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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

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.62

An FPRAS for Two Terminal Reliability in Directed Acyclic Graphs

Authors: Weiming Feng and Heng Guo

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

We give a fully polynomial-time randomized approximation scheme (FPRAS) for two terminal reliability in directed acyclic graphs (DAGs). In contrast, we also show the complementing problem of approximating two terminal unreliability in DAGs is #BIS-hard.

Cite as

Weiming Feng and Heng Guo. An FPRAS for Two Terminal Reliability in Directed Acyclic Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 62:1-62:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{feng_et_al:LIPIcs.ICALP.2024.62,
  author =	{Feng, Weiming and Guo, Heng},
  title =	{{An FPRAS for Two Terminal Reliability in Directed Acyclic Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{62:1--62:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.62},
  URN =		{urn:nbn:de:0030-drops-202057},
  doi =		{10.4230/LIPIcs.ICALP.2024.62},
  annote =	{Keywords: Approximate counting, Network reliability, Sampling algorithm}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.70

BQP, Meet NP: Search-To-Decision Reductions and Approximate Counting

Authors: Sevag Gharibian and Jonas Kamminga

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

What is the power of polynomial-time quantum computation with access to an NP oracle? In this work, we focus on two fundamental tasks from the study of Boolean satisfiability (SAT) problems: search-to-decision reductions, and approximate counting. We first show that, in strong contrast to the classical setting where a poly-time Turing machine requires Θ(n) queries to an NP oracle to compute a witness to a given SAT formula, quantumly Θ(log n) queries suffice. We then show this is tight in the black-box model - any quantum algorithm with "NP-like" query access to a formula requires Ω(log n) queries to extract a solution with constant probability. Moving to approximate counting of SAT solutions, by exploiting a quantum link between search-to-decision reductions and approximate counting, we show that existing classical approximate counting algorithms are likely optimal. First, we give a lower bound in the "NP-like" black-box query setting: Approximate counting requires Ω(log n) queries, even on a quantum computer. We then give a "white-box" lower bound (i.e. where the input formula is not hidden in the oracle) - if there exists a randomized poly-time classical or quantum algorithm for approximate counting making o(log n) NP queries, then BPP^NP[o(n)] contains a 𝖯^NP-complete problem if the algorithm is classical and FBQP^NP[o(n)] contains an FP^NP-complete problem if the algorithm is quantum.

Cite as

Sevag Gharibian and Jonas Kamminga. BQP, Meet NP: Search-To-Decision Reductions and Approximate Counting. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 70:1-70:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gharibian_et_al:LIPIcs.ICALP.2024.70,
  author =	{Gharibian, Sevag and Kamminga, Jonas},
  title =	{{BQP, Meet NP: Search-To-Decision Reductions and Approximate Counting}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{70:1--70:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.70},
  URN =		{urn:nbn:de:0030-drops-202134},
  doi =		{10.4230/LIPIcs.ICALP.2024.70},
  annote =	{Keywords: Approximate Counting, Search to Decision Reduction, BQP, NP, Oracle Complexity Class}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.78

Isomorphism for Tournaments of Small Twin Width

Authors: Martin Grohe and Daniel Neuen

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

We prove that isomorphism of tournaments of twin width at most k can be decided in time k^O(log k) n^O(1). This implies that the isomorphism problem for classes of tournaments of bounded or moderately growing twin width is in polynomial time. By comparison, there are classes of undirected graphs of bounded twin width that are isomorphism complete, that is, the isomorphism problem for the classes is as hard as the general graph isomorphism problem. Twin width is a graph parameter that has been introduced only recently (Bonnet et al., FOCS 2020), but has received a lot of attention in structural graph theory since then. On directed graphs, it is functionally smaller than clique width. We prove that on tournaments (but not on general directed graphs) it is also functionally smaller than directed tree width (and thus, the same also holds for cut width and directed path width). Hence, our result implies that tournament isomorphism testing is also fixed-parameter tractable when parameterized by any of these parameters. Our isomorphism algorithm heavily employs group-theoretic techniques. This seems to be necessary: as a second main result, we show that the combinatorial Weisfeiler-Leman algorithm does not decide isomorphism of tournaments of twin width at most 35 if its dimension is o(n). (Throughout this abstract, n is the order of the input graphs.)

