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A solver for quantified Boolean and linear constraints

Authors:

Lucas Bordeaux,

Lintao ZhangAuthors Info & Claims

SAC '07: Proceedings of the 2007 ACM symposium on Applied computing

Pages 321 - 325

https://doi.org/10.1145/1244002.1244078

Published: 11 March 2007 Publication History

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Abstract

We make a number of contributions to the understanding and practical resolution of quantified constraints. Unlike previous work in the CP literature that was essentially focused on constraints expressed as binary tables, we focus on Presburger Arithmetics, i.e., Boolean combinations of linear constraints. From a theoretical perspective, we clarify the problem of the treatment of universal quantifiers by proposing a "symmetric" version of the notion of quantified consistency. This notion imposes to maintain two constraint stores, which will be used to reason on universal and existential variables, respectively. We then describe a branch & bound algorithm that integrates both forms of propagation. Its implementation is, to the best of our knowledge, the first CP solver for this class of quantified constraints.

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Cited By

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Vincent BStéphan I(2014)The Cut Tool for QCSPProceedings of the 2014 IEEE 26th International Conference on Tools with Artificial Intelligence10.1109/ICTAI.2014.135(883-890)Online publication date: 10-Nov-2014
https://dl.acm.org/doi/10.1109/ICTAI.2014.135
Bordeaux LCadoli MMancini T(2009)Generalizing consistency and other constraint properties to quantified constraintsACM Transactions on Computational Logic10.1145/1507244.150724710:3(1-25)Online publication date: 8-Apr-2009
https://dl.acm.org/doi/10.1145/1507244.1507247
Nightingale P(2009)Non-binary quantified CSPConstraints10.1007/s10601-009-9068-114:4(539-581)Online publication date: 1-Dec-2009
https://dl.acm.org/doi/10.1007/s10601-009-9068-1
Show More Cited By

Index Terms

A solver for quantified Boolean and linear constraints
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation

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Published In

SAC '07: Proceedings of the 2007 ACM symposium on Applied computing

March 2007

1688 pages

ISBN:1595934804

DOI:10.1145/1244002

Conference Chairs:
Yookun Cho
Seoul National University, Seoul, Korea
,
Roger L. Wainwright
University of Tulsa, Tulsa, Oklahoma
,
Hisham M. Haddad
Kennesaw State University, Kennesaw, Georgia
,
Sung Y. Shin
South Dakota State University, Brookings, South Dakota
,
Program Chair:
Yong Wan Koo
The University of Suwon, Gyeongggi-do, Korea

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 ACM 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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Published: 11 March 2007

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SAC07: The 2007 ACM Symposium on Applied Computing

March 11 - 15, 2007

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Overall Acceptance Rate 1,650 of 6,669 submissions, 25%

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Vincent BStéphan I(2014)The Cut Tool for QCSPProceedings of the 2014 IEEE 26th International Conference on Tools with Artificial Intelligence10.1109/ICTAI.2014.135(883-890)Online publication date: 10-Nov-2014
https://dl.acm.org/doi/10.1109/ICTAI.2014.135
Bordeaux LCadoli MMancini T(2009)Generalizing consistency and other constraint properties to quantified constraintsACM Transactions on Computational Logic10.1145/1507244.150724710:3(1-25)Online publication date: 8-Apr-2009
https://dl.acm.org/doi/10.1145/1507244.1507247
Nightingale P(2009)Non-binary quantified CSPConstraints10.1007/s10601-009-9068-114:4(539-581)Online publication date: 1-Dec-2009
https://dl.acm.org/doi/10.1007/s10601-009-9068-1
Samer M(2008)Variable Dependencies of Quantified CSPsProceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning10.1007/978-3-540-89439-1_36(512-527)Online publication date: 22-Nov-2008
https://dl.acm.org/doi/10.1007/978-3-540-89439-1_36

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A satisfiability procedure for quantified boolean formulae

Backjumping for quantified Boolean logic satisfiability

Algorithms for quantified Boolean formulas

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