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The Z-polyhedral model by Gautam Gupta; Sanjay Rajopadhye is a scholarly article available to read on EtoBox.

What is The Z-polyhedral model about?

The polyhedral model is a well developed formalism and has been extensively used in a variety of contexts viz. the automatic parallelization of loop programs, program verification, locality, hardware generation and more recently, in the automatic reduction of asymptotic program complexity. Such analyses and transformations rely on certain closure properties. However, the model is limited in expressivity and the need for a more general class of programs is widely known.We provide the extension to Z-polyhedra which are the intersection of polyhedra and lattices. We prove the required closure properties using a novel representation and interpretation of Zpolyhedra. In addition, we also prove closure in the Z-polyhedral model under images by dependence functions-thereby proving that unions of LBLs, widely assumed to be a richer class of sets, is equal to unions of Z-polyhedra. Another corollary of this result is the equivalence of the unions of Z-polyhedra and Presburger sets. Our representation and closure properties constitute the foundations of the Z-polyhedral model. As an example, we present the transformation for automatic reduction of complexity in the Zpolyhedral model.

Author

Gautam Gupta; Sanjay Rajopadhye

Publisher

ACM

Published

2007

Language

EN