Cite as

Martin Grohe and Daniel Neuen. Isomorphism for Tournaments of Small Twin Width. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{grohe_et_al:LIPIcs.ICALP.2024.78,
  author =	{Grohe, Martin and Neuen, Daniel},
  title =	{{Isomorphism for Tournaments of Small Twin Width}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{78:1--78:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.78},
  URN =		{urn:nbn:de:0030-drops-202216},
  doi =		{10.4230/LIPIcs.ICALP.2024.78},
  annote =	{Keywords: tournament isomorphism, twin width, fixed-parameter tractability, Weisfeiler-Leman algorithm}
}

Document

DOI: 10.4230/DagMan.10.1.1

Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)

Authors: James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter

Published in: Dagstuhl Manifestos, Volume 10, Issue 1 (2024)

Abstract

Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022,sser a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade.

Cite as

James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282). In Dagstuhl Manifestos, Volume 10, Issue 1, pp. 1-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{delgrande_et_al:DagMan.10.1.1,
  author =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  title =	{{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)}},
  pages =	{1--61},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2024},
  volume =	{10},
  number =	{1},
  editor =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.10.1.1},
  URN =		{urn:nbn:de:0030-drops-201403},
  doi =		{10.4230/DagMan.10.1.1},
  annote =	{Keywords: Knowledge representation and reasoning, Applications of logics, Declarative representations, Formal logic}
}

Document

DOI: 10.4230/LIPIcs.ICDT.2024.15

Conjunctive Queries on Probabilistic Graphs: The Limits of Approximability

Authors: Antoine Amarilli, Timothy van Bremen, and Kuldeep S. Meel

Published in: LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)

Abstract

Query evaluation over probabilistic databases is a notoriously intractable problem - not only in combined complexity, but for many natural queries in data complexity as well [Antoine Amarilli et al., 2017; Nilesh N. Dalvi and Dan Suciu, 2012]. This motivates the study of probabilistic query evaluation through the lens of approximation algorithms, and particularly of combined FPRASes, whose runtime is polynomial in both the query and instance size. In this paper, we focus on tuple-independent probabilistic databases over binary signatures, which can be equivalently viewed as probabilistic graphs. We study in which cases we can devise combined FPRASes for probabilistic query evaluation in this setting. We settle the complexity of this problem for a variety of query and instance classes, by proving both approximability and (conditional) inapproximability results. This allows us to deduce many corollaries of possible independent interest. For example, we show how the results of [Marcelo Arenas et al., 2021] on counting fixed-length strings accepted by an NFA imply the existence of an FPRAS for the two-terminal network reliability problem on directed acyclic graphs: this was an open problem until now [Rico Zenklusen and Marco Laumanns, 2011]. We also show that one cannot extend a recent result [Timothy van Bremen and Kuldeep S. Meel, 2023] that gives a combined FPRAS for self-join-free conjunctive queries of bounded hypertree width on probabilistic databases: neither the bounded-hypertree-width condition nor the self-join-freeness hypothesis can be relaxed. Finally, we complement all our inapproximability results with unconditional lower bounds, showing that DNNF provenance circuits must have at least moderately exponential size in combined complexity.

Cite as

Antoine Amarilli, Timothy van Bremen, and Kuldeep S. Meel. Conjunctive Queries on Probabilistic Graphs: The Limits of Approximability. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{amarilli_et_al:LIPIcs.ICDT.2024.15,
  author =	{Amarilli, Antoine and van Bremen, Timothy and Meel, Kuldeep S.},
  title =	{{Conjunctive Queries on Probabilistic Graphs: The Limits of Approximability}},
  booktitle =	{27th International Conference on Database Theory (ICDT 2024)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-312-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{290},
  editor =	{Cormode, Graham and Shekelyan, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.15},
  URN =		{urn:nbn:de:0030-drops-197978},
  doi =		{10.4230/LIPIcs.ICDT.2024.15},
  annote =	{Keywords: Probabilistic query evaluation, tuple-independent databases, approximation}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2023.33

