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Small Resolution Proofs for QBF using Dependency Treewidth [article]

Eduard Eiben, Robert Ganian, Sebastian Ordyniak
2017 arXiv   pre-print
Dependency treewidth pushes the frontiers of tractability for QBF by overcoming the limitations of previously introduced variants of treewidth for QBF.  ...  In this work we introduce and develop dependency treewidth, a new structural parameter based on treewidth which allows the efficient solution of QBF instances.  ...  The authors wish to thank the anonymous reviewers for their helpful comments. Eduard Eiben acknowledges support by the Austrian Science Fund (FWF, projects P26696 and W1255-N23).  ... 
arXiv:1711.02120v1 fatcat:dvyygn3dyrdudn7hqchxyg53j4

Small Resolution Proofs for QBF using Dependency Treewidth

Eduard Eiben, Robert Ganian, Sebastian Ordyniak
unpublished
Dependency treewidth pushes the frontiers of tractability for QBF by overcoming the limitations of previously introduced variants of treewidth for QBF.  ...  In this work we introduce and develop dependency treewidth, a new structural parameter based on treewidth which allows the efficient solution of QBF instances.  ...  E has unbounded dependency treewidth w.r.t. any dependency poset but CD-width at most 1. 28:8 Small Resolution Proofs for QBF using Dependency Treewidth Sketch of Proof.  ... 
fatcat:u467b5oodbbg5ibfv5hexj7tme

Using Decomposition-Parameters for QBF: Mind the Prefix!

Eduard Eiben, Robert Ganian, Sebastian Ordyniak
2020 Journal of computer and system sciences (Print)  
Recently, Atserias and Oliva (2014) showed that, unlike for SAT, many of the well-known decompositional parameters (such as treewidth and pathwidth) do not allow efficient algorithms for QBF.  ...  The main reason for this seems to be the lack of awareness of these parameters towards the dependencies between variables of a QBF formula.  ...  Dependency Schemes and Posets for QBF We use dependency posets to provide a general and formal way of speaking about the various dependency schemes introduced for QBF [32] .  ... 
doi:10.1016/j.jcss.2019.12.005 fatcat:nwxsvrkltja5xj6ygvdwfukq6y

Front Matter, Table of Contents, Preface, Conference Organization

Rolf Niedermeier, Brigitte Vallée, Marc Herbstritt
2018 Symposium on Theoretical Aspects of Computer Science  
Paweł Rzążewski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27:1-27:15 Small Resolution Proofs for QBF using Dependency Treewidth Eduard Eiben, Robert Ganian, and Sebastian Ordyniak  ...  . . . . . . . . . . . . . . . . . . . . . . 26:1-26:15 Finding List Homomorphisms from Bounded-treewidth Graphs to Reflexive Graphs: a Complete Complexity Characterization László Egri, Dániel Marx, and  ...  Moreover, we thank Michael Wagner from the Dagstuhl/LIPIcs team for assisting us in the publication process and the final production of the proceedings.  ... 
doi:10.4230/lipics.stacs.2018.0 dblp:conf/stacs/X18 fatcat:jgvgsziyhbc6jkcm4wszlwgrsa

The Power of Non-Ground Rules in Answer Set Programming [article]

Manuel Bichler, Michael Morak, Stefan Woltran
2016 arXiv   pre-print
Here, we propose a novel paradigm for encoding hard problems in ASP by making explicit use of large rules which depend on the actual instance of the problem.  ...  This paper is under consideration for acceptance into TPLP.  ...  very small rules that are easy to process for the grounder.  ... 
arXiv:1608.01856v1 fatcat:6l6xwqzf6re3bhrwfgb7g6y4v4

Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology [chapter]

Markus Hecher, Patrick Thier, Stefan Woltran
2020 Lecture Notes in Computer Science  
Treewidth is one of the most prominent structural parameters.  ...  Finally, we provide nested DP algorithms and implementations relying on database technology for variants and extensions of Boolean satisfiability.  ...  For Sat, these solvers are of particular interest as there is a well-known correspondence between treewidth and resolution width [2] .  ... 
doi:10.1007/978-3-030-51825-7_25 fatcat:5cdjcgdqrfgzrckiqrnzdox2qy

Proof Complexity of Symbolic QBF Reasoning [article]

Stefan Mengel, Friedrich Slivovsky
2021 arXiv   pre-print
We introduce and investigate symbolic proof systems for Quantified Boolean Formulas (QBF) operating on Ordered Binary Decision Diagrams (OBDDs).  ...  This allows us to derive strong lower bounds against symbolic QBF proof systems that are independent of the variable ordering of the underlying OBDDs, and that hold even if the proof system is allowed  ...  We simulate QU-resolution line by line, using the fact that all clauses have small OBDD representations.  ... 
arXiv:2104.02563v1 fatcat:cgfyt72dibezhewfnm4znldgy4

Fighting Perebor: New and Improved Algorithms for Formula and QBF Satisfiability

Rahul Santhanam
2010 2010 IEEE 51st Annual Symposium on Foundations of Computer Science  
Our second main result is a deterministic algorithm running in time 2 n−Ω(n/ log(n)) for solving QBFs in which the number of occurrences of any variable is bounded by a constant.  ...  As a byproduct of the technique used to establish our first main result, we show that every function computable by linear-size formulae can be represented by decision trees of size 2 n−Ω(n) .  ...  We attempt to give some intuition for how the lemma will be used in the proof of the main result.  ... 
doi:10.1109/focs.2010.25 dblp:conf/focs/Santhanam10 fatcat:kwv6bp73jfe6dmm5rn3byo324a

