DROPS

Volume

LIPIcs, Volume 271

26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

SAT 2023, July 4-8, 2023, Alghero, Italy

Editors: Meena Mahajan and Friedrich Slivovsky

Volume

LIPIcs, Volume 8

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

FSTTCS 2010, December 15-18, 2010, Chennai, India

Editors: Kamal Lodaya and Meena Mahajan

Document

DOI: 10.4230/LIPIcs.CONCUR.2024.14

As Soon as Possible but Rationally

Authors: Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract

This paper addresses complexity problems in rational verification and synthesis for multi-player games played on weighted graphs, where the objective of each player is to minimize the cost of reaching a specific set of target vertices. In these games, one player, referred to as the system, declares his strategy upfront. The other players, composing the environment, then rationally make their moves according to their objectives. The rational behavior of these responding players is captured through two models: they opt for strategies that either represent a Nash equilibrium or lead to a play with a Pareto-optimal cost tuple.

Cite as

Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin. As Soon as Possible but Rationally. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bruyere_et_al:LIPIcs.CONCUR.2024.14,
  author =	{Bruy\`{e}re, V\'{e}ronique and Grandmont, Christophe and Raskin, Jean-Fran\c{c}ois},
  title =	{{As Soon as Possible but Rationally}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.14},
  URN =		{urn:nbn:de:0030-drops-207869},
  doi =		{10.4230/LIPIcs.CONCUR.2024.14},
  annote =	{Keywords: Games played on graphs, rational verification, rational synthesis, Nash equilibrium, Pareto-optimality, quantitative reachability objectives}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2024.29

Strategic Dominance: A New Preorder for Nondeterministic Processes

Authors: Thomas A. Henzinger, Nicolas Mazzocchi, and N. Ege Saraç

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract

We study the following refinement relation between nondeterministic state-transition models: model ℬ strategically dominates model 𝒜 iff every deterministic refinement of 𝒜 is language contained in some deterministic refinement of ℬ. While language containment is trace inclusion, and the (fair) simulation preorder coincides with tree inclusion, strategic dominance falls strictly between the two and can be characterized as "strategy inclusion" between 𝒜 and ℬ: every strategy that resolves the nondeterminism of 𝒜 is dominated by a strategy that resolves the nondeterminism of ℬ. Strategic dominance can be checked in 2-ExpTime by a decidable first-order Presburger logic with quantification over words and strategies, called resolver logic. We give several other applications of resolver logic, including checking the co-safety, co-liveness, and history-determinism of boolean and quantitative automata, and checking the inclusion between hyperproperties that are specified by nondeterministic boolean and quantitative automata.

Cite as

Thomas A. Henzinger, Nicolas Mazzocchi, and N. Ege Saraç. Strategic Dominance: A New Preorder for Nondeterministic Processes. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{henzinger_et_al:LIPIcs.CONCUR.2024.29,
  author =	{Henzinger, Thomas A. and Mazzocchi, Nicolas and Sara\c{c}, N. Ege},
  title =	{{Strategic Dominance: A New Preorder for Nondeterministic Processes}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.29},
  URN =		{urn:nbn:de:0030-drops-208011},
  doi =		{10.4230/LIPIcs.CONCUR.2024.29},
  annote =	{Keywords: quantitative automata, refinement relation, resolver, strategy, history-determinism}
}

Document

Short Paper

DOI: 10.4230/LIPIcs.CP.2024.37

Computing Small Rainbow Cycle Numbers with SAT Modulo Symmetries (Short Paper)

Authors: Markus Kirchweger and Stefan Szeider

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract

Envy-freeness up to any good (EFX) is a key concept in Computational Social Choice for the fair division of indivisible goods, where no agent envies another’s allocation after removing any single item. A deeper understanding of EFX allocations is facilitated by exploring the rainbow cycle number (R_f(d)), the largest number of independent sets in a certain class of directed graphs. Upper bounds on R_f(d) provide guarantees to the feasibility of EFX allocations (Chaudhury et al., EC 2021). In this work, we precisely compute the numbers R_f(d) for small values of d, employing the SAT modulo Symmetries framework (Kirchweger and Szeider, CP 2021). SAT modulo Symmetries is tailored specifically for the constraint-based isomorph-free generation of combinatorial structures. We provide an efficient encoding for the rainbow cycle number, comparing eager and lazy approaches. To cope with the huge search space, we extend the encoding with invariant pruning, a new method that significantly speeds up computation.

