set of codes from the PERFECT, SPEC, and NCSA benchmark suites.