35 Search Results for "Strichman, Ofer"


Volume

LIPIcs, Volume 236

25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)

SAT 2022, August 2-5, 2022, Haifa, Israel

Editors: Kuldeep S. Meel and Ofer Strichman

Document
Complete Volume
LIPIcs, Volume 236, SAT 2022, Complete Volume

Authors: Kuldeep S. Meel and Ofer Strichman

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
LIPIcs, Volume 236, SAT 2022, Complete Volume

Cite as

25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 1-618, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@Proceedings{meel_et_al:LIPIcs.SAT.2022,
  title =	{{LIPIcs, Volume 236, SAT 2022, Complete Volume}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{1--618},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022},
  URN =		{urn:nbn:de:0030-drops-166736},
  doi =		{10.4230/LIPIcs.SAT.2022},
  annote =	{Keywords: LIPIcs, Volume 236, SAT 2022, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Kuldeep S. Meel and Ofer Strichman

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{meel_et_al:LIPIcs.SAT.2022.0,
  author =	{Meel, Kuldeep S. and Strichman, Ofer},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.0},
  URN =		{urn:nbn:de:0030-drops-166746},
  doi =		{10.4230/LIPIcs.SAT.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
SAT Preprocessors and Symmetry

Authors: Markus Anders

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
Exploitation of symmetries is an indispensable approach to solve certain classes of difficult SAT instances. Numerous techniques for the use of symmetry in SAT have evolved over the past few decades. But no matter how symmetries are used precisely, they have to be detected first. We investigate how to detect more symmetry, faster. The initial idea is to reap the benefits of SAT preprocessing for symmetry detection. As it turns out, applying an off-the-shelf preprocessor before handling symmetry runs into problems: the preprocessor can haphazardly remove symmetry from formulas, severely impeding symmetry exploitation. Our main contribution is a theoretical framework that captures the relationship of SAT preprocessing techniques and symmetry. Based on this, we create a symmetry-aware preprocessor that can be applied safely before handling symmetry. We then demonstrate that applying the preprocessor does not only substantially decrease symmetry detection and breaking times, but also uncovers hidden symmetry not detectable in the original instances. Overall, we depart the conventional view of treating symmetry detection as a black-box, presenting a new application-specific approach to symmetry detection in SAT.

Cite as

Markus Anders. SAT Preprocessors and Symmetry. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{anders:LIPIcs.SAT.2022.1,
  author =	{Anders, Markus},
  title =	{{SAT Preprocessors and Symmetry}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.1},
  URN =		{urn:nbn:de:0030-drops-166752},
  doi =		{10.4230/LIPIcs.SAT.2022.1},
  annote =	{Keywords: boolean satisfiability, symmetry exploitation, graph isomorphism}
}
Document
A Comprehensive Study of k-Portfolios of Recent SAT Solvers

Authors: Jakob Bach, Markus Iser, and Klemens Böhm

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
Hard combinatorial problems such as propositional satisfiability are ubiquitous. The holy grail are solution methods that show good performance on all problem instances. However, new approaches emerge regularly, some of which are complementary to existing solvers in that they only run faster on some instances but not on many others. While portfolios, i.e., sets of solvers, have been touted as useful, putting together such portfolios also needs to be efficient. In particular, it remains an open question how well portfolios can exploit the complementarity of solvers. This paper features a comprehensive analysis of portfolios of recent SAT solvers, the ones from the SAT Competitions 2020 and 2021. We determine optimal portfolios with exact and approximate approaches and study the impact of portfolio size k on performance. We also investigate how effective off-the-shelf prediction models are for instance-specific solver recommendations. One result is that the portfolios found with an approximate approach are as good as the optimal solution in practice. We also observe that marginal returns decrease very quickly with larger k, and our prediction models do not give way to better performance beyond very small portfolio sizes.

