Download xb-bid-qsts

xb-bid-qsts: Using Nested SAT Solvers to
Solve QBFs
Bart Bogaerts1 , Jo Devriendt2 , Tomi Janhunen1 , and Shahab
Tasharrofi1
1
Information and Computer Science Department, Aalto University,
{bart.bogaerts,tommi.janhunen,shahab.tasharrofi}@aalto.fi
2
Department of Computing, KU Leuven,
[email protected]
1
General Description
xb-bid-qsts, by the Aalto team, is based on nested SAT solving, some QBF
theory transformations, symmetry breaking and QBF preprocessors. The main
tools utilized here are:
• sat-to-sat [6]: A (Non-)Prenex Non-CNF QBF solver that is based on
nested SAT solving. sat-to-sat is developed on top of glucose [1].
Unlike other QBF solvers, sat-to-sat is able to do early propagation of
information between nested solvers.
• qbf2sts [3]: A translator from QDIMACS/QCIR input format to satto-sat input format with the ability to reverse engineer circuits and apply
several theory transformations to simplify the representation of QBF formulas.
• breakid [4]: A SAT symmetry breaker that has been modified to detect
a (limited) class of symmetries in QBF instances.
• QxBF [7] and Bloqqer [2]: QBF preprocessors.
xb-bid-qsts works in four steps as follows: (1) Firstly, QBF formulas
pass a preprocessing step using QxBF and Bloqqer preprocessors. (2) Secondly, qbf2sts is called in order to reverse engineer the input and optimize
the extracted circuitry for sat-to-sat. (3) Thirdly, breakid is used to break
symmetries that are local to some quantification level in the resulting formula.
(4) Finally, sat-to-sat is called with early propagation disabled to solve the
final QBF formula. .
1
2
Acknowledgments
We are grateful to the developers of glucose [1] and minisat [5] on which our
sat-to-sat solver is based. We are also grateful to the developers of QxBF
[7] and Bloqqer [2] that we use as a black box. This work was supported by
the Natural Sciences and Engineering Research Council of Canada (NSERC),
the Mathematics of Information Technology and Complex Systems (MITACS),
LogicBlox Inc., and the Academy of Finland (Finnish Centre of Excellence in
Computational Inference Research COIN, 251170).
References
[1] Gilles Audemard and Laurent Simon. Predicting learnt clauses quality in
modern SAT solvers. In Craig Boutilier, editor, IJCAI 2009, Proceedings of
the 21st International Joint Conference on Artificial Intelligence, Pasadena,
California, USA, July 11-17, 2009, pages 399–404, 2009.
[2] Armin Biere, Florian Lonsing, and Martina Seidl. Blocked clause elimination for QBF. In Nikolaj Bjørner and Viorica Sofronie-Stokkermans, editors,
Automated Deduction - CADE-23 - 23rd International Conference on Automated Deduction, Wroclaw, Poland, July 31 - August 5, 2011. Proceedings,
volume 6803 of Lecture Notes in Computer Science, pages 101–115. Springer,
2011.
[3] Bart Bogaerts, Tomi Janhunen, and Shahab Tasharrofi. Solving QBF instances with nested SAT solvers. In Proceedings of BeyondNP’16, 2016.
[4] Jo Devriendt, Bart Bogaerts, and Maurice Bruynooghe. BreakIDGlucose:
On the importance of row symmetry in SAT. In CSPSAT, Vienna, 18 July
2014, pages 1–17, July 2014.
[5] Niklas Eén and Niklas Sörensson. An extensible sat-solver. In Enrico Giunchiglia and Armando Tacchella, editors, Theory and Applications
of Satisfiability Testing, 6th International Conference, SAT 2003. Santa
Margherita Ligure, Italy, May 5-8, 2003 Selected Revised Papers, volume
2919 of Lecture Notes in Computer Science, pages 502–518. Springer, 2003.
[6] Tomi Janhunen, Shahab Tasharrofi, and Eugenia Ternovska. SAT-to-SAT:
Declarative extension of sat solvers with new propagators. In Thirtieth AAAI
Conference on Artificial Intelligence (AAAI-16), Proceedings of, AAAI,
2016.
[7] Florian Lonsing and Armin Biere. Failed literal detection for QBF. In
Karem A. Sakallah and Laurent Simon, editors, Theory and Applications
of Satisfiability Testing - SAT 2011 - 14th International Conference, SAT
2011, Ann Arbor, MI, USA, June 19-22, 2011. Proceedings, volume 6695 of
Lecture Notes in Computer Science, pages 259–272. Springer, 2011.
2