A Polynomial-Time Dependence Test for Determining Integer-Valued Solutions in Multi-Dimensional Arrays Under Variable Bounds

Abstract

Multi-dimensional arrays with linear subscripts occur quite frequently in real programs. For multi-dimensional linear arrays under variable bounds as well as any given direction vectors, the generalized Lambda test is an efficient and precise data dependence method to check whether there exist real-valued solutions. In this paper, we propose a multi-dimensional generalized interval test—a polynomial-time dependence test that can be applied towards testing whether there are integer-valued solutions for multi-dimensional linear arrays under variablelimits and any given direction vectors. Experimental results with benchmark showing the effects of the multi-dimensional generalized interval test over the generalized Lambda test are also presented.