Cite as

Jakob Bach, Markus Iser, and Klemens Böhm. A Comprehensive Study of k-Portfolios of Recent SAT Solvers. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bach_et_al:LIPIcs.SAT.2022.2,
  author =	{Bach, Jakob and Iser, Markus and B\"{o}hm, Klemens},
  title =	{{A Comprehensive Study of k-Portfolios of Recent SAT Solvers}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{2:1--2:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.2},
  URN =		{urn:nbn:de:0030-drops-166767},
  doi =		{10.4230/LIPIcs.SAT.2022.2},
  annote =	{Keywords: Propositional satisfiability, solver portfolios, runtime prediction, machine learning, integer programming}
}
Document
On the Performance of Deep Generative Models of Realistic SAT Instances

Authors: Iván Garzón, Pablo Mesejo, and Jesús Giráldez-Cru

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
Generating realistic random SAT instances - random SAT formulas with computational characteristics similar to the ones of application SAT benchmarks - is a challenging problem in order to understand the success of modern SAT solvers solving this kind of problems. Traditional approaches are based on probabilistic models, where a probability distribution characterizes the occurrences of variables into clauses in order to mimic a certain feature exhibited in most application formulas (e.g., community structure), but they may be unable to reproduce others. Alternatively, deep generative models have been recently proposed to address this problem. The goal of these models is to learn the whole structure of the formula without focusing on any predefined feature, in order to reproduce all its computational characteristics at once. In this work, we propose two new deep generative models of realistic SAT instances, and carry out an exhaustive experimental evaluation of these and other existing models in order to analyze their performances. Our results show that models based on graph convolutional networks, possibly enhanced with edge features, return the best results in terms of structural properties and SAT solver performance.

Cite as

Iván Garzón, Pablo Mesejo, and Jesús Giráldez-Cru. On the Performance of Deep Generative Models of Realistic SAT Instances. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{garzon_et_al:LIPIcs.SAT.2022.3,
  author =	{Garz\'{o}n, Iv\'{a}n and Mesejo, Pablo and Gir\'{a}ldez-Cru, Jes\'{u}s},
  title =	{{On the Performance of Deep Generative Models of Realistic SAT Instances}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{3:1--3:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.3},
  URN =		{urn:nbn:de:0030-drops-166775},
  doi =		{10.4230/LIPIcs.SAT.2022.3},
  annote =	{Keywords: Realistic SAT generators, pseudo-industrial random SAT, deep generative models, deep learning}
}
Document
A SAT Attack on Rota’s Basis Conjecture

Authors: Markus Kirchweger, Manfred Scheucher, and Stefan Szeider

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
The SAT modulo Symmetries (SMS) is a recently introduced framework for dynamic symmetry breaking in SAT instances. It combines a CDCL SAT solver with an external lexicographic minimality checking algorithm. We extend SMS from graphs to matroids and use it to progress on Rota’s Basis Conjecture (1989), which states that one can always decompose a collection of r disjoint bases of a rank r matroid into r disjoint rainbow bases. Through SMS, we establish that the conjecture holds for all matroids of rank 4 and certain special cases of matroids of rank 5. Furthermore, we extend SMS with the facility to produce DRAT proofs. External tools can then be used to verify the validity of additional axioms produced by the lexicographic minimality check. As a byproduct, we have utilized our framework to enumerate matroids modulo isomorphism and to support the investigation of various other problems on matroids.

Cite as

Markus Kirchweger, Manfred Scheucher, and Stefan Szeider. A SAT Attack on Rota’s Basis Conjecture. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{kirchweger_et_al:LIPIcs.SAT.2022.4,
  author =	{Kirchweger, Markus and Scheucher, Manfred and Szeider, Stefan},
  title =	{{A SAT Attack on Rota’s Basis Conjecture}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.4},
  URN =		{urn:nbn:de:0030-drops-166780},
  doi =		{10.4230/LIPIcs.SAT.2022.4},
  annote =	{Keywords: SAT modulo Symmetry (SMS), dynamic symmetry breaking, Rota’s basis conjecture, matroid}
}
Document
Classes of Hard Formulas for QBF Resolution

Authors: Agnes Schleitzer and Olaf Beyersdorff

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
To date, we know only a few handcrafted quantified Boolean formulas (QBFs) that are hard for central QBF resolution systems such as Q-Res and QU-Res, and only one specific QBF family to separate Q-Res and QU-Res. Here we provide a general method to construct hard formulas for Q-Res and QU-Res. The construction uses simple propositional formulas (e.g. minimally unsatisfiable formulas) in combination with easy QBF gadgets (Σ₂^b formulas without constant winning strategies). This leads to a host of new hard formulas, including new classes of hard random QBFs. We further present generic constructions for formulas separating Q-Res and QU-Res, and for separating Q-Res and LD-Q-Res.