Support Size Estimation: The Power of Conditioning

Authors: Diptarka Chakraborty, Gunjan Kumar, and Kuldeep S. Meel

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract

We consider the problem of estimating the support size of a distribution D. Our investigations are pursued through the lens of distribution testing and seek to understand the power of conditional sampling (denoted as COND), wherein one is allowed to query the given distribution conditioned on an arbitrary subset S. The primary contribution of this work is to introduce a new approach to lower bounds for the COND model that relies on using powerful tools from information theory and communication complexity. Our approach allows us to obtain surprisingly strong lower bounds for the COND model and its extensions. - We bridge the longstanding gap between the upper bound O(log log n + 1/ε²) and the lower bound Ω(√{log log n}) for the COND model by providing a nearly matching lower bound. Surprisingly, we show that even if we get to know the actual probabilities along with COND samples, still Ω(log log n + 1/{ε² log (1/ε)}) queries are necessary. - We obtain the first non-trivial lower bound for the COND equipped with an additional oracle that reveals the actual as well as the conditional probabilities of the samples (to the best of our knowledge, this subsumes all of the models previously studied): in particular, we demonstrate that Ω(log log log n + 1/{ε² log (1/ε)}) queries are necessary.

Cite as

Diptarka Chakraborty, Gunjan Kumar, and Kuldeep S. Meel. Support Size Estimation: The Power of Conditioning. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 33:1-33:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chakraborty_et_al:LIPIcs.MFCS.2023.33,
  author =	{Chakraborty, Diptarka and Kumar, Gunjan and Meel, Kuldeep S.},
  title =	{{Support Size Estimation: The Power of Conditioning}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{33:1--33:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.33},
  URN =		{urn:nbn:de:0030-drops-185675},
  doi =		{10.4230/LIPIcs.MFCS.2023.33},
  annote =	{Keywords: Support-size estimation, Distribution testing, Conditional sampling, Lower bound}
}

Document

DOI: 10.4230/LIPIcs.SAT.2023.28

Explaining SAT Solving Using Causal Reasoning

Authors: Jiong Yang, Arijit Shaw, Teodora Baluta, Mate Soos, and Kuldeep S. Meel

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract

The past three decades have witnessed notable success in designing efficient SAT solvers, with modern solvers capable of solving industrial benchmarks containing millions of variables in just a few seconds. The success of modern SAT solvers owes to the widely-used CDCL algorithm, which lacks comprehensive theoretical investigation. Furthermore, it has been observed that CDCL solvers still struggle to deal with specific classes of benchmarks comprising only hundreds of variables, which contrasts with their widespread use in real-world applications. Consequently, there is an urgent need to uncover the inner workings of these seemingly weak yet powerful black boxes. In this paper, we present a first step towards this goal by introducing an approach called {CausalSAT}, which employs causal reasoning to gain insights into the functioning of modern SAT solvers. {CausalSAT} initially generates observational data from the execution of SAT solvers and learns a structured graph representing the causal relationships between the components of a SAT solver. Subsequently, given a query such as whether a clause with low literals blocks distance (LBD) has a higher clause utility, {CausalSAT} calculates the causal effect of LBD on clause utility and provides an answer to the question. We use {CausalSAT} to quantitatively verify hypotheses previously regarded as "rules of thumb" or empirical findings, such as the query above or the notion that clauses with high LBD experience a rapid drop in utility over time. Moreover, {CausalSAT} can address previously unexplored questions, like which branching heuristic leads to greater clause utility in order to study the relationship between branching and clause management. Experimental evaluations using practical benchmarks demonstrate that {CausalSAT} effectively fits the data, verifies four "rules of thumb", and provides answers to three questions closely related to implementing modern solvers.

Cite as

Jiong Yang, Arijit Shaw, Teodora Baluta, Mate Soos, and Kuldeep S. Meel. Explaining SAT Solving Using Causal Reasoning. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{yang_et_al:LIPIcs.SAT.2023.28,
  author =	{Yang, Jiong and Shaw, Arijit and Baluta, Teodora and Soos, Mate and Meel, Kuldeep S.},
  title =	{{Explaining SAT Solving Using Causal Reasoning}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{28:1--28:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.28},
  URN =		{urn:nbn:de:0030-drops-184909},
  doi =		{10.4230/LIPIcs.SAT.2023.28},
  annote =	{Keywords: Satisfiability, Causality, SAT solver, Clause management}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2023.123

Approximate Model Counting: Is SAT Oracle More Powerful Than NP Oracle?