Recent Trends in Knowledge Compilation (Dagstuhl Seminar 17381)

Adnan Darwiche, Pierre Marquis, Dan Suciu, Stefan Szeider, Marc Herbstritt
2018 Dagstuhl Reports  
A closely related question is the following: Do unsatisfiable CNFs admit FPT-size resolution refutations, parameterized by incidence treewidth?  ...  In this talk, we focus on queries whose lineages admit circuit implementations with small treewidth, and investigate their compilability within tame classes of decision diagrams.  ...  Dependency Learning for QBF. SAT 2017 ForcLift and PySDD Wannes Meert (KU Leuven, BE)  ... 
doi:10.4230/dagrep.7.9.62 dblp:journals/dagstuhl-reports/DarwicheMSS17 fatcat:gitzmlyoxjaapcyjhtpsaqxs3e

Augmenting tractable fragments of abstract argumentation

Wolfgang Dvořák, Sebastian Ordyniak, Stefan Szeider
2012 Artificial Intelligence  
For our study we use a broad setting and consider several different semantics. For the algorithmic results we utilize recent advances in fixed-parameter tractability.  ...  Our approach makes known algorithms defined for restricted fragments generally applicable, at a computational cost that scales with the distance from the fragment.  ...  Acknowledgements We thank the anonymous reviewers for their valuable suggestions that helped to improve the presentation of the paper.  ... 
doi:10.1016/j.artint.2012.03.002 fatcat:zi5kasv7ufej3cxgxswvjkrk4i

Deduction Beyond Satisfiability (Dagstuhl Seminar 19371)

Carsten Fuhs, Philipp Rümmer, Renate Schmidt, Cesare Tinelli, Michael Wagner
2020 Dagstuhl Reports  
However, automated deduction methods and tools are increasingly being used to address problems with more complex answers, for instance to generate programs from formal specifications, compute complexity  ...  ., to count the number of models of a formula, compute the set of all consequences of an ontology, identify missing information in a knowledge base, transform and mine proofs, or analyze probabilistic  ...  We show how knowledge compilation can be used as a tool for solving QBF and more.  ... 
doi:10.4230/dagrep.9.9.23 dblp:journals/dagstuhl-reports/FuhsRST19 fatcat:j6moci5zgvgjzgpsqblemwsrlm

On the combination of logical and probabilistic models for information analysis

Jingsong Wang, John Byrnes, Marco Valtorta, Michael Huhns
2011 Applied intelligence (Boston)  
In particular, we show that hard evidential updates in which the premises of a proof are found to be true force the conclusions of the proof to be true with probability one, regardless of any dependencies  ...  We define a formalism for the conversion of automatically generated natural deduction proof trees into Bayesian networks.  ...  QBF is known to be PSPACEcomplete.  ... 
doi:10.1007/s10489-010-0272-x fatcat:htgeqdq56nfrlpjcmwrebwiexy

Confronting intractability via parameters

Rodney G. Downey, Dimitrios M. Thilikos
2011 Computer Science Review  
Whilst the theory has been widely used in a number of areas of applications including computational biology, linguistics, VLSI design, learning theory and many others, knowledge of the area is highly varied  ...  Kolliopoulos, Moritz Müller, Saket Saurabh, and Geoff Whittle for corrections and helpful comments.  ...  We designate a gate as large or small depending on the fan-in allowed, where small will be some fixed number.  ... 
doi:10.1016/j.cosrev.2011.09.002 fatcat:4efih5lobfbjdgyuu2ccbqlbbq

Confronting Intractability via Parameters [article]

Rodney G. Downey, Dimitrios M. Thilikos
2011 arXiv   pre-print
Whilst the theory has been widely used in a number of areas of applications including computational biology, linguistics, VLSI design, learning theory and many others, knowledge of the area is highly varied  ...  Kolliopoulos, Moritz Müller, Saket Saurabh, and Geoff Whittle for corrections and helpful comments.  ...  We designate a gate as large or small depending on the fan-in allowed, where small will be some fixed number.  ... 
arXiv:1106.3161v6 fatcat:6eqwtzfmunffzokn47lqyb6xwq

Methods for solving reasoning problems in abstract argumentation – A survey

Günther Charwat, Wolfgang Dvořák, Sarah A. Gaggl, Johannes P. Wallner, Stefan Woltran
2015 Artificial Intelligence  
This calls for advanced techniques when it comes to implementation issues, a challenge which has been recently faced from different angles.  ...  In this survey, we give an overview on different methods for solving reasoning problems in abstract argumentation and compare their particular features.  ...  The authors are grateful to the anonymous reviewers for their detailed reviews and helpful comments as well as to all colleagues who discussed their works and systems with the authors.  ... 
doi:10.1016/j.artint.2014.11.008 pmid:25737590 pmcid:PMC4318991 fatcat:qrw6bic4vjc5zdqkvi5tlhcs7m
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