Cite as

Markus Kirchweger and Stefan Szeider. Computing Small Rainbow Cycle Numbers with SAT Modulo Symmetries (Short Paper). In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 37:1-37:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kirchweger_et_al:LIPIcs.CP.2024.37,
  author =	{Kirchweger, Markus and Szeider, Stefan},
  title =	{{Computing Small Rainbow Cycle Numbers with SAT Modulo Symmetries}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{37:1--37:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.37},
  URN =		{urn:nbn:de:0030-drops-207221},
  doi =		{10.4230/LIPIcs.CP.2024.37},
  annote =	{Keywords: EFX, rainbow cycle number, SAT modulo Symmetries, combinatorial search}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2024.27

Polynomial Calculus for Quantified Boolean Logic: Lower Bounds Through Circuits and Degree

Authors: Olaf Beyersdorff, Tim Hoffmann, Kaspar Kasche, and Luc Nicolas Spachmann

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract

We initiate an in-depth proof-complexity analysis of polynomial calculus (𝒬-PC) for Quantified Boolean Formulas (QBF). In the course of this we establish a tight proof-size characterisation of 𝒬-PC in terms of a suitable circuit model (polynomial decision lists). Using this correspondence we show a size-degree relation for 𝒬-PC, similar in spirit, yet different from the classic size-degree formula for propositional PC by Impagliazzo, Pudlák and Sgall (1999). We use the circuit characterisation together with the size-degree relation to obtain various new lower bounds on proof size in 𝒬-PC. This leads to incomparability results for 𝒬-PC systems over different fields.

Cite as

Olaf Beyersdorff, Tim Hoffmann, Kaspar Kasche, and Luc Nicolas Spachmann. Polynomial Calculus for Quantified Boolean Logic: Lower Bounds Through Circuits and Degree. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{beyersdorff_et_al:LIPIcs.MFCS.2024.27,
  author =	{Beyersdorff, Olaf and Hoffmann, Tim and Kasche, Kaspar and Spachmann, Luc Nicolas},
  title =	{{Polynomial Calculus for Quantified Boolean Logic: Lower Bounds Through Circuits and Degree}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{27:1--27:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.27},
  URN =		{urn:nbn:de:0030-drops-205834},
  doi =		{10.4230/LIPIcs.MFCS.2024.27},
  annote =	{Keywords: proof complexity, QBF, polynomial calculus, circuits, lower bounds}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.SAT.2024.1

Models and Counter-Models of Quantified Boolean Formulas (Invited Talk)

Authors: Martina Seidl

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract

Because of the duality of universal and existential quantification, quantified Boolean formulas (QBF), the extension of propositional logic with quantifiers over the Boolean variables, have not only solutions in terms of models for true formulas like in SAT. Also false QBFs have solutions in terms of counter-models. Both models and counter-models can be represented as certain binary trees or as sets of Boolean functions reflecting the dependencies among the variables of a formula. Such solutions encode the answers to application problems for which QBF solvers are employed like the plan for a planning problem or the error trace of a verification problem. Therefore, models and counter-models are at the core of theory and practice of QBF solving. In this invited talk, we survey approaches that deal with models and counter-models of QBFs and identify some open challenges.

Cite as

Martina Seidl. Models and Counter-Models of Quantified Boolean Formulas (Invited Talk). In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 1:1-1:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{seidl:LIPIcs.SAT.2024.1,
  author =	{Seidl, Martina},
  title =	{{Models and Counter-Models of Quantified Boolean Formulas}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{1:1--1:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.1},
  URN =		{urn:nbn:de:0030-drops-205238},
  doi =		{10.4230/LIPIcs.SAT.2024.1},
  annote =	{Keywords: Quantified Boolean Formula, Solution Extraction, Solution Counting}
}

Document

DOI: 10.4230/LIPIcs.SAT.2024.6

Clausal Congruence Closure

Authors: Armin Biere, Katalin Fazekas, Mathias Fleury, and Nils Froleyks

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract

Many practical applications of satisfiability solving employ multiple steps to encode an original problem formulation into conjunctive normal form. Often circuits are used as intermediate representation before encoding those circuits into clausal form. These circuits however might contain redundant isomorphic sub-circuits. If blindly translated into clausal form, this redundancy is retained and increases solving time unless specific preprocessing algorithms are used. Furthermore, such redundant sub-formula structure might only emerge during solving and needs to be addressed by inprocessing. This paper presents a new approach which extracts gate information from the formula and applies congruence closure to match and eliminate redundant gates. Besides new algorithms for gate extraction, we also describe previous unpublished attempts to tackle this problem. Experiments focus on the important problem of combinational equivalence checking for hardware designs and show that our new approach yields a substantial gain in CNF solver performance.

