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On the Exact Complexity of Evaluating Quantified k -CNF

Chris Calabro, Russell Impagliazzo, Ramamohan Paturi
2012 Algorithmica  
We relate the exponential complexities 2 s(k)n of k-sat and the exponential complexity 2 s(Π 2 3-sat)n of Π23-sat (evaluating formulas of the form ∀x∃yφ(x, y) where φ is a 3-CNF in x variables and y variables  ...  Our proofs involve the construction of efficient minimally unsatisfiable k-cnfs and the application of the Sparsification Lemma.  ...  Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.  ... 
doi:10.1007/s00453-012-9648-0 fatcat:pqo7syfxsre4znksn3ds5ixwlu

Solving Stochastic Boolean Satisfiability under Random-Exist Quantification

Nian-Ze Lee, Yen-Shi Wang, Jie-Hong R. Jiang
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
Experimental results show that our method outperforms the state-of-the-art algorithm on random k-CNF formulas and has effective application to approximate SSAT on circuit benchmarks.  ...  Solving SSAT formulas lies in the same complexity class (PSPACE-complete) as solving Quantified Boolean Formula (QBF).  ...  Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  ... 
doi:10.24963/ijcai.2017/96 dblp:conf/ijcai/LeeWJ17 fatcat:lcgtk2zz75gqvcz2jwzzikvq3q

A Study of the Learnability of Relational Properties (Model Counting Meets Machine Learning) [article]

Muhammad Usman, Wenxi Wang, Kaiyuan Wang, Marko Vasic, Haris Vikalo, Sarfraz Khurshid
2019 arXiv   pre-print
MCML reduces the quantification problems to the classic complexity theory problem of model counting, and employs state-of-the-art approximate and exact model counters for high efficiency.  ...  However, the use of MCML metrics based on model counting shows that the performance can degrade substantially when tested against the whole (bounded) input space, indicating the high complexity of precisely  ...  If there are k features, the size of the CNF formula is O(nk): each PC has ≤ k conditions, each condition is a literal, and the formula is a conjunction of the negation of each PC.  ... 
arXiv:1912.11580v1 fatcat:u4663pifvfdujeugko434aotam

Using QBF to increase accuracy of SAT-based debugging

Andre Sulflow, Gorschwin Fey, Rolf Drechsler
2010 Proceedings of 2010 IEEE International Symposium on Circuits and Systems  
Debugging significantly slows down the design process of complex systems. Only limited tool support is available and often fixing one problem leads to finding the next one.  ...  The approach is based on Quantified Boolean Formulas (QBF) and ensures, that counterexamples of high quality are returned.  ...  f evaluates to one.  ... 
doi:10.1109/iscas.2010.5537506 dblp:conf/iscas/SulflowFD10 fatcat:ez22jjpe4vcptkfzsck5wd4cte

Backdoors to Satisfaction [article]

Serge Gaspers, Stefan Szeider
2011 arXiv   pre-print
In this survey we review parameterized complexity results for problems that arise in the context of backdoor sets, such as the problem of finding a backdoor set of size at most k, parameterized by k.  ...  If we know a small backdoor set we can reduce the question of whether the given formula is satisfiable to the same question for one or several easy formulas that belong to the tractable class under consideration  ...  Acknowledgment We thank Ryan Williams for his comments on an earlier version of this survey.  ... 
arXiv:1110.6387v2 fatcat:4k2qifbdyvd6hi5qvhlp6w2uaq

Satisfiability on Mixed Instances

Ruiwen Chen, Rahul Santhanam
2016 Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16  
For certain kinds of conjunctive mixing, such as mixtures of k-CNFs and CNFs of bounded size, and of k-CNFs and Boolean formulas, we obtain improved savings over subcube partitioning by combining existing  ...  We use the perspective of compositional mixing to show the first non-trivial algorithm for satisfiability of quantified Boolean formulas, where there is no depth restriction on the formula.  ...  Upper and lower bounds on the exact complexity of satisfiability for mixed instances translate to these other problems.  ... 
doi:10.1145/2840728.2840768 dblp:conf/innovations/ChenS16 fatcat:pkhlcnd75beernitffblimhuvm

Guest Editorial: Special Issue on Parameterized and Exact Computation, Part II

Venkatesh Raman, Saket Saurabh
2013 Algorithmica  
The papers in this issue form the second part of the two parts special issue in the area of parameterized and exact exponential algorithms and complexity.  ...  While some of these are selected and extended papers from International Symposium on Parameterized and Exact Computation (IPEC) 2010, the rest were selected from the submissions received for our call for  ...  The paper 'On the exact complexity of evaluating quantified k-CNF' addresses the exponential complexity of evaluating quantified boolean formula.  ... 
doi:10.1007/s00453-013-9744-9 fatcat:j2ya4p5u7zcvlgvxwotywr7f34

