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<p><it>Abstract—</it>We present a new method to determine whether a convex region contains any integer points. The method is designed for array subscript analysis in parallel programs. The general problem is whether a system of linear equalities and inequalities has an integer solution. A set of known techniques is used to transform the problem to that of finding whether a convex region contains any integer points. The main result of the paper is a set of new search procedures that identify an integer solution in a convex region, or prove that no integer solutions exist. They are based on the geometrical properties of convex regions that are not empty, but also do not contain any integer points. The results contribute to exact and efficient dependence and synchronization analysis of parallel programs.</p><p><it>Index Terms—</it>Subscript analysis, dependence testing, integer programming, parallelizing compilers, parallel program analysis, synchronization analysis.</p>

J. Subhlok and K. Kennedy, "Integer Programming for Array Subscript Analysis," in IEEE Transactions on Parallel & Distributed Systems, vol. 6, no. , pp. 662-668, 1995.
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