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Clausal Abstraction for DQBF (full version) [article]

Leander Tentrup, Markus N. Rabe
2019 arXiv   pre-print
In this paper, we lift the clausal abstraction algorithm for quantified Boolean formulas (QBF) to DQBF.  ...  For DQBF we need to generalize this principle to partial orders of abstractions.  ...  Lifting Clausal Abstraction In this section, we lift clausal abstraction to DQBF.  ... 
arXiv:1808.08759v3 fatcat:2pcvwmnnpfh2bhw7aqrzxgzmai

A Resolution-Style Proof System for DQBF [chapter]

Markus N. Rabe
2017 Lecture Notes in Computer Science  
This paper presents a sound and complete proof system for Dependency Quantified Boolean Formulas (DQBF) using resolution, universal reduction, and a new proof rule that we call fork extension.  ...  Seshia, Martin Suda, Leander Tentrup, and Ralf Wimmer for supportive comments and detailed discussions on this work.  ...  For all other clauses soundness follows from the soundness of QU-resolution for DQBF [2, 30] . ∀Red.  ... 
doi:10.1007/978-3-319-66263-3_20 fatcat:5lcx2lrb4bgcjafbclxwopblve

Dependency Stochastic Boolean Satisfiability: A Logical Formalism for NEXPTIME Decision Problems with Uncertainty [article]

Nian-Ze Lee, Jie-Hong R. Jiang
2021 arXiv   pre-print
With the theoretical foundations paved in this work, we hope to encourage the development of DSSAT solvers for potential broad applications.  ...  To provide a logical formalism of such problems, we extend the Dependency Quantified Boolean Formula (DQBF), a representative problem in the NEXPTIME-complete class, to its stochastic variant, named Dependency  ...  Acknowledgments The authors are grateful to Christoph Scholl, Ralf Wimmer, and Bernd Becker for valuable discussions motivating this work.  ... 
arXiv:1911.04112v3 fatcat:dpvqiz7pava2xn5vbupitorqga

Certified DQBF Solving by Definition Extraction [article]

Franz-Xaver Reichl, Friedrich Slivovsky, Stefan Szeider
2021 arXiv   pre-print
Towards certification of false formulas, we prove that clauses can be derived in an expansion-based proof system for DQBF.  ...  A key feature of the proposed procedure is that it is certifying by design: for true DQBF, models can be returned at minimal overhead.  ...  The solver dCAQE lifts clausal abstraction from QBF to DQBF [47] .  ... 
arXiv:2106.02550v1 fatcat:t2p3tmhlrzfgxbcjcrunqzxgbq

Building Strategies into QBF Proofs

Olaf Beyersdorff, Joshua Blinkhorn, Meena Mahajan
2020 Journal of automated reasoning  
Our approach also naturally lifts to dependency QBFs (DQBF), where it yields the first sound and complete CDCL-style calculus for DQBF, thus opening future avenues into CDCL-based DQBF solving.  ...  Strategy extraction is of great importance for quantified Boolean formulas (QBF), both in solving and proof complexity.  ...  Certainly, the associated solver DCAQE [55] belongs to the paradigm of clausal abstraction, rather than conflict-driven clause learning.  ... 
doi:10.1007/s10817-020-09560-1 pmid:33487785 pmcid:PMC7808293 fatcat:loc7yqxzyfckvg4wz32svv43ji

CAQE and QuAbS: Abstraction Based QBF Solvers

Leander Tentrup, Martina Seidl, Luca Pulina
2019 Journal on Satisfiability, Boolean Modeling and Computation  
We present a detailed description, analysis, and evaluation of the clausal abstraction approach for solving quantified Boolean formulas (QBF).  ...  This article gives a complete overview over the clausal abstraction approach for QBF and is partially based on prior published work [36, 66, 72] .  ...  Algorithm 1 Clausal Abstraction Algorithm for 2QBF1: procedure solve ∀∃ (∀X.  ... 
doi:10.3233/sat190121 fatcat:xup2acwn5jg2loexwb6fk5nfie

Program Synthesis as Dependency Quantified Formula Modulo Theory

Priyanka Golia, Subhajit Roy, Kuldeep S. Meel
2021 Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence   unpublished
We rely on the progress in DQBF solving to design DQBF-based synthesizers that outperform the domain-specific program synthesis techniques; thereby positioning DQBF as a core representation language for  ...  Furthermore, the general-purpose DQBF solvers perform on par with domain-specific synthesis techniques.  ...  [2012] proposed the first DPLL based algorithm to lift the QBF solving to DQBF; Tentrup and Rabe [2019] followed the same direction, and proposed the idea of using clausal abstraction for DQBF solving  ... 
doi:10.24963/ijcai.2021/261 fatcat:gmouqyvlunfupfjkewudtaagai

QBFRelay, QRATPre+, and DepQBF: Incremental Preprocessing Meets Search-Based QBF Solving

Florian Lonsing, Martina Seidl, Luca Pulina
2019 Journal on Satisfiability, Boolean Modeling and Computation  
The submitted one comes with a built-in module for limited preprocessing based on detecting clausal patterns that result from Tseitin translation [35] .  ...  This kind of abstractions are a restricted form of those applied in QRATPre + .  ... 
doi:10.3233/sat190122 fatcat:wog5nj2kh5acpivxlthxmcqjhq

Towards Smarter MACE-style Model Finders

Mikolas Janota, Martin Suda
unpublished
Further, finite model finders provide useful information for counter-satisfiable conjectures.  ...  Finite model finders represent a powerful tool for deciding problems with the finite model property, such as the Bernays-Sch ̈onfinkel fragment (EPR).  ...  This is practically useful in clausal inputs where the input is of the form (∀ x 1 )(C 1 ) ∧ · · · ∧ (∀ x n )(C n ).  ... 
doi:10.29007/w42s fatcat:26yg3melqzejrdue7emmtandgu