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How QBF Expansion Makes Strategy Extraction Hard [chapter]

Leroy Chew, Judith Clymo
2020 Lecture Notes in Computer Science  
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.  ...  In this paper we show that the QBF proof checking format QRAT (Quantified Resolution Asymmetric Tautologies) by Heule, Biere and Seidl cannot have polynomial time strategy extraction unless P=PSPACE.  ...  This is due to QRAT providing short proofs to formulas that have PSPACE-hard strategies. Thus we show an asymmetry between the refutation of false QBF and proof of true QBF in the QRAT system.  ... 
doi:10.1007/978-3-030-51074-9_5 fatcat:kmkx2rdyivcsngizzk4tpf5vru

Lower Bounds

Olaf Beyersdorff, Ilario Bonacina, Chew Leroy
2016 Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16  
Here we provide such a formal relation between lower bounds for circuit classes and lower bounds for Frege systems for quantified Boolean formulas (QBF).  ...  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  ...  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

Frege Systems for Quantified Boolean Logic

Olaf Beyersdorff, Ilario Bonacina, Leroy Chew, Jan Pich
2020 Journal of the ACM  
We define and investigate Frege systems for quantified Boolean formulas (QBF).  ...  Such a direct transfer from circuit to proof complexity lower bounds has often been postulated for propositional systems but had not been formally established in such generality for any proof systems prior  ...  ACKNOWLEDGMENTS The authors are grateful to Nicola Galesi and Albert Atserias for interesting discussions on this work and circuit complexity in general, and to Emil Jeřábek for pointing out the separation  ... 
doi:10.1145/3381881 fatcat:sz33byvb2vfg5bttavp4ic3e2i

Symmetries of Quantified Boolean Formulas [chapter]

Manuel Kauers, Martina Seidl
2018 Lecture Notes in Computer Science  
Our framework naturally incorporates the duality of universal and existential symmetries resulting in a general basis for QBF symmetry breaking.  ...  While symmetries are well understood for Boolean formulas and successfully exploited in practical SAT solving, less is known about symmetries in quantified Boolean formulas (QBF).  ...  Our goal in this paper is to develop an explicit, uniform, and general theory for symmetries of QBFs. The theory is developed from scratch, and we include detailed proofs of all theorems.  ... 
doi:10.1007/978-3-319-94144-8_13 fatcat:g45zy4a7j5fnzep445llndguzq

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.  ...  Clearly, this is a false QBF as it expresses that x is both in and outside L.  ... 
doi:10.4230/lipics.stacs.2015.76 dblp:conf/stacs/BeyersdorffCJ15 fatcat:qsslfqhadrc3thcwgjhfibky7e

Satisfiability-Based Methods for Reactive Synthesis from Safety Specifications [article]

Roderick Bloem and Uwe Egly and Patrick Klampfl and Robert Könighofer and Florian Lonsing and Martina Seidl
2016 arXiv   pre-print
We present novel algorithms for safety specifications that use decision procedures for propositional formulas (SAT solvers), Quantified Boolean Formulas (QBF solvers), or Effectively Propositional Logic  ...  Our optimizations expand quantifiers and utilize unreachable states and variable independencies. Our approach outperforms a simple BDD-based tool and is competitive with a highly optimized one.  ...  , and Fabian Tschiatschek and Mario Werner for their BDD-based synthesis tool.  ... 
arXiv:1604.06204v1 fatcat:vp2t4tiu55bvjfsdkh7ntaezku

Understanding Gentzen and Frege Systems for QBF

Olaf Beyersdorff, Ján Pich
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
Recently Beyersdorff, Bonacina, and Chew [10] introduced a natural class of Frege systems for quantified Boolean formulas (QBF) and showed strong lower bounds for restricted versions of these systems.  ...  Technically, our results rest on a formalised strategy extraction theorem for EF + ∀red akin to witnessing in intuitionistic S 1 2 and a normal form for EF + ∀red proofs.  ...  Acknowledgments This research was supported by grant no. 48138 from the John Templeton Foundation and EPSRC grant EP/L024233/1.  ... 
doi:10.1145/2933575.2933597 dblp:conf/lics/BeyersdorffP16 fatcat:drqb2sqeybhzfgbrlwbjaiosni

A game characterisation of tree-like Q-Resolution size

Olaf Beyersdorff, Leroy Chew, Karteek Sreenivasaiah
2017 Journal of computer and system sciences (Print)  
In particular, we give a proof of the hardness of the formulas of Kleine Büning et al. [20] for tree-like Q-Resolution.  ...  We provide a characterisation for the size of proofs in treelike Q-Resolution by a Prover-Delayer game, which is inspired by a similar characterisation for the proof size in classical tree-like Resolution  ...  Very recently, the paper [8] introduces a general proof technique for QBF systems based on strategy extraction, that transfers circuit lower bounds to proof size lower bounds.  ... 
doi:10.1016/j.jcss.2016.11.011 fatcat:7umbb73lxvhyvci742qwx4qz44

