2009年3月11日星期三

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replica watches The Omega project has two major components. One component is the Omega test, a system for manipulating sets of affine constraints over integer variables. When we started work on the Omega test for dependence testing, it was designed as a decision test for the existence of integer solutions to affine constraints. We found that by having the Omega test return symbolic answers, rather than yes/no answers, watches replica we could perform standard data dependence analysis quicker. As we have explored more difficult issues in analysis and transformation of scientific programs, we have extended the Omega test to the point where it is a watches replica complete system for simplifying and verifying Presburger formulas (Presburger formulas contain affine constraints, the usual logical connectives, swiss replica watches and and quantifiers). Of course, the Omega test cannot simplify all Presburger formulas efficiently (there is a nondeterministic lower bound and a deterministic upper bound on the time required to verify Presburger formulas). However, in practice the Omega test is reasonably efficient for the tasks replica watches for which we currently use it swiss replica watches.

watches replica The other component of my research is developing frameworks for analyzing and transforming programs.swiss replica watches We have utilized the Omega test in research on asking more sophisticated questions than are usually asked when analyzing programs; on using this information to pinpoint parallelism unexploited by conventional techniques; and on developing a unified replica watches framework for reordering transformations. These methods are described using simple cases of Presburger formulas. The descriptions and implementations of these techniques can be simple and clear since they need not be concerned with the techniques used by the Omega test to simplify the formulas swiss replica watches.

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