Quantifier elimination in automatic loop parallelization

We present an application of quantifier elimination techniques in the automatic parallelization of nested loop programs. The technical goal is to simplify affine inequalities whose coefficients may be unevaluated symbolic constants. The values of these so-called structure parameters are determined at run time and reflect the problem size. Our purpose here is to make the research community of quantifier elimination, in a tutorial style, aware of our application domain–loop parallelization–and to highlight the role of quantifier elimination, as opposed to alternative techniques, in this domain. Technically, we focus on the elimination method of Weispfenning.