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QBF as an Alternative to Courcelle's Theorem [article]

Michael Lampis and Stefan Mengel and Valia Mitsou
2018 arXiv   pre-print
We propose reductions to quantified Boolean formulas (QBF) as a new approach to showing fixed-parameter linear algorithms for problems parameterized by treewidth.  ...  techniques: on the one hand, in contrast to Courcelle's Theorem, we get concrete and tight guarantees for the runtime dependence on the treewidth.  ...  Treewidth has been used as an approach for finding tractable fragments of ∀∃-QBF and more generally bounded alternation QBF.  ... 
arXiv:1805.08456v1 fatcat:5bsuvghmzzfw5d6lo5joxns3wa

Lower Bounds for QBFs of Bounded Treewidth [article]

Johannes Klaus Fichte, Markus Hecher, Andreas Pfandler
2020 arXiv   pre-print
Still, an important question is to settle this as general as possible and to cover the whole polynomial hierarchy.  ...  The problem of deciding the validity (QSAT) of quantified Boolean formulas (QBF) is a vivid research area in both theory and practice.  ...  We would like to thank the reviewers as well as Stefan Szeider and Stefan Woltran for their support. Special appreciation goes to Michael Morak for early discussions.  ... 
arXiv:1910.01047v2 fatcat:fer6kppntzajxgp65mf4us6vxu

Practical algorithms for MSO model-checking on tree-decomposable graphs

Alexander Langer, Felix Reidl, Peter Rossmanith, Somnath Sikdar
2014 Computer Science Review  
Courcelle's Theorem has been used thus far as a theoretic tool to establish that linear-time algorithms exist for graph problems by demonstrating that the problem in question is expressible by an MSO formula  ...  A straightforward implementation of the algorithm in the proof of Courcelle's Theorem is useless as it runs into space-explosion problems even for small values of treewidth.  ...  Alternative Proofs of Courcelle's Theorem There are several alternative ways to prove Courcelle's Theorem.  ... 
doi:10.1016/j.cosrev.2014.08.001 fatcat:4eogxn65frdy5hr7syli5qjd5m

Bounded fixed-parameter tractability and log2n nondeterministic bits

Jörg Flum, Martin Grohe, Mark Weyer
2006 Journal of computer and system sciences (Print)  
We develop a basic theory that is centred around the class EPT of tractable problems and an EW-hierarchy of classes of intractable problems, both in the bounded sense.  ...  uses log 2 n nondeterministic bits, and in particular to the classes LOGSNP and LOGNP introduced by Papadimitriou and Yannakakis.  ...  We only sketch the changes with respect to the proof of the preceding theorem. p-QBF ept p-MC(WORDS, MSO): Let of alternation depth k be given.  ... 
doi:10.1016/j.jcss.2005.06.003 fatcat:uj645fmvhvct5ostyaf7lsdszy

On the Parameterized Intractability of Monadic Second-Order Logic

Stephan Kreutzer, Erich Grädel
2012 Logical Methods in Computer Science  
An immediate question is whether this is best possible or whether the result can be extended to classes of unbounded tree-width.  ...  In this paper we show that in terms of tree-width, the theorem cannot be extended much further.  ...  Compared to Courcelle's theorem, there is a gap between constant tree-width to which Courcelle's theorem applies and tree-width not bounded by log 84 n to which our theorem applies.  ... 
doi:10.2168/lmcs-8(1:27)2012 fatcat:ag76yqoyifbbpk53qawr5it6su

Stable Model Semantics for Tuple-Generating Dependencies Revisited

Mario Alviano, Michael Morak, Andreas Pieris
2017 Proceedings of the 36th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems - PODS '17  
This reveals the need to adopt an alternative approach to stable model semantics that is directly applicable to NTGDs with existentially quantified variables.  ...  However, as we discuss in the paper, Skolemization is not appropriate in the presence of default negation since it fails to capture the intended meaning of NTGDs, while the operational semantics mentioned  ...  Finally, they have been employed for knowledge representation purposes, and in fact as an alternative way to model ontologies [4, 9] .  ... 
doi:10.1145/3034786.3034794 dblp:conf/pods/AlvianoMP17 fatcat:jbbnvkoxijf6bpdku2wdkfaz6u

Towards fixed-parameter tractable algorithms for abstract argumentation

Wolfgang Dvořák, Reinhard Pichler, Stefan Woltran
2012 Artificial Intelligence  
However, these tractability results, which were obtained via Courcelle's Theorem, do not directly lead to efficient algorithms.  ...  As a by-product, we will sharpen some known complexity results.  ...  use Courcelle's meta-theorem to obtain that result).  ... 
doi:10.1016/j.artint.2012.03.005 fatcat:dzs4pe5mlzccdoakfydlaa6une

Algorithmic Meta-Theorems [article]