Cite as

Agnes Schleitzer and Olaf Beyersdorff. Classes of Hard Formulas for QBF Resolution. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{schleitzer_et_al:LIPIcs.SAT.2022.5,
  author =	{Schleitzer, Agnes and Beyersdorff, Olaf},
  title =	{{Classes of Hard Formulas for QBF Resolution}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.5},
  URN =		{urn:nbn:de:0030-drops-166792},
  doi =		{10.4230/LIPIcs.SAT.2022.5},
  annote =	{Keywords: QBF, proof complexity, resolution, separations}
}
Document
Tight Bounds for Tseitin Formulas

Authors: Dmitry Itsykson, Artur Riazanov, and Petr Smirnov

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
We show that for any connected graph G the size of any regular resolution or OBDD(∧, reordering) refutation of a Tseitin formula based on G is at least 2^Ω(tw(G)), where tw(G) is the treewidth of G. These lower bounds improve upon the previously known bounds and, moreover, they are tight. For both of the proof systems, there are constructive upper bounds that almost match the obtained lower bounds, hence the class of Tseitin formulas is almost automatable for regular resolution and for OBDD(∧, reordering).

Cite as

Dmitry Itsykson, Artur Riazanov, and Petr Smirnov. Tight Bounds for Tseitin Formulas. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{itsykson_et_al:LIPIcs.SAT.2022.6,
  author =	{Itsykson, Dmitry and Riazanov, Artur and Smirnov, Petr},
  title =	{{Tight Bounds for Tseitin Formulas}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{6:1--6:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.6},
  URN =		{urn:nbn:de:0030-drops-166805},
  doi =		{10.4230/LIPIcs.SAT.2022.6},
  annote =	{Keywords: Proof complexity, Tseitin formulas, treewidth, resolution, OBDD-based proof systems}
}
Document
Towards Learning Quantifier Instantiation in SMT

Authors: Mikoláš Janota, Jelle Piepenbrock, and Bartosz Piotrowski

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
This paper applies machine learning (ML) to solve quantified satisfiability modulo theories (SMT) problems more efficiently. The motivating idea is that the solver should learn from already solved formulas to solve new ones. This is especially relevant in classes of similar formulas. We focus on the enumerative instantiation - a well-established approach to solving quantified formulas anchored in the Herbrand’s theorem. The task is to select the right ground terms to be instantiated. In ML parlance, this means learning to rank ground terms. We devise a series of features of the considered terms and train on them using boosted decision trees. In particular, we integrate the LightGBM library into the SMT solver cvc5. The experimental results demonstrate that the ML-guided solver enables us to solve more formulas than the base solver and reduce the number of quantifier instantiations. We also do an ablation study on the features used in the machine learning component, showing the contributions of the various additions.

Cite as

Mikoláš Janota, Jelle Piepenbrock, and Bartosz Piotrowski. Towards Learning Quantifier Instantiation in SMT. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{janota_et_al:LIPIcs.SAT.2022.7,
  author =	{Janota, Mikol\'{a}\v{s} and Piepenbrock, Jelle and Piotrowski, Bartosz},
  title =	{{Towards Learning Quantifier Instantiation in SMT}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.7},
  URN =		{urn:nbn:de:0030-drops-166810},
  doi =		{10.4230/LIPIcs.SAT.2022.7},
  annote =	{Keywords: satisfiability modulo theories, quantifier instantiation, machine learning}
}
Document
Introducing Intel(R) SAT Solver