Cite as

Armin Biere, Katalin Fazekas, Mathias Fleury, and Nils Froleyks. Clausal Congruence Closure. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 6:1-6:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{biere_et_al:LIPIcs.SAT.2024.6,
  author =	{Biere, Armin and Fazekas, Katalin and Fleury, Mathias and Froleyks, Nils},
  title =	{{Clausal Congruence Closure}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{6:1--6:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.6},
  URN =		{urn:nbn:de:0030-drops-205287},
  doi =		{10.4230/LIPIcs.SAT.2024.6},
  annote =	{Keywords: Satisfiability Solving, Congruence Closure, Structural Hashing, SAT Sweeping, Conjunctive Normal Form, Combinational Equivalence Checking, Hardware Equivalence Checking}
}

Document

DOI: 10.4230/LIPIcs.SAT.2024.10

New Lower Bounds for Polynomial Calculus over Non-Boolean Bases

Authors: Yogesh Dahiya, Meena Mahajan, and Sasank Mouli

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract

In this paper, we obtain new size lower bounds for proofs in the Polynomial Calculus (PC) proof system, in two different settings. - When the Boolean variables are encoded using ±1 (as opposed to 0,1): We establish a lifting theorem using an asymmetric gadget G, showing that for an unsatisfiable formula F, the lifted formula F∘G requires PC size 2^{Ω(d)}, where d is the degree required to refute F. Our lower bound does not depend on the number of variables n, and holds over every field. The only previously known size lower bounds in this setting were established quite recently in [Sokolov, STOC 2020] using lifting with another (symmetric) gadget. The size lower bound there is 2^{Ω((d-d₀)²/n)} (where d₀ is the degree of the initial equations arising from the formula), and is shown to hold only over the reals. - When the PC refutation proceeds over a finite field 𝔽_p and is allowed to use extension variables: We show that there is an unsatisfiable AC⁰[p] formula with N variables for which any PC refutation using N^{1+ε(1-δ)} extension variables, each of arity at most N^{1-ε} and size at most N^c, must have size exp(Ω(N^{εδ}/polylog N)). Our proof achieves these bounds by an XOR-ification of the generalised PHP^{m,r}_n formulas from [Razborov, CC 1998]. The only previously known lower bounds for PC in this setting are those obtained in [Impagliazzo-Mouli-Pitassi, CCC 2023]; in those bounds the number of extension variables is required to be sub-quadratic, and their arity is restricted to logarithmic in the number of original variables. Our result generalises these, and demonstrates a tradeoff between the number and the arity of extension variables. Since our tautology is represented by a small AC⁰[p] formula, our results imply lower bounds for a reasonably strong fragment of AC⁰[p]-Frege.

Cite as

Yogesh Dahiya, Meena Mahajan, and Sasank Mouli. New Lower Bounds for Polynomial Calculus over Non-Boolean Bases. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dahiya_et_al:LIPIcs.SAT.2024.10,
  author =	{Dahiya, Yogesh and Mahajan, Meena and Mouli, Sasank},
  title =	{{New Lower Bounds for Polynomial Calculus over Non-Boolean Bases}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.10},
  URN =		{urn:nbn:de:0030-drops-205327},
  doi =		{10.4230/LIPIcs.SAT.2024.10},
  annote =	{Keywords: Proof Complexity, Polynomial Calculus, degree, Fourier basis, extension variables}
}

Document

DOI: 10.4230/LIPIcs.SAT.2024.13

Entailing Generalization Boosts Enumeration

Authors: Dror Fried, Alexander Nadel, Roberto Sebastiani, and Yogev Shalmon

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract

Given a combinational circuit Γ with a single output o, AllSAT-CT is the problem of enumerating all solutions of Γ. Recently, we introduced several state-of-the-art AllSAT-CT algorithms based on satisfying generalization, which generalizes a given total Boolean solution to a smaller ternary solution that still satisfies the circuit. We implemented them in our open-source tool HALL. In this work we draw upon recent theoretical works suggesting that utilizing generalization algorithms, which can produce solutions that entail the circuit without satisfying it, may enhance enumeration. After considering the theory and adapting it to our needs, we enrich HALL’s AllSAT-CT algorithms by incorporating several newly implemented generalization schemes and additional SAT solvers. By conducting extensive experiments we show that entailing generalization substantially boosts HALL’s performance and quality (where quality corresponds to the number of reported generalized solutions per instance), with the best results achieved by combining satisfying and entailing generalization.

