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Using machine learning to decide when to precondition cylindrical algebraic decomposition with groebner bases

Accepted version
Peer-reviewed

Type

Conference Object

Change log

Authors

Huang, Z 
England, M 
Davenport, JH 
Paulson, LC 

Abstract

Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. However, it can be expensive, with worst case complexity doubly exponential in the size of the input. Hence it is important to formulate the problem in the best manner for the CAD algorithm. One possibility is to precondition the input polynomials using Groebner Basis (GB) theory. Previous experiments have shown that while this can often be very beneficial to the CAD algorithm, for some problems it can significantly worsen the CAD performance. In the present paper we investigate whether machine learning, specifically a support vector machine (SVM), may be used to identify those CAD problems which benefit from GB preconditioning. We run experiments with over 1000 problems (many times larger than previous studies) and find that the machine learned choice does better than the human-made heuristic.

Description

Keywords

cs.SC, cs.SC, cs.LG, 68W30, 68T05, I.2.6; I.1.0

Journal Title

Proceedings - 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2016

Conference Name

2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)

Journal ISSN

Volume Title

Publisher

IEEE

Rights

All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/I011005/1)