Authors: Alexander Nadel

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
We introduce Intel(R) SAT Solver (IntelSAT) - a new open-source CDCL SAT solver, written from scratch. IntelSAT is optimized for applications which generate many mostly satisfiable incremental SAT queries. We apply the following Incremental Lazy Backtracking (ILB) principle: in-between incremental queries, backtrack only when necessary and to the highest possible decision level. ILB is enabled by a novel reimplication procedure, which can reimply an assigned literal at a lower level without backtracking. Reimplication also helped us to restore the following two properties, lost in the modern solvers with the introduction of chronological backtracking: no assigned literal can be implied at a lower level, conflict analysis always starts with a clause falsified at the lowest possible level. In addition, we apply some new heuristics. Integrating IntelSAT into the MaxSAT solver TT-Open-WBO-Inc resulted in a significant performance boost on incomplete unweighted MaxSAT Evaluation benchmarks and improved the state-of-the-art in anytime unweighted MaxSAT solving.

Cite as

Alexander Nadel. Introducing Intel(R) SAT Solver. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 8:1-8:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{nadel:LIPIcs.SAT.2022.8,
  author =	{Nadel, Alexander},
  title =	{{Introducing Intel(R) SAT Solver}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{8:1--8:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.8},
  URN =		{urn:nbn:de:0030-drops-166825},
  doi =		{10.4230/LIPIcs.SAT.2022.8},
  annote =	{Keywords: SAT, CDCL, MaxSAT}
}
Document
A Generalization of the Satisfiability Coding Lemma and Its Applications

Authors: Milan Mossé, Harry Sha, and Li-Yang Tan

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
The seminal Satisfiability Coding Lemma of Paturi, Pudlák, and Zane is a coding scheme for satisfying assignments of k-CNF formulas. We generalize it to give a coding scheme for implicants and use this generalized scheme to establish new structural and algorithmic properties of prime implicants of k-CNF formulas. Our first application is a near-optimal bound of n⋅ 3^{n(1-Ω(1/k))} on the number of prime implicants of any n-variable k-CNF formula. This resolves an open problem from the Ph.D. thesis of Talebanfard, who proved such a bound for the special case of constant-read k-CNF formulas. Our proof is algorithmic in nature, yielding an algorithm for computing the set of all prime implicants - the Blake Canonical Form - of a given k-CNF formula. The problem of computing the Blake Canonical Form of a given function is a classic one, dating back to Quine, and our work gives the first non-trivial algorithm for k-CNF formulas.

Cite as

Milan Mossé, Harry Sha, and Li-Yang Tan. A Generalization of the Satisfiability Coding Lemma and Its Applications. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{mosse_et_al:LIPIcs.SAT.2022.9,
  author =	{Moss\'{e}, Milan and Sha, Harry and Tan, Li-Yang},
  title =	{{A Generalization of the Satisfiability Coding Lemma and Its Applications}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.9},
  URN =		{urn:nbn:de:0030-drops-166837},
  doi =		{10.4230/LIPIcs.SAT.2022.9},
  annote =	{Keywords: Prime Implicants, Satisfiability Coding Lemma, Blake Canonical Form, k-SAT}
}
Document
Relating Existing Powerful Proof Systems for QBF

Authors: Leroy Chew and Marijn J. H. Heule

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
We advance the theory of QBF proof systems by showing the first simulation of the universal checking format QRAT by a theory-friendly system. We show that the sequent system G fully p-simulates QRAT, including the Extended Universal Reduction (EUR) rule which was recently used to show QRAT does not have strategy extraction. Because EUR heavily uses resolution paths our technique also brings resolution path dependency and sequent systems closer together. While we do not recommend G for practical applications this work can potentially show what features are needed for a new QBF checking format stronger than QRAT.

