research-article

Formula Simplification for Real Quantifier Elimination Using Geometric Invariance

Authors:

Hirokazu AnaiAuthors Info & Claims

ISSAC '17: Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation

Pages 213 - 220

https://doi.org/10.1145/3087604.3087627

Published: 23 July 2017 Publication History

Abstract

Formulating a simple and adequate quantified first-order formula is crucial for applying real quantifier elimination (QE) efficiently. In general, generating simple formulas or simplifying formulas for efficient QE involves human interaction. In this paper, we present simplification algorithms for quantified first-order formulas over the real numbers to speed up QE. We present experimental results for more than 10,000 benchmark problems to examine the effectiveness of our simplification algorithms.

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Cited By

Matsuzaki TFujita T(2022)Formula Simplification via Invariance Detection by Algebraically Indexed TypesAutomated Reasoning10.1007/978-3-031-10769-6_24(388-406)Online publication date: 8-Aug-2022
https://dl.acm.org/doi/10.1007/978-3-031-10769-6_24
Matsuzaki TIwane HKobayashi MZhan YFukasaku RKudo JAnai HArai NFontaine PKaliszyk CSchulz SUrban J(2018)Can an A.I. win a medal in the mathematical olympiad? – Benchmarking mechanized mathematics on pre-university problemsAI Communications10.3233/AIC-18076231:3(251-266)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.3233/AIC-180762

Index Terms

Formula Simplification for Real Quantifier Elimination Using Geometric Invariance
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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cover image ACM Other conferences

ISSAC '17: Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation

July 2017

466 pages

ISBN:9781450350648

DOI:10.1145/3087604

Editor:
Michael Burr
Clemson University, USA
,
General Chair:
Chee K. Yap
New York University, USA
,
Program Chair:
Mohab Safey El Din
University Pierre et Marie Curie, France

Copyright © 2017 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

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Association for Computing Machinery

New York, NY, United States

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Published: 23 July 2017

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ISSAC '17

ISSAC '17: International Symposium on Symbolic and Algebraic Computation

July 23 - 28, 2017

Kaiserslautern, Germany

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Cited By

Matsuzaki TFujita T(2022)Formula Simplification via Invariance Detection by Algebraically Indexed TypesAutomated Reasoning10.1007/978-3-031-10769-6_24(388-406)Online publication date: 8-Aug-2022
https://dl.acm.org/doi/10.1007/978-3-031-10769-6_24
Matsuzaki TIwane HKobayashi MZhan YFukasaku RKudo JAnai HArai NFontaine PKaliszyk CSchulz SUrban J(2018)Can an A.I. win a medal in the mathematical olympiad? – Benchmarking mechanized mathematics on pre-university problemsAI Communications10.3233/AIC-18076231:3(251-266)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.3233/AIC-180762

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