Authors: Diptarka Chakraborty, Sourav Chakraborty, Gunjan Kumar, and Kuldeep S. Meel

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract

Given a Boolean formula ϕ over n variables, the problem of model counting is to compute the number of solutions of ϕ. Model counting is a fundamental problem in computer science with wide-ranging applications in domains such as quantified information leakage, probabilistic reasoning, network reliability, neural network verification, and more. Owing to the #P-hardness of the problems, Stockmeyer initiated the study of the complexity of approximate counting. Stockmeyer showed that log n calls to an NP oracle are necessary and sufficient to achieve (ε,δ) guarantees. The hashing-based framework proposed by Stockmeyer has been very influential in designing practical counters over the past decade, wherein the SAT solver substitutes the NP oracle calls in practice. It is well known that an NP oracle does not fully capture the behavior of SAT solvers, as SAT solvers are also designed to provide satisfying assignments when a formula is satisfiable, without additional overhead. Accordingly, the notion of SAT oracle has been proposed to capture the behavior of SAT solver wherein given a Boolean formula, an SAT oracle returns a satisfying assignment if the formula is satisfiable or returns unsatisfiable otherwise. Since the practical state-of-the-art approximate counting techniques use SAT solvers, a natural question is whether an SAT oracle is more powerful than an NP oracle in the context of approximate model counting. The primary contribution of this work is to study the relative power of the NP oracle and SAT oracle in the context of approximate model counting. The previous techniques proposed in the context of an NP oracle are weak to provide strong bounds in the context of SAT oracle since, in contrast to an NP oracle that provides only one bit of information, a SAT oracle can provide n bits of information. We therefore develop a new methodology to achieve the main result: a SAT oracle is no more powerful than an NP oracle in the context of approximate model counting.

Cite as

Diptarka Chakraborty, Sourav Chakraborty, Gunjan Kumar, and Kuldeep S. Meel. Approximate Model Counting: Is SAT Oracle More Powerful Than NP Oracle?. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 123:1-123:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chakraborty_et_al:LIPIcs.ICALP.2023.123,
  author =	{Chakraborty, Diptarka and Chakraborty, Sourav and Kumar, Gunjan and Meel, Kuldeep S.},
  title =	{{Approximate Model Counting: Is SAT Oracle More Powerful Than NP Oracle?}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{123:1--123:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.123},
  URN =		{urn:nbn:de:0030-drops-181750},
  doi =		{10.4230/LIPIcs.ICALP.2023.123},
  annote =	{Keywords: Model counting, Approximation, Satisfiability, NP oracle, SAT oracle}
}

Document

DOI: 10.4230/LIPIcs.ESA.2022.34

Distinct Elements in Streams: An Algorithm for the (Text) Book

Authors: Sourav Chakraborty, N. V. Vinodchandran¹, and Kuldeep S. Meel

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract

Given a data stream 𝒟 = ⟨ a₁, a₂, …, a_m ⟩ of m elements where each a_i ∈ [n], the Distinct Elements problem is to estimate the number of distinct elements in 𝒟. Distinct Elements has been a subject of theoretical and empirical investigations over the past four decades resulting in space optimal algorithms for it. All the current state-of-the-art algorithms are, however, beyond the reach of an undergraduate textbook owing to their reliance on the usage of notions such as pairwise independence and universal hash functions. We present a simple, intuitive, sampling-based space-efficient algorithm whose description and the proof are accessible to undergraduates with the knowledge of basic probability theory.

Cite as

Sourav Chakraborty, N. V. Vinodchandran¹, and Kuldeep S. Meel. Distinct Elements in Streams: An Algorithm for the (Text) Book. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 34:1-34:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chakraborty_et_al:LIPIcs.ESA.2022.34,
  author =	{Chakraborty, Sourav and Vinodchandran¹, N. V. and Meel, Kuldeep S.},
  title =	{{Distinct Elements in Streams: An Algorithm for the (Text) Book}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{34:1--34:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.34},
  URN =		{urn:nbn:de:0030-drops-169725},
  doi =		{10.4230/LIPIcs.ESA.2022.34},
  annote =	{Keywords: F₀ Estimation, Streaming, Sampling}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.SAT.2022

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.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

DOI: 10.4230/LIPIcs.SAT.2022.0

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

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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.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

DOI: 10.4230/LIPIcs.SAT.2022.1

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.

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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.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

DOI: 10.4230/LIPIcs.SAT.2022.2

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.

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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.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

DOI: 10.4230/LIPIcs.SAT.2022.3

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.

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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.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}
}

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