Cite as

Leroy Chew and Marijn J. H. Heule. Relating Existing Powerful Proof Systems for QBF. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{chew_et_al:LIPIcs.SAT.2022.10,
  author =	{Chew, Leroy and Heule, Marijn J. H.},
  title =	{{Relating Existing Powerful Proof Systems for QBF}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{10:1--10:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.10},
  URN =		{urn:nbn:de:0030-drops-166845},
  doi =		{10.4230/LIPIcs.SAT.2022.10},
  annote =	{Keywords: QBF, Proof Complexity, Verification, Strategy Extraction, Sequent Calculus}
}
Document
Should Decisions in QCDCL Follow Prefix Order?

Authors: Benjamin Böhm, Tomáš Peitl, and Olaf Beyersdorff

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
Quantified conflict-driven clause learning (QCDCL) is one of the main solving approaches for quantified Boolean formulas (QBF). One of the differences between QCDCL and propositional CDCL is that QCDCL typically follows the prefix order of the QBF for making decisions. We investigate an alternative model for QCDCL solving where decisions can be made in arbitrary order. The resulting system QCDCL^ANY is still sound and terminating, but does not necessarily allow to always learn asserting clauses or cubes. To address this potential drawback, we additionally introduce two subsystems that guarantee to always learn asserting clauses (QCDCL^UNI-ANI) and asserting cubes (QCDCL^EXI-ANY), respectively. We model all four approaches by formal proof systems and show that QCDCL^UNI-ANY is exponentially better than QCDCL on false formulas, whereas QCDCL^EXI-ANY is exponentially better than QCDCL on true QBFs. Technically, this involves constructing specific QBF families and showing lower and upper bounds in the respective proof systems. We complement our theoretical study with some initial experiments that confirm our theoretical findings.

Cite as

Benjamin Böhm, Tomáš Peitl, and Olaf Beyersdorff. Should Decisions in QCDCL Follow Prefix Order?. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bohm_et_al:LIPIcs.SAT.2022.11,
  author =	{B\"{o}hm, Benjamin and Peitl, Tom\'{a}\v{s} and Beyersdorff, Olaf},
  title =	{{Should Decisions in QCDCL Follow Prefix Order?}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.11},
  URN =		{urn:nbn:de:0030-drops-166850},
  doi =		{10.4230/LIPIcs.SAT.2022.11},
  annote =	{Keywords: QBF, CDCL, proof complexity, lower bounds}
}
Document
MaxSAT-Based Bi-Objective Boolean Optimization

Authors: Christoph Jabs, Jeremias Berg, Andreas Niskanen, and Matti Järvisalo

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)


Abstract
We explore a maximum satisfiability (MaxSAT) based approach to bi-objective optimization. Bi-objective optimization refers to the task of finding so-called Pareto-optimal solutions in terms of two objective functions. Bi-objective optimization problems naturally arise in various real-world settings. For example, in the context of learning interpretable representations, such as decision rules, from data, one wishes to balance between two objectives, the classification error and the size of the representation. Our approach is generally applicable to bi-objective optimizations which allow for propositional encodings. The approach makes heavy use of incremental Boolean satisfiability (SAT) solving and draws inspiration from modern MaxSAT solving approaches. In particular, we describe several variants of the approach which arise from different approaches to MaxSAT solving. In addition to computing a single representative solution per each point of the Pareto front, the approach allows for enumerating all Pareto-optimal solutions. We empirically compare the efficiency of the approach to recent competing approaches, showing practical benefits of our approach in the contexts of learning interpretable classification rules and bi-objective set covering.

Cite as

Christoph Jabs, Jeremias Berg, Andreas Niskanen, and Matti Järvisalo. MaxSAT-Based Bi-Objective Boolean Optimization. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{jabs_et_al:LIPIcs.SAT.2022.12,
  author =	{Jabs, Christoph and Berg, Jeremias and Niskanen, Andreas and J\"{a}rvisalo, Matti},
  title =	{{MaxSAT-Based Bi-Objective Boolean Optimization}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{12:1--12:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.12},
  URN =		{urn:nbn:de:0030-drops-166863},
  doi =		{10.4230/LIPIcs.SAT.2022.12},
  annote =	{Keywords: Multi-objective optimization, Pareto front enumeration, bi-objective optimization, maximum satisfiability, incremental SAT}
}
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