Cite as

Dror Fried, Alexander Nadel, Roberto Sebastiani, and Yogev Shalmon. Entailing Generalization Boosts Enumeration. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fried_et_al:LIPIcs.SAT.2024.13,
  author =	{Fried, Dror and Nadel, Alexander and Sebastiani, Roberto and Shalmon, Yogev},
  title =	{{Entailing Generalization Boosts Enumeration}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{13:1--13:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.13},
  URN =		{urn:nbn:de:0030-drops-205351},
  doi =		{10.4230/LIPIcs.SAT.2024.13},
  annote =	{Keywords: Generalization, Minimization, Prime Implicant, AllSAT, SAT, Circuits}
}

Document

DOI: 10.4230/LIPIcs.SAT.2024.19

On Limits of Symbolic Approach to SAT Solving

Authors: Dmitry Itsykson and Sergei Ovcharov

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract

We study the symbolic approach to the propositional satisfiability problem proposed by Aguirre and Vardi in 2001 based on OBDDs and symbolic quantifier elimination. We study the theoretical limitations of the most general version of this approach where it is allowed to dynamically change variable order in OBDD. We refer to algorithms based on this approach as OBDD(∧, ∃, reordering) algorithms. We prove the first exponential lower bound of OBDD(∧, ∃, reordering) algorithms on unsatisfiable formulas, and give an example of formulas having short tree-like resolution proofs that are exponentially hard for OBDD(∧, ∃, reordering) algorithms. We also present the first exponential lower bound for natural formulas with clear combinatorial meaning: every OBDD(∧, ∃, reordering) algorithm runs exponentially long on the binary pigeonhole principle BPHP^{n+1}_n.

Cite as

Dmitry Itsykson and Sergei Ovcharov. On Limits of Symbolic Approach to SAT Solving. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 19:1-19:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{itsykson_et_al:LIPIcs.SAT.2024.19,
  author =	{Itsykson, Dmitry and Ovcharov, Sergei},
  title =	{{On Limits of Symbolic Approach to SAT Solving}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{19:1--19:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.19},
  URN =		{urn:nbn:de:0030-drops-205415},
  doi =		{10.4230/LIPIcs.SAT.2024.19},
  annote =	{Keywords: Symbolic quantifier elimination, OBDD, lower bounds, tree-like resolution, proof complexity, error-correcting codes, binary pigeonhole principle}
}

Document

DOI: 10.4230/LIPIcs.SAT.2024.28

Strategy Extraction by Interpolation

Authors: Friedrich Slivovsky

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract

In applications, QBF solvers are often required to generate strategies. This typically involves a process known as strategy extraction, where a Boolean circuit encoding a strategy is computed from a proof. It has previously been observed that Craig interpolation in propositional logic can be seen as a special case of QBF strategy extraction. In this paper we explore this connection further and show that, conversely, any strategy for a false QBF corresponds to a sequence of interpolants in its complete (Herbrand) expansion. Inspired by this correspondence, we present a new strategy extraction algorithm for the expansion-based proof system Exp+Res. Its asymptotic running time matches the best known bound of O(mn) for a proof with m lines and n universally quantified variables. We report on experiments comparing this algorithm with a strategy extraction algorithm based on combining partial strategies, as well as with round-based strategy extraction.

Cite as

Friedrich Slivovsky. Strategy Extraction by Interpolation. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{slivovsky:LIPIcs.SAT.2024.28,
  author =	{Slivovsky, Friedrich},
  title =	{{Strategy Extraction by Interpolation}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.28},
  URN =		{urn:nbn:de:0030-drops-205509},
  doi =		{10.4230/LIPIcs.SAT.2024.28},
  annote =	{Keywords: QBF, Expansion, Strategy Extraction, Interpolation}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.23

Exponential Separation Between Powers of Regular and General Resolution over Parities

Authors: Sreejata Kishor Bhattacharya, Arkadev Chattopadhyay, and Pavel Dvořák

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

Proving super-polynomial lower bounds on the size of proofs of unsatisfiability of Boolean formulas using resolution over parities is an outstanding problem that has received a lot of attention after its introduction by Itsykson and Sokolov [Dmitry Itsykson and Dmitry Sokolov, 2014]. Very recently, Efremenko, Garlík and Itsykson [Klim Efremenko et al., 2023] proved the first exponential lower bounds on the size of ResLin proofs that were additionally restricted to be bottom-regular. We show that there are formulas for which such regular ResLin proofs of unsatisfiability continue to have exponential size even though there exist short proofs of their unsatisfiability in ordinary, non-regular resolution. This is the first super-polynomial separation between the power of general ResLin and that of regular ResLin for any natural notion of regularity. Our argument, while building upon the work of Efremenko et al. [Klim Efremenko et al., 2023], uses additional ideas from the literature on lifting theorems.

