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Worst Case Bounds for Some NP-Complete Modified Horn-SAT Problems [chapter]

Stefan Porschen, Ewald Speckenmeyer
2005 Lecture Notes in Computer Science  
We show that SAT remains NP-complete for such instances and also that any SAT instance can be encoded in terms of a mixed formula in polynomial time.  ...  We consider the satisfiability problem for CNF instances that contain a (hidden) Horn and a 2-CNF part, called mixed formulas.  ...  Since X is a vertex cover of C it is also one for K |c | . On the other hand, every vertex cover of a complete graph K n obviously contains at least n − 1 vertices.  ... 
doi:10.1007/11527695_20 fatcat:2eclsw3h3jd2lbjd22siu37w64

Tradeoffs in the complexity of backdoors to satisfiability: dynamic sub-solvers and learning during search

Bistra Dilkina, Carla P. Gomes, Ashish Sabharwal
2014 Annals of Mathematics and Artificial Intelligence  
There has been considerable interest in the identification of structural properties of combinatorial problems that lead to efficient algorithms for solving them.  ...  case) and on the size of the resulting backdoor (which can become arbitrarily smaller).  ...  The authors would like to thank Jörg Hoffmann for providing the generator for the MAP domain.  ... 
doi:10.1007/s10472-014-9407-9 fatcat:twcqxbtbybd2xmviixsstjhloa

Satisfiability of mixed Horn formulas

Stefan Porschen, Ewald Speckenmeyer
2007 Discrete Applied Mathematics  
We show that SAT remains NP-complete for such instances and also that any CNF formula can be encoded in terms of a mixed Horn formula in polynomial time.  ...  We further show that the NP-hard optimization problem minimum weight SAT for mixed Horn formulas can be solved in time O(2 0.5284n ) if non-negative weights are assigned to the variables.  ...  Each of these classes is NP-complete w.r.t. SAT as follows by the above described reduction from the NP-complete graph coloring problem [6] .  ... 
doi:10.1016/j.dam.2007.02.010 fatcat:7gxh6rf2yjhi7cewoh4pewpek4

Some Computational Aspects of distance-sat

Olivier Bailleux, Pierre Marquis
2007 Journal of automated reasoning  
Two algorithms based on the well-known Davis/Logemann/Loveland search procedure for the satisfiability problem sat are presented so as to solve distance-sat for CNF formulas.  ...  The empirical evaluation allows for drawing firm conclusions about the respective performances of the algorithms, and to relate the difficulty of distance-sat with the difficulty of sat from the practical  ...  Acknowledgements Many thanks to Vincent Vidal for his help.  ... 
doi:10.1007/s10817-006-9063-9 fatcat:nrlxmghv3vhupkaxcnciyrihhm

Page 9544 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
This bound improves the previously known bound poly(|E})-2!£!/3 of 68 COMPUTER SCIENCE 9544 [J. Gramm et al., “New worst-case upper bounds for MAX-2-SAT with application to MAX-CUT”, Tech. Rep.  ...  In case that such ordering is not specified and the resulting OBDD must be of minimum size, its decision version becomes NP-complete.  ... 

Perceptron Learning of SAT

Alex Flint, Matthew B. Blaschko
2012 Neural Information Processing Systems  
Boolean satisfiability (SAT) as a canonical NP-complete decision problem is one of the most important problems in computer science.  ...  We derive a linear time computable set of features and show analytically that margins exist for important polynomial special cases of SAT.  ...  Introduction SAT was originally shown to be a canonical NP-complete problem in Cook's seminal work [5] .  ... 
dblp:conf/nips/FlintB12 fatcat:lkyvjx2jjjc5dcrr3kxtosynfq

An exact algorithm for the Boolean connectivity problem for k-CNF

Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto
2011 Theoretical Computer Science  
The problem is known to be PSPACE-complete for k ≥ 3, and polynomial solvable for k ≤ 2 ( Gopalan et al., 2009) [6].  ...  This result is considered to be interesting due to the following fact shown by Calabro [5]: QBF-3-SAT, which is a typical PSPACE-complete problem, is not solvable in time O((2−ϵ) n ) for any constant ϵ  ...  For showing the worst-case running time, it suffices to estimate an upper bound of |E ϕ |.  ... 
doi:10.1016/j.tcs.2011.04.041 fatcat:jc65muc7cvfcfnstkind7uc4mu

An Exact Algorithm for the Boolean Connectivity Problem for k-CNF [chapter]

Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto
2010 Lecture Notes in Computer Science  
The problem is known to be PSPACE-complete for k ≥ 3, and polynomial solvable for k ≤ 2 [6].  ...  This result is considered to be interesting due to the following fact shown by [5]: QBF-3-SAT, which is a typical PSPACE-complete problem, is not solvable in time O((2 − ) n ) for any constant > 0, provided  ...  For showing the worst-case running time, it suffices to estimate an upper bound of |E ϕ |.  ... 
doi:10.1007/978-3-642-14186-7_15 fatcat:uywyeojbbbgnfinv7zkgae57ca

