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

2005
*
Lecture Notes in Computer Science
*

We show that

doi:10.1007/11527695_20
fatcat:2eclsw3h3jd2lbjd22siu37w64
*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. ...##
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Tradeoffs in the complexity of backdoors to satisfiability: dynamic sub-solvers and learning during search

2014
*
Annals of Mathematics and Artificial Intelligence
*

There has been considerable interest in the identification of structural properties of combinatorial

doi:10.1007/s10472-014-9407-9
fatcat:twcqxbtbybd2xmviixsstjhloa
*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. ...##
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Satisfiability of mixed Horn formulas

2007
*
Discrete Applied Mathematics
*

We show that

doi:10.1016/j.dam.2007.02.010
fatcat:7gxh6rf2yjhi7cewoh4pewpek4
*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] . ...##
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Some Computational Aspects of distance-sat

2007
*
Journal of automated reasoning
*

Two algorithms based on the well-known Davis/Logemann/Loveland search procedure

doi:10.1007/s10817-006-9063-9
fatcat:nrlxmghv3vhupkaxcnciyrihhm
*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. ...##
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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*. ...##
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Perceptron Learning of SAT

2012
*
Neural Information Processing Systems
*

Boolean satisfiability (

dblp:conf/nips/FlintB12
fatcat:lkyvjx2jjjc5dcrr3kxtosynfq
*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] . ...##
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An exact algorithm for the Boolean connectivity problem for k-CNF

2011
*
Theoretical Computer Science
*

The

doi:10.1016/j.tcs.2011.04.041
fatcat:jc65muc7cvfcfnstkind7uc4mu
*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 |. ...##
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An Exact Algorithm for the Boolean Connectivity Problem for k-CNF
[chapter]

2010
*
Lecture Notes in Computer Science
*

The

doi:10.1007/978-3-642-14186-7_15
fatcat:uywyeojbbbgnfinv7zkgae57ca
*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 |. ...##
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The complete classification for quantified equality constraints
[article]

2022
*
arXiv
*
pre-print

Such

arXiv:2104.00406v2
fatcat:6rr2qusydrdizjvwhfw3n75yay
*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. ...##
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Knowledge compilation and theory approximation

1996
*
Journal of the ACM
*

The procedures are extended to other tractable languages (

doi:10.1145/226643.226644
fatcat:ucvzt4zqm5abnkp34pzv5huznm
*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 ...##
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On the Complexity of Quadratization for Polynomial Differential Equations
[article]

2020
*
arXiv
*
pre-print

We present an encoding of those

arXiv:2007.08910v2
fatcat:z5pj4dq2q5e7dhngt55za6up5i
*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 ...##
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Default reasoning from conditional knowledge bases: Complexity and tractable cases

2000
*
Artificial Intelligence
*

We classify the complexity of this

doi:10.1016/s0004-3702(00)00073-4
fatcat:vzuuicqvkvgrdbpdscgn3ktmmi
*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. ...##
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Axiom Pinpointing
[article]

2020
*
arXiv
*
pre-print

This should serve as a starting point

arXiv:2003.08298v1
fatcat:znb734movje3xa4okyecy3wveq
*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. ...##
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Randomness and Structure
[chapter]

2006
*
Foundations of Artificial Intelligence
*

In each

doi:10.1016/s1574-6526(06)80022-2
fatcat:yyqvtdkjxnfjhkfjuhpnfqsbyu
*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*. ...##
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Let the Solver Deal with Redundancy

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. ...

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