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How QBF Expansion Makes Strategy Extraction Hard [chapter]

Leroy Chew, Judith Clymo
2020 Lecture Notes in Computer Science  
While expansion reasoning used in other QBF calculi can admit polynomial time strategy extraction, we find this is conditional on a property studied in proof complexity theory.  ...  In our proof, the crucial property that makes strategy extraction PSPACE-hard for this proof format is universal expansion, even expansion on a single variable.  ...  QRAT has short uniform proofs of Select(Πφ) for any QBF Πφ. Proof.  ... 
doi:10.1007/978-3-030-51074-9_5 fatcat:kmkx2rdyivcsngizzk4tpf5vru

QRAT Polynomially Simulates Merge Resolution [article]

Sravanthi Chede, Anil Shukla
2021 arXiv   pre-print
Reason.'2017] proof system was designed to capture QBF preprocessing. QRAT can simulate both the expansion-based proof system ∀Exp+Res and CDCL-based QBF proof system LD-Q-Res.  ...  In this paper, we show a short QRAT refutation of the SquaredEquality formulas. We further show that QRAT strictly p-simulates MRes.  ...  In this short paper, we extend the importance of QRAT among QBF proof systems by showing that QRAT even polynomially simulates MRes.  ... 
arXiv:2107.09320v1 fatcat:khn37rgxojaydolrvm4ofvpwqi

Expansion-Based QBF Solving Without Recursion [article]

Roderick Bloem, Nicolas Braud-Santoni, Vedad Hadzic, Uwe Egly, Florian Lonsing, Martina Seidl
2018 arXiv   pre-print
In recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential  ...  In this paper, we present a novel algorithm for expansion-based QBF solving that deals with the whole quantifier prefix at once. Hence recursive applications of the expansion principle are avoided.  ...  After a short recapitulation of expansion in Section IV, our novel non-recursive expansionbased algorithm is presented in Section V.  ... 
arXiv:1807.08964v2 fatcat:mtkeig64inhvjmgghjkrbtosl4

SAT and Interactions (Dagstuhl Seminar 20061)

Olaf Beyersdorff, Uwe Egly, Meena Mahajan, Cláudia Nalon
2020 Dagstuhl Reports  
The seminar brought together theoreticians and practitioners from the areas of proof complexity and proof theory, SAT and QBF solving, MaxSAT, and modal logics, who discussed recent developments in their  ...  We show this calculus is the result of a Curry-Howard style interpretation of a deep-inference proof system, and prove that it has natural properties with respect to the lambda-calculus: confluence and  ...  References Tractable QBF via Knowledge Compilation References How QBF Expansion Makes Strategy Extraction Hard While expansion reasoning used in other QBF calculi can admit polynomial time strategy  ... 
doi:10.4230/dagrep.10.2.1 dblp:journals/dagstuhl-reports/BeyersdorffEMN20 fatcat:q6vjxmce4bd2nkm3vym2qkvqam

Lower Bounds

Olaf Beyersdorff, Ilario Bonacina, Chew Leroy
2016 Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16  
A general and long-standing belief in the proof complexity community asserts that there is a close connection between progress in lower bounds for Boolean circuits and progress in proof size lower bounds  ...  For us the most important case is a new and natural hierarchy of QBF Frege systems C-Frege + ∀red that parallels the well-studied propositional hierarchy of C-Frege systems, where lines in proofs are restricted  ...  The authors are grateful to Nicola Galesi and Albert Atserias for interesting discussions about this work and circuit complexity in general.  ... 
doi:10.1145/2840728.2840740 dblp:conf/innovations/BeyersdorffBC16 fatcat:bhoydv233rgo3gnpc6hgdto76u

Strong (D)QBF Dependency Schemes via Tautology-Free Resolution Paths [chapter]

Olaf Beyersdorff, Joshua Blinkhorn, Tomáš Peitl
2020 Lecture Notes in Computer Science  
path dependency scheme when used in the expansion DQBF system ∀Exp+Res.  ...  More precisely, in our framework a proof of Φ in P(D) is simply a P proof of D(Φ), where D is a mapping between DQBFs.  ...  Tautology-Free Dependencies for QBF We now turn our attention to dedicated QBF proof complexity, in particular to the QBF proof systems Q-Res(D) [35] that were introduced to model dependency-aware QBF  ... 
doi:10.1007/978-3-030-51825-7_28 fatcat:xtbh2tdbdbc35c7x7mtm53uoka

Understanding cutting planes for QBFs

Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla
2018 Information and Computation  
weaker than QBF Frege and stronger than the CDCL-based QBF resolution systems Q-Res and QU-Res, it turns out to be incomparable to even the weakest expansion-based QBF resolution system ∀Exp+Res.  ...  We define a cutting planes system CP+∀red for quantified Boolean formulas (QBF) and analyse the proof-theoretic strength of this new calculus.  ...  Semantic cutting planes for QBFs The classical Cutting Planes proof system can be extended to the semantic Cutting Planes proof system by allowing the following semantic inference rule: from inequalities  ... 
doi:10.1016/j.ic.2018.08.002 fatcat:v5qjxywoqnexldwvfwrvsrj4l4

A Unified Proof System for QBF Preprocessing [chapter]