The complete classification for quantified equality constraints [article]

Dmitriy Zhuk, Barnaby Martin, Michal Wrona
2022 arXiv   pre-print
Such problems are either in Logspace, NP-complete, co-NP-complete or rise in complexity in the Polynomial Hierarchy.  ...  We additionally settle the classification for bounded alternation QCSP(Γ), for Γ an equality language.  ...  . • Else, if Γ is positive, then Π k -QCSP(Γ) is NP-complete. • Else, if Γ is Horn, then Π k -QCSP(Γ) is Co-NP-complete. • Else, Π k -QCSP(Γ) is Π P k−2 -hard.  ... 
arXiv:2104.00406v2 fatcat:6rr2qusydrdizjvwhfw3n75yay

Knowledge compilation and theory approximation

Bart Selman, Henry Kautz
1996 Journal of the ACM  
The procedures are extended to other tractable languages (for example, binary clauses) and to the first-order case.  ...  The approximations bound the original theory from below and above in terms of logical strength.  ...  Acknowledgements We thank Daniel Bobrow for getting us to think more about the issue of how to make practical use of restricted, tractable representation languages and Ray Reiter for pointing us to the  ... 
doi:10.1145/226643.226644 fatcat:ucvzt4zqm5abnkp34pzv5huznm

On the Complexity of Quadratization for Polynomial Differential Equations [article]

Mathieu Hemery
2020 arXiv   pre-print
We present an encoding of those problems in MAX-SAT and show the practical complexity of this algorithm on a benchmark of quadratization problems inspired from CRN design problems.  ...  We show that both problems of minimizing either the number of variables (i.e., molecular species) or the number of monomials (i.e. elementary reactions) in a quadratic transformation of a PIVP are NP-hard  ...  Acknowledgements This work was jointly supported by ANR-MOST BIOPSY Biochemical Programming System grant ANR-16-CE18-0029 and ANR-DFG SYMBIONT Symbolic Methods for Biological Networks grant ANR-17-CE40  ... 
arXiv:2007.08910v2 fatcat:z5pj4dq2q5e7dhngt55za6up5i

Default reasoning from conditional knowledge bases: Complexity and tractable cases

Thomas Eiter, Thomas Lukasiewicz
2000 Artificial Intelligence  
We classify the complexity of this problem for a number of well-known approaches (including Goldszmidt et al.'  ...  Furthermore, we generalize previous tractability results from Horn to q-Horn conditional knowledge bases, which allow for a limited use of disjunction.  ...  Acknowledgements We are very grateful to the anonymous referees for carefully reading through the manuscript and for many useful comments and suggestions, which helped to improve this paper.  ... 
doi:10.1016/s0004-3702(00)00073-4 fatcat:vzuuicqvkvgrdbpdscgn3ktmmi

Axiom Pinpointing [article]

Rafael Peñaloza
2020 arXiv   pre-print
This should serve as a starting point for researchers interested in related problems, with an ample bibliography for delving deeper into the details.  ...  In this work, we present a general overview to axiom pinpointing, providing the basic notions, different approaches for solving it, and some variations and applications which have been considered in the  ...  There is also a language with NP-complete entailment problem for which the exact complexity of all-just is unknown.  ... 
arXiv:2003.08298v1 fatcat:znb734movje3xa4okyecy3wveq

Randomness and Structure [chapter]

Carla Gomes, Toby Walsh
2006 Foundations of Artificial Intelligence  
In each case, we can describe problems by the tuple n, m, p 1 , p 2 , where n is the number of variables, m is the uniform domain size, p 1 is a measure of the density of the constraint graph, and p 2  ...  Associated with this rapid transition in satisfiability of problems, is a peak in problem hardness for a wide range both of systematic and local search methods [12, 67, 73, 80] .  ...  From the perspective of worst-case complexity, 2+p-SAT is rather unexciting. For any fixed p > 0, the problem class is NP-complete.  ... 
doi:10.1016/s1574-6526(06)80022-2 fatcat:yyqvtdkjxnfjhkfjuhpnfqsbyu

Let the Solver Deal with Redundancy

Cédric Piette
2008 2008 20th IEEE International Conference on Tools with Artificial Intelligence  
For instance, the complexity of some redundancy-related problems for CNF formulae and for their 2-SAT and Horn SAT fragments have been recently studied.  ...  However, this issue is not actually addressed in practice in modern SAT solvers, and is most of the time just ignored.  ...  Acknowledgement The author would like to thank Bertrand Mazure and Lakhdar Saïs for very helpful discussions.  ... 
doi:10.1109/ictai.2008.38 dblp:conf/ictai/Piette08 fatcat:bu5iguxurjcyzkxagfobujsmhm
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