Computing the Shapley Value of Facts in Query Answering

Daniel Deutch, Nave Frost, Benny Kimelfeld, Mikaël Monet
2022 Proceedings of the 2022 International Conference on Management of Data  
Our experiments on TPC-H and IMDB demonstrate the practical effectiveness of our solutions.  ...  We start by establishing a tight theoretical connection to the extensively studied problem of query evaluation over probabilistic databases, which allows us to obtain a polynomial-time algorithm for the  ...  Exact computation We evaluated our solution for exact Shapley (Section 4.2) on each of the 40 queries.  ... 
doi:10.1145/3514221.3517912 fatcat:t57vamgvlfbwdkwtpxyzggs25q

On the complexity of equational problems in CNF

Reinhard Pichler
2003 Journal of symbolic computation  
The goal of this work is a complexity analysis of the satisfiability problem of equational problems.  ...  The main results will be a proof of the NP-completeness (and, in particular, the NP-membership) of equational problems in CNF over an infinite domain and of the Σ p 2 -completeness in the case of CNF over  ...  Acknowledgement I am very grateful to the anonymous referees for their comments which helped to significantly improve the presentation of this work.  ... 
doi:10.1016/s0747-7171(03)00029-4 fatcat:l2tmi5ibhjbk3jpyqdvx43daqm

A Study of Symmetry Breaking Predicates and Model Counting [chapter]

Wenxi Wang, Muhammad Usman, Alyas Almaawi, Kaiyuan Wang, Kuldeep S. Meel, Sarfraz Khurshid
2020 Lecture Notes in Computer Science  
We study the use of CNF-level and domain-level symmetry breaking predicates in the context of the state-of-the-art in model counting, specifically the leading approximate model counter ApproxMC and the  ...  As benchmarks, we use a range of problems, including structurally complex specifications of software systems and constraint satisfaction problems.  ...  Acknowledgments This work was supported in part by the U.S.  ... 
doi:10.1007/978-3-030-45190-5_7 fatcat:s6f7rm3n5jckdasgxdkulk3lni

Computing the Shapley Value of Facts in Query Answering [article]

Daniel Deutch, Nave Frost, Benny Kimelfeld, Mikaël Monet
2022 arXiv   pre-print
Our experiments on TPC-H and IMDB demonstrate the practical effectiveness of our solutions.  ...  We start by establishing a tight theoretical connection to the extensively studied problem of query evaluation over probabilistic databases, which allows us to obtain a polynomial-time algorithm for the  ...  Exact computation We have evaluated our solution for exact Shapley computation, presented in Section 4.2, on each of the 40 queries.  ... 
arXiv:2112.08874v2 fatcat:swmqnbzmrzgf7bel2oukmm6upu

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  ...  This report documents the programme and outcomes of Dagstuhl Seminar 16381 "SAT and Interactions".  ...  In this talk we concentrate on the complexity of the isomorphism problem of solution graphs of Boolean formulas and on how this complexity depends on the formula type.  ... 
doi:10.4230/dagrep.6.9.74 dblp:journals/dagstuhl-reports/BeyersdorffCEV16 fatcat:boyfegt3erba5j5hbdheironmu

BIRD: Engineering an Efficient CNF-XOR SAT Solver and Its Applications to Approximate Model Counting

Mate Soos, Kuldeep S. Meel
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
To the best of our knowledge, we conducted the most comprehensive study of evaluation performance of counting algorithms involving 1896 benchmarks with computational effort totaling 86400 computational  ...  The primary contribution of this paper is an affirmative answer to the above question. We present a novel architecture, called BIRD, to handle CNF-XOR formulas arising from hashingbased techniques.  ...  The computational work for this article was performed on resources of the National Supercomputing Centre, Singapore https://www.nscc.sg.  ... 
doi:10.1609/aaai.v33i01.33011592 fatcat:jfq2fifo6vemxmggx5sagyukp4

Succinct Encodings of Graph Isomorphism [chapter]

Bireswar Das, Patrick Scharpfenecker, Jacobo Torán
2014 Lecture Notes in Computer Science  
Although the exact complexity of these problems is still unknown, we show that under most existing succinct models the different versions of the problem are equivalent.  ...  We introduce a new way for encoding graph problems, based on CNF or DNF formulas.  ...  Although the exact complexity of the succinct versions of GI is still unknown, we prove that in most of the encoding models there is no difference in the complexity of the succinct problem.  ... 
doi:10.1007/978-3-319-04921-2_23 fatcat:hs4quarecrgelc77d4ojd2hdhm

The threshold for random (1,2)-QSAT [article]

Nadia Creignou, Herve Daude, Uwe Egly, Raphael Rossignol
2009 arXiv   pre-print
We show the existence of a threshold effect for the phase transition associated with the satisfiability of random quantified extended 2-CNF formulas.  ...  The QSAT problem is the quantified version of the SAT problem.  ...  In this paper, we focus on a certain subclass of closed quantified Boolean formulas, which can be seen as quantified extended 2-CNF-formulas.  ... 
arXiv:0907.0937v1 fatcat:46cff2ka65gbzmwfl3jshm3y34
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