Marijn J. H. Heule, Martina Seidl, Armin Biere
2014 Lecture Notes in Computer Science  
Especially for universal expansion proof checking was not possible so far.  ...  In combination with an extended version of universal reduction, they are sufficient to efficiently express all preprocessing techniques used in state-of-the-art preprocessors including universal expansion  ...  Third, our proof system can simulate universal expansion and other existing techniques.  ... 
doi:10.1007/978-3-319-08587-6_7 fatcat:ew3o4nk5j5f2dktgx3avwvnw3e

SAT and Interactions (Dagstuhl Seminar 16381)

Olaf Beyersdorff, Nadia Creignou, Uwe Egly, Heribert Vollmer, Marc Herbstritt
2017 Dagstuhl Reports  
A key objective of the seminar has been to initiate or consolidate discussions among the different groups for a fresh attack on one of the most important problems in theoretical computer science and mathematics  ...  Unlike in SAT solving, where CDCL is the dominating approach, in QBF solving QCDCL is complemented by variable expansion.  ...  Several proof systems have been designed in the last couple of decades to handle QBFs, starting from the most basic Q-Resolution and Expansion+∀-Reduction and going up to Frege+∀-Reduction.  ... 
doi:10.4230/dagrep.6.9.74 dblp:journals/dagstuhl-reports/BeyersdorffCEV16 fatcat:boyfegt3erba5j5hbdheironmu

Proof Complexity of Resolution-based QBF Calculi

Olaf Beyersdorff, Leroy Chew, Mikolás Janota, Marc Herbstritt
2015 Symposium on Theoretical Aspects of Computer Science  
In this paper we exhibit a new and elegant proof technique for showing lower bounds in QBF proof systems based on strategy extraction.  ...  Proof systems for quantified Boolean formulas (QBFs) provide a theoretical underpinning for the performance of important QBF solvers.  ...  Most importantly, our results show striking separations between all proof systems modelling CDCLbased QBF solving vs. proof systems modelling expansion-based solving.  ... 
doi:10.4230/lipics.stacs.2015.76 dblp:conf/stacs/BeyersdorffCJ15 fatcat:qsslfqhadrc3thcwgjhfibky7e

Conformant Planning as a Case Study of Incremental QBF Solving [chapter]

Uwe Egly, Martin Kronegger, Florian Lonsing, Andreas Pfandler
2014 Lecture Notes in Computer Science  
Since the generated QBFs have many clauses and variables in common, our approach avoids redundancy both in the encoding phase and in the solving phase.  ...  Our results are the first empirical study of incremental QBF solving in the context of planning and motivate its use in other application domains.  ...  distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in  ... 
doi:10.1007/978-3-319-13770-4_11 fatcat:fkrtsv4ez5hslhtuek24o2mzs4

Conformant planning as a case study of incremental QBF solving

Uwe Egly, Martin Kronegger, Florian Lonsing, Andreas Pfandler
2016 Annals of Mathematics and Artificial Intelligence  
Since the generated QBFs have many clauses and variables in common, our approach avoids redundancy both in the encoding phase as well as in the solving phase.  ...  QBCE allows to eliminate certain clauses from a QBF in a satisfiability preserving way.  ...  distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in  ... 
doi:10.1007/s10472-016-9501-2 fatcat:2pgojtu73jdebhorc36337xqpq

Feasible Interpolation for QBF Resolution Calculi [chapter]

Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla
2015 Lecture Notes in Computer Science  
In sharp contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems.  ...  In this paper we establish the feasible interpolation technique for all resolution-based QBF systems, whether modelling CDCL or expansion-based solving.  ...  Acknowledgements We thank Pavel Pudlák and Mikoláš Janota for helpful discussions on the relation between feasible interpolation and strategy extraction during the Dagstuhl Seminar 'Optimal Agorithms and Proofs  ... 
doi:10.1007/978-3-662-47672-7_15 fatcat:bxgxi6fck5cbtc5jozl7qqdlkq

Expansion-based QBF solving versus Q-resolution

Mikoláš Janota, Joao Marques-Silva
2015 Theoretical Computer Science  
Also, expansion can be used in QBF preprocessing [18, 19] . This practical importance of expansion motivates the theoretical study carried out in this article.  ...  In practice, Q-resolution enables producing proofs from conflict-driven DPLL-based QBF solvers. The system ∀Exp+Res can on the other hand certify certain expansion-based solvers.  ...  We would like to thank Uwe Egly and Will Klieber for various helpful conversations on QBFs. We would also like to thank the anonymous reviewers for their stimulating feedback.  ... 
doi:10.1016/j.tcs.2015.01.048 fatcat:ejpfeirhvfb3fghyodkibwxuvu

Feasible Interpolation for QBF Resolution Calculi [article]

Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla
2017 arXiv   pre-print
In sharp contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems.  ...  In this paper we establish the feasible interpolation technique for all resolution-based QBF systems, whether modelling CDCL or expansion-based solving.  ...  Acknowledgements We thank Pavel Pudlák and Mikoláš Janota for helpful discussions on the relation between feasible interpolation and strategy extraction during the Dagstuhl Seminar 'Optimal Agorithms and Proofs  ... 
arXiv:1611.01328v2 fatcat:lchhyka6arb4vkdiwmrm5sksim
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