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Generating Extended Resolution Proofs with a BDD-Based SAT Solver [chapter]

Randal E. Bryant, Marijn J. H. Heule
<span title="">2021</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We demonstrate the utility of this approach by applying a prototype solver to obtain polynomially sized proofs on benchmarks for the mutilated chessboard and pigeonhole problems—ones that are very challenging  ...  Through this, a BDD-based Boolean satisfiability (SAT) solver can generate a checkable proof of unsatisfiability.  ...  Mutilated Chessboard The mutilated chessboard problem considers an n × n chessboard, with the corners on the upper left and the lower right removed.  ... 
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Generating Extended Resolution Proofs with a BDD-Based SAT Solver [article]

Randal E. Bryant, Marijn J. H. Heule
<span title="2021-06-14">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
for parity formulas, as well as the Urquhart, mutilated chessboard, and pigeonhole problems.  ...  Through this, a BDD-based Boolean satisfiability (SAT) solver can generate a checkable proof of unsatisfiability for a set of clauses.  ...  Mutilated Chessboard The mutilated chessboard problem considers an n × n chessboard, with the corners on the upper left and the lower right removed.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2105.00885v2">arXiv:2105.00885v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kczbgq72rzehtgdejryy3nh6ua">fatcat:kczbgq72rzehtgdejryy3nh6ua</a> </span>
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Encoding Redundancy for Satisfaction-Driven Clause Learning [chapter]

Marijn J. H. Heule, Benjamin Kiesl, Armin Biere
<span title="">2019</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
For the first time, we are able to generate and automatically check clausal proofs for large instances of these problems.  ...  Using one of these variants allows SDCL to solve harder problems, in particular the well-known Tseitin formulas and mutilated chessboard problems.  ...  Resolution proofs of mutilated chessboard problems are exponential in size [1] , which explains the poor performance of CDCL solvers.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-17462-0_3">doi:10.1007/978-3-030-17462-0_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jm3wxiwjubhnpiq5wvdqto77j4">fatcat:jm3wxiwjubhnpiq5wvdqto77j4</a> </span>
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:{unav)

Etienne de Klerk, Hans van Maaren, Joost P. Warners
<span title="2012-12-27">2012</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2ewief65xnegfh2slwulpgsnba" style="color: black;">Journal of automated reasoning</a> </i> &nbsp;
We show that using the relaxation, a proof of the unsatisfiability of the notorious pigeonhole and mutilated chessboard problems can be computed in polynomial time.  ...  We derive a semidefinite relaxation of the satisfiability (SAT) problem and discuss its strength. We give both the primal and dual formulation of the relaxation.  ...  Figure 4 . 4 The mutilated chessboard for s = 2. LEMMA 7. 1 . 1 Suppose is a pure 3SAT problem. It holds that gap( ) = 0. Proof.  ... 
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Resolution for Max-SAT

María Luisa Bonet, Jordi Levy, Felip Manyà
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/weoplee4x5anpi62cco5v4higa" style="color: black;">Artificial Intelligence</a> </i> &nbsp;
We also prove the completeness of some refinements of this calculus. From the completeness proof we derive an exact algorithm for Max-SAT and a time upper bound.  ...  We also define a weighted Max-SAT resolution-like rule, and show how to adapt the soundness and completeness proofs of the Max-SAT rule to the weighted Max-SAT rule.  ...  There are resolution lower bounds (as in Theorem 16) for other combinatorial principles like Tseitin formulas [11, 31] , Random formulas [9, 11] , Mutilated chessboard [1] , Reflexion principle [6,  ... 
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"Planar" tautologies hard for resolution

S. Dantchev, S. Riis
<i title="IEEE Comput. Soc"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v4uclqixrrhlnk5pbw4wii6cfq" style="color: black;">Proceedings 2001 IEEE International Conference on Cluster Computing</a> </i> &nbsp;
More specifically, we show a ¾ ª´Òµ lower bound for any resolution proof of the mutilated chessboard problem on a ¾Ò ¢ ¾Ò chessboard as well as for the Tseitin tautology based on the Ò ¢ Ò rectangular  ...  Abstract We prove exponential lower bounds on the resolution proofs of some tautologies, based on rectangular grid graphs.  ...  We prove the following two theorems: Theorem 2.1 Any resolution proof of the Mutilated Chessboard problem is of size ¾ ª´Òµ .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/sfcs.2001.959896">doi:10.1109/sfcs.2001.959896</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/focs/DantchevR01.html">dblp:conf/focs/DantchevR01</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bbsez7cdtzgbfijhzcyo4xg3nm">fatcat:bbsez7cdtzgbfijhzcyo4xg3nm</a> </span>
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Page 2352 of Mathematical Reviews Vol. , Issue Index [page]

<i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Mutilated chessboard problem is exponentially hard for resolution. (English summary) 2004i:03017 Ambler, Simon J.  ...  (English summary) (see 2004k:68010) (Baumgartner, Peter) sce First order theorem proving Beckert, Bernhard Depth-first proof search without backtracking for free-variable clausal tableaux.  ... 
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Non-clausal redundancy properties

Lee Barnett, Armin Biere
<span title="">2021</span>
Using a form of reverse unit propagation over conjunctions of BDDs, these systems capture, for instance, Gaussian elimination reasoning over XOR constraints encoded in a formula, without the need for clausal  ...  State-of-the-art refutation systems for SAT are largely based on the derivation of clauses meeting some redundancy criteria, ensuring their addition to a formula does not alter its satisfiability.  ...  We extend our thanks to Marijn Heule for his helpful comments on an earlier draft of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.35011/fmvtr.2021-2">doi:10.35011/fmvtr.2021-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5hlqsf7oq5hs3gowprgstjt7yi">fatcat:5hlqsf7oq5hs3gowprgstjt7yi</a> </span>
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A tetrachotomy of ontology-mediated queries with a covering axiom [article]

Olga Gerasimova, Stanislav Kikot, Agi Kurucz, Vladimir Podolskii, Michael Zakharyaschev
<span title="2022-05-05">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
of d-sirups being 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive  ...  On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d-sirups.  ...  Acknowledgements The work of O. Gerasimova was funded by RFBR, project number 20-31-90123. The work of V. Podolskii was supported by the HSE University Basic Research Program. The work of M.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.04167v4">arXiv:2006.04167v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pjgkhitmprd7zodu3tlzd7inia">fatcat:pjgkhitmprd7zodu3tlzd7inia</a> </span>
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