Transforming Quantified Boolean Formulas Using Biclique Covers-Reference-Cited by-同舟云学术

Transforming Quantified Boolean Formulas Using Biclique Covers

Published:2023 Issue: Volume: Page:372-390
ISSN:0302-9743
Container-title:Tools and Algorithms for the Construction and Analysis of Systems
language:
Short-container-title:

Author:

Kullmann Oliver,Shukla Ankit

Abstract

AbstractWe introduce the global conflict graph of DQCNFs (dependency quantified conjunctive normal forms), recording clashes between clauses on such universal variables on which all existential variables depend (called “global variables”). The biclique covers of this graph correspond to the eligible clause-slices of the DQCNF which consider only the global variables. We show that all such slices yield satisfiability-equivalent variations. This opens the possibility to realise this slice using as few global variables as possible. We give basic theoretical results and first supporting experimental data.

Publisher

Springer Nature Switzerland

Link

https://link.springer.com/content/pdf/10.1007/978-3-031-30820-8_23

Reference27 articles.

1. Valeriy Balabanov, Jie-Hong Roland Jiang, Christoph Scholl, Alan Mishchenko, and Robert K. Brayton. 2QBF: Challenges and solutions. In Nadia Creignou and Daniel Le Berre, editors, Theory and Applications of Satisfiability Testing - SAT 2016 - 19th International Conference, Bordeaux, France, July 5-8, 2016, Proceedings, volume 9710 of Lecture Notes in Computer Science, pages 453–469. Springer, 2016. URL: https://doi.org/10.1007/978-3-319-40970-2_28, https://doi.org/10.1007/978-3-319-40970-2_28.

2. Olaf Beyersdorff, Mikolás Janota, Florian Lonsing, and Martina Seidl. Quantified Boolean Formulas. In Armin Biere, Marijn Heule, Hans van Maaren, and Toby Walsh, editors, Handbook of Satisfiability - Second Edition, volume 336 of Frontiers in Artificial Intelligence and Applications, pages 1177–1221. IOS Press, 2021. https://doi.org/10.3233/FAIA201015.

3. Joshua Blinkhorn, Tomás Peitl, and Friedrich Slivovsky. Davis and Putnam meet Henkin: Solving DQBF with resolution. In Chu-Min Li and Felip Manyà, editors, Theory and Applications of Satisfiability Testing - SAT 2021 - 24th International Conference, Barcelona, Spain, July 5-9, 2021, Proceedings, volume 12831 of Lecture Notes in Computer Science, pages 30–46. Springer, 2021. https://doi.org/10.1007/978-3-030-80223-3_4.

4. Sunil Chandran, Davis Issac, and Andreas Karrenbauer. On the Parameterized Complexity of Biclique Cover and Partition. In Jiong Guo and Danny Hermelin, editors, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016), volume 63 of Leibniz International Proceedings in Informatics (LIPIcs), pages 11:1–11:13. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2017. https://doi.org/10.4230/LIPIcs.IPEC.2016.11.

5. Gennady Davydov, Inna Davydova, and Hans Kleine Büning. An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF. Annals of Mathematics and Artificial Intelligence, 23(3-4):229–245, 1998. https://doi.org/10.1023/A:1018924526592.