Cite as

Sreejata Kishor Bhattacharya, Arkadev Chattopadhyay, and Pavel Dvořák. Exponential Separation Between Powers of Regular and General Resolution over Parities. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 23:1-23:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhattacharya_et_al:LIPIcs.CCC.2024.23,
  author =	{Bhattacharya, Sreejata Kishor and Chattopadhyay, Arkadev and Dvo\v{r}\'{a}k, Pavel},
  title =	{{Exponential Separation Between Powers of Regular and General Resolution over Parities}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{23:1--23:32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.23},
  URN =		{urn:nbn:de:0030-drops-204191},
  doi =		{10.4230/LIPIcs.CCC.2024.23},
  annote =	{Keywords: Proof Complexity, Regular Reslin, Branching Programs, Lifting}
}

Document

DOI: 10.4230/LIPIcs.SEA.2024.7

Local Search k-means++ with Foresight

Authors: Theo Conrads, Lukas Drexler, Joshua Könen, Daniel R. Schmidt, and Melanie Schmidt

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract

Since its introduction in 1957, Lloyd’s algorithm for k-means clustering has been extensively studied and has undergone several improvements. While in its original form it does not guarantee any approximation factor at all, Arthur and Vassilvitskii (SODA 2007) proposed k-means++ which enhances Lloyd’s algorithm by a seeding method which guarantees a 𝒪(log k)-approximation in expectation. More recently, Lattanzi and Sohler (ICML 2019) proposed LS++ which further improves the solution quality of k-means++ by local search techniques to obtain a 𝒪(1)-approximation. On the practical side, the greedy variant of k-means++ is often used although its worst-case behaviour is provably worse than for the standard k-means++ variant. We investigate how to improve LS++ further in practice. We study two options for improving the practical performance: (a) Combining LS++ with greedy k-means++ instead of k-means++, and (b) Improving LS++ by better entangling it with Lloyd’s algorithm. Option (a) worsens the theoretical guarantees of k-means++ but improves the practical quality also in combination with LS++ as we confirm in our experiments. Option (b) is our new algorithm, Foresight LS++. We experimentally show that FLS++ improves upon the solution quality of LS++. It retains its asymptotic runtime and its worst-case approximation bounds.

Cite as

Theo Conrads, Lukas Drexler, Joshua Könen, Daniel R. Schmidt, and Melanie Schmidt. Local Search k-means++ with Foresight. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{conrads_et_al:LIPIcs.SEA.2024.7,
  author =	{Conrads, Theo and Drexler, Lukas and K\"{o}nen, Joshua and Schmidt, Daniel R. and Schmidt, Melanie},
  title =	{{Local Search k-means++ with Foresight}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.7},
  URN =		{urn:nbn:de:0030-drops-203727},
  doi =		{10.4230/LIPIcs.SEA.2024.7},
  annote =	{Keywords: k-means clustering, kmeans++, greedy, local search}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2024.18

Representation of Peano Arithmetic in Separation Logic

Authors: Sohei Ito and Makoto Tatsuta

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

Separation logic is successful for software verification of heap-manipulating programs. Numbers are necessary to be added to separation logic for verification of practical software where numbers are important. However, properties of the validity such as decidability and complexity for separation logic with numbers have not been fully studied yet. This paper presents the translation of Pi-0-1 formulas in Peano arithmetic to formulas in a small fragment of separation logic with numbers, which consists only of the intuitionistic points-to predicate, 0 and the successor function. Then this paper proves that a formula in Peano arithmetic is valid in the standard model if and only if its translation in this fragment is valid in the standard interpretation. As a corollary, this paper also gives a perspective proof for the undecidability of the validity in this fragment. Since Pi-0-1 formulas can describe consistency of logical systems and non-termination of computations, this result also shows that these properties discussed in Peano arithmetic can also be discussed in such a small fragment of separation logic with numbers.

Cite as

Sohei Ito and Makoto Tatsuta. Representation of Peano Arithmetic in Separation Logic. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ito_et_al:LIPIcs.FSCD.2024.18,
  author =	{Ito, Sohei and Tatsuta, Makoto},
  title =	{{Representation of Peano Arithmetic in Separation Logic}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.18},
  URN =		{urn:nbn:de:0030-drops-203476},
  doi =		{10.4230/LIPIcs.FSCD.2024.18},
  annote =	{Keywords: First order logic, Separation logic, Peano arithmetic, Presburger arithmetic}
}

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