Parallel Solving of Quantified Boolean Formulas [chapter]

Florian Lonsing, Martina Seidl
2018 Handbook of Parallel Constraint Reasoning  
In this chapter, we review and compare approaches for solving QBFs in parallel.  ...  Quantified Boolean formulas (QBFs) extend propositional logic by universal and existential quantifiers over the propositional variables.  ...  For the development of robust parallel QBF solvers, it may be useful to combine the generation of proofs and strategies outlined above with approaches to automated testing and debugging.  ... 
doi:10.1007/978-3-319-63516-3_4 fatcat:i4s2rjgx3zfi3ll7npc77poiua

Extending Merge Resolution to a Family of Proof Systems [article]

Sravanthi Chede, Anil Shukla
2021 arXiv   pre-print
Reason.'2021]) is a recently introduced proof system for false QBFs. It stores the countermodels as merge maps.  ...  Hence corresponding to each such R, we have a sound and refutationally complete QBF-proof system in MRes-R.  ...  Acknowledgements We would like to thank Gaurav Sood for many important discussions, comments and suggestions regarding this paper.  ... 
arXiv:2112.11044v1 fatcat:od3ewtk5qnetlfudrjcssum7ny

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] .  ...  We refer to the set of free variables of formula ϕ as free(ϕ). A closed QBF is a formula without free variables. Closed QBFs are either true or false.  ... 
doi:10.3233/sat190121 fatcat:xup2acwn5jg2loexwb6fk5nfie

cc{\rm T}: A Tool for Checking Advanced Correspondence Problems in Answer-Set Programming

Johannes Oetsch, Martina Seidl, Hans Tompits, Stefan Woltran
2006 2006 15th International Conference on Computing  
In recent work, a general framework for specifying correspondences between logic programs under the answer-set semantics has been defined.  ...  In this paper, we describe a system, called cc , to verify program correspondences in this general framework, relying on linear-time constructible reductions to quantified propositional logic using extant  ...  We use here a parameterisation for the generation of random QBFs such that the benchmark set yields a nearly 50% distribution between the true and false instances.  ... 
doi:10.1109/cic.2006.29 fatcat:xoy3fhuulfar3fxrtxkhvjnhde

Moving in a network under random failures: A complexity analysis

Dominik Klein, Frank G. Radmacher, Wolfgang Thomas
2012 Science of Computer Programming  
resp. an LTL formula ϕ), and also a probability p ∈ [p − ε, p + ε], is there a strategy for Runner to reach F (resp. to satisfy ϕ) with a probability ≥ p ?  ...  Runner wins if the generated finite path satisfies a "winning condition", namely that a vertex of some predefined target set is reached, or -more generallythat the generated path satisfies a given formula  ...  We thank Lukasz Kaiser for his help regarding Lemma 15. We also thank the anonymous referees for their valuable comments and suggestions in improving this paper.  ... 
doi:10.1016/j.scico.2010.05.009 fatcat:gupasnb42rbp5irlljvdt6tnse

cc⊤ on Stage: Generalised Uniform Equivalence Testing for Verifying Student Assignment Solutions [chapter]

Johannes Oetsch, Martina Seidl, Hans Tompits, Stefan Woltran
2009 Lecture Notes in Computer Science  
One such notion is relativised uniform equivalence with projection, which extends standard uniform equivalence via two additional parameters: one for specifying the input alphabet and one for specifying  ...  In this paper, we discuss an application of cc for verifying the correctness of students' solutions drawn from a laboratory course on logic programming, employing relativised uniform equivalence with projection  ...  We use superscripts as a general renaming scheme for formulas and rules.  ... 
doi:10.1007/978-3-642-04238-6_32 fatcat:l3vmucfz2rft7glydxmaqzvtia

Detecting Unrealizability of Distributed Fault-tolerant Systems

Bernd Finkbeiner, Leander Tentrup, Erika Abraham
2015 Logical Methods in Computer Science  
We present a method for finding such counterexamples both for the classic distributed realizability problem and for the fault-tolerant realizability problem.  ...  Experimental results, obtained with a QBF-based prototype implementation, show that our method finds simple errors very quickly, and even problems with high combinatorial complexity, like the Byzantine  ...  We thank Swen Jacobs for comments on an earlier version of this paper.  ... 
doi:10.2168/lmcs-11(3:12)2015 fatcat:gq2nxd7q7bboficu2h5srjt6rq
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