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A Preprocessor Based on Clause Normal Forms and Virtual Substitutions to Parallelize Cylindrical Algebraic Decomposition

Discrete Mathematics 2013-01-22 v3

Abstract

The Cylindrical Algebraic Decomposition (CAD) algorithm is a comprehensive tool to perform quantifier elimination over real closed fields. CAD has doubly exponential running time, making it infeasible for practical purposes. We propose to use the notions of clause normal forms and virtual substitutions to develop a preprocessor for CAD, that will enable an input-level parallelism. We study the performance of CAD in the presence of the preprocessor by extensive experimentation. Since parallelizability of CAD depends on the structure of given prenex formula, we introduce some structural notions to study the performance of CAD with the proposed preprocessor.

Keywords

Cite

@article{arxiv.1112.5352,
  title  = {A Preprocessor Based on Clause Normal Forms and Virtual Substitutions to Parallelize Cylindrical Algebraic Decomposition},
  author = {Hari Krishna Malladi and Ambedkar Dukkipati},
  journal= {arXiv preprint arXiv:1112.5352},
  year   = {2013}
}

Comments

8 pages

R2 v1 2026-06-21T19:55:53.192Z