Stephan Kreutzer
2009 arXiv   pre-print
consequences of this theory as far as they are needed in the theory of algorithmic meta-theorems.  ...  As many meta-theorems use results from graph minor theory, we give a brief introduction to the theory developed by Robertson and Seymour for their proof of the graph minor theorem and state the main algorithmic  ...  Many thanks to Javier Esparza for proofreading this manuscript and for his patience as an editor.  ... 
arXiv:0902.3616v1 fatcat:wsuguljgrvfndhxlsps2ibes2i

Confronting Intractability via Parameters [article]

Rodney G. Downey, Dimitrios M. Thilikos
2011 arXiv   pre-print
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks.  ...  It is not hard to imagine that some parameters contribute more intractability than others and it seems reasonable to develop a theory of computational complexity which seeks to exploit this fact.  ...  Many thanks to Mike Fellows, Fedor V. Fomin, Bart M. P. Jansen, Stavros G. Kolliopoulos, Moritz Müller, Saket Saurabh, and Geoff Whittle for corrections and helpful comments.  ... 
arXiv:1106.3161v6 fatcat:6eqwtzfmunffzokn47lqyb6xwq

Confronting intractability via parameters

Rodney G. Downey, Dimitrios M. Thilikos
2011 Computer Science Review  
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks.  ...  It is not hard to imagine that some parameters contribute more intractability than others and it seems reasonable to develop a theory of computational complexity which seeks to exploit this fact.  ...  Many thanks to Mike Fellows, Fedor V. Fomin, Bart M. P. Jansen, Stavros G. Kolliopoulos, Moritz Müller, Saket Saurabh, and Geoff Whittle for corrections and helpful comments.  ... 
doi:10.1016/j.cosrev.2011.09.002 fatcat:4efih5lobfbjdgyuu2ccbqlbbq

Model-checking hierarchical structures

Markus Lohrey
2012 Journal of computer and system sciences (Print)  
As a consequence, several new complete problems for the levels of the polynomial time hierarchy and the exponential time hierarchy are obtained.  ...  Beside this modularity, hierarchical graph definitions allow us to specify structures of exponential size using polynomial size descriptions.  ...  We just have to start with an instance of QBF (quantified boolean satisfiability) and carry out the construction in the proof of Theorem 16.  ... 
doi:10.1016/j.jcss.2011.05.006 fatcat:prgmpfk4mbdrhkrlfsevmy6ckm

Second-Order Logic over Strings: Regular and Non-regular Fragments [chapter]

Thomas Eiter, Georg Gottlob, Thomas Schwentick
2002 Lecture Notes in Computer Science  
By a well-known result due to Büchi and Trakhtenbrot, all monadic second-order sentences over words describe regular languages.  ...  We give an exhaustive classification of the regular and nonregular prefix classes of this form, and derive of complexity results for the corresponding model checking problems.  ...  Observe that this representation of a string is a successor structure as discussed e.g. in [7] . An alternative representation uses a standard linear order on Í instead of the successor Succ.  ... 
doi:10.1007/3-540-46011-x_4 fatcat:wnrmwktrprhhnm4cuxl4zwwc2i

Structural Decompositions of Epistemic Logic Programs

Markus Hecher, Michael Morak, Stefan Woltran
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Finally, we show that applying treewidth to a novel dependency structure—given in terms of epistemic literals—allows to bound the number of ASP solver calls in typical ELP solving procedures.  ...  We also provide a full dynamic programming algorithm that adheres to these bounds.  ...  We obtain the following by the same argument as the one for Theorem 5: Theorem 6. Let Π, G, and k be as in Theorem 5, and let ϕ be a propositional formula.  ... 
doi:10.1609/aaai.v34i03.5672 fatcat:3rjf6e7g4jbmfnpzolj4e7qiue

Structural Decompositions of Epistemic Logic Programs [article]

Markus Hecher, Michael Morak, Stefan Woltran
2020 arXiv   pre-print
We also provide a full dynamic programming algorithm that adheres to these bounds.  ...  Finally, we show that applying treewidth to a novel dependency structure---given in terms of epistemic literals---allows to bound the number of ASP solver calls in typical ELP solving procedures.  ...  We obtain the following by the same argument as the one for Theorem 5: Theorem 6. Let Π, G, and k be as in Theorem 5, and let ϕ be a propositional formula.  ... 
arXiv:2001.04219v1 fatcat:jktvdkcruzeptn5wu2x5le7alu

Fixed-Parameter Tractability and Completeness I: Basic Results

Rod G. Downey, Michael R. Fellows
1995 SIAM journal on computing (Print)  
We also give a compendium of currently known hardness results as an appendix.  ...  DOMINATING SET is shown to be complete for W[2], and thus is not fixed-parameter tractable unless INDEPENDENT SET, CLIQUE, IRREDUNDANT SET, and many other natural problems in W[2] are also fixed-parameter  ...  Thanks to Karl Abrahamson for useful early discussions about this work, and for suggestions on improving the exposition. Special thanks to Mike Hallett and H.  ... 
doi:10.1137/s0097539792228228 fatcat:lrps5o3r3jg7jcy7ellmmdytoa
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