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On Problems as Hard as CNF-SAT

2016
*
ACM Transactions on Algorithms
*

Graph Coloring, Hamiltonian Path, Dominating Set and 3-

doi:10.1145/2925416
fatcat:qowmvgp7nnh5tf2en7fr5lvkay
*CNF*-*Sat*. ... The*CNF*-*Sat**problem*is the canonical example of a*problem*for which the trivial exhaustive search algorithm runs in time O(2^n), where n is the number of variables in the input formula. ... In addition to these two basic*problems*, we can name new*problems*by adding*one*of the following modifiers to their names (which we do by example just for*CNF*-*Sat*). • k-*CNF*-*Sat*is the*problem*in which ...##
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From Non-Clausal to Clausal MinSAT
[chapter]

2021
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Frontiers in Artificial Intelligence and Applications
*

We tackle the

doi:10.3233/faia210113
fatcat:fssdjyylyrcsniqgjvr6joupzy
*problem*of solving MinSAT for multisets of propositional formulas that are not necessarily in clausal form. ... Our approach reduces non-clausal to clausal MinSAT, since this allows us to rely*on*the much developed clause-based MinSAT solvers. ... These*problems*are significant because many practical questions can be solved by first encoding them*as*a*SAT*, MaxSAT or MinSAT*problems*, and then finding a solution by solving the resulting encoding with ...##
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Complexity and Approximability of Parameterized MAX-CSPs

2017
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Algorithmica
*

W[1]-

doi:10.1007/s00453-017-0310-8
fatcat:ofab3wvgwjg75kehvxwaecmytm
*hardness*results. ... In standard CSPs, we want to decide whether this fraction equals*one*. ... There exists an FPT-*AS*which, given > 0 and an instance φ of MAX-THRESHOLD, computes a (1 − )-approximate solution and runs in time f (fvs * , ) · poly(n), where fvs * is the size of the smallest feedback ...##
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Extended Conjunctive Normal Form and An Efficient Algorithm for Cardinality Constraints

2020
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Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
*

*SAT*and MaxSAT are expressed in

*CNF*, which is difficult to deal with cardinality constraints. ... Satisfiability (

*SAT*) and Maximum Satisfiability (MaxSAT) are two basic and important constraint

*problems*with many important applications. ... Proceedings of the Twenty-Ninth International Joint Conference

*on*Artificial Intelligence ...

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On the Exact Complexity of Evaluating Quantified k -CNF

2012
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Algorithmica
*

) and show that s(∞) (the limit of s(k)

doi:10.1007/s00453-012-9648-0
fatcat:pqo7syfxsre4znksn3ds5ixwlu
*as*k → ∞) is at most s(Π23-*sat*). ... 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 ...*As*with*cnf*-*sat*, we will consider various syntactic restrictions of quantified k-*sat*to arrive at a minimally complex set of formulas which are*as**hard**as*the standard existentially quantified 3-*CNFs**as*...##
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Solving Over-Constrained Problems with SAT
[chapter]

2005
*
Lecture Notes in Computer Science
*

We present a new generic

doi:10.1007/11564751_76
fatcat:unin35gvyvgfzhjnu6mseckzwe
*problem*solving approach for overconstrained*problems*based*on*Max-*SAT*. ... We first define a clausal form formalism that deals with blocks of clauses and distinguish between*hard*and soft blocks. ... The Soft-*SAT**problem*is the*problem*of finding a solution to a Soft*CNF*formula. ...##
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Hypergraph Acyclicity and Propositional Model Counting
[chapter]

2014
*
Lecture Notes in Computer Science
*

We show that the propositional model counting

doi:10.1007/978-3-319-09284-3_29
fatcat:4q5lsbvphzawrb3p2nhygjarte
*problem*#*SAT*for*CNF*-formulas with hypergraphs that allow a disjoint branches decomposition can be solved in polynomial time. ... We show that this class of hypergraphs is incomparable to hypergraphs of bounded incidence cliquewidth which were the biggest class of hypergraphs for which #*SAT*was known to be solvable in polynomial ... In fact, most classical decision results based*on*tractability of resolution (such*as*for 2−*SAT*) or unit propagation (Horn−*SAT*) do not extend to counting*as*the respective counting*problems*are*hard*(see ...##
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A criterion for "easiness" of certain SAT problems
[article]

2017
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arXiv
*
pre-print

Also individual instances can be checked for easiness with respect to a given

arXiv:1707.00118v1
fatcat:lplyy7jqfnemzkkgfke4ywahwa
*SAT**problem*. ... A generalized 1-in-3SAT*problem*is defined and found to be in complexity class P when restricted to a certain subset of*CNF*expressions. ... Similarly we can argue that the 1-in-kSAT*problem*, i.e. the same*problem*without restrictions*on*the number of literals per clause, is NP-*hard*,*as*well. ...##
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Backdoors into Two Occurrences

2020
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Journal on Satisfiability, Boolean Modeling and Computation
*

The question whether there exists a

doi:10.3233/sat-200125
fatcat:ywyuvpjffzc5rhu65xgfgvunsa
*CNF*(2)-backdoor set of size k is*hard*for the class W[2], for both weak and strong backdoors, and in both cases it becomes fixed-parameter tractable when restricted ... to inputs in d-*CNF*for a fixed d. ... The research leading to the results in this paper was initiated at Dagstuhl Seminar 12471 "*SAT*Interactions". ...##
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Solving Over-Constrained Problems with SAT Technology
[chapter]

2005
*
Lecture Notes in Computer Science
*

We present a new generic

doi:10.1007/11499107_1
fatcat:deqhgvnybfdj7jutifhwvrt4hy
*problem*solving approach for overconstrained*problems*based*on*Max-*SAT*. ... We first define a clausal form formalism that deals with blocks of clauses instead of individual clauses, and that allows*one*to declare each block either*as**hard*(i.e., must be satisfied by any solution ... The Soft-*SAT**problem*is the*problem*of finding a solution to a Soft*CNF*formula. ...##
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Satisfiability of mixed Horn formulas

2007
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Discrete Applied Mathematics
*

A satisfiability formulation of

doi:10.1016/j.dam.2007.02.010
fatcat:7gxh6rf2yjhi7cewoh4pewpek4
*problems**on*level graphs, ENDM 9 (2001)] and graph colorability formulas. ... 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. ... a maximum Horn model, which is an NP-*hard*optimization*problem*. ...##
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Logical Analysis of Hash Functions
[chapter]

2005
*
Lecture Notes in Computer Science
*

In addition,

doi:10.1007/11559306_11
fatcat:jgqmmw4qtzcjzapnqa6t2mpfwq
*one*can finely tune the*hardness*of generated formulae. This can be very important for different applications, including testing (complete or incomplete)*sat*solvers. ... satisfiability*problem*. ... We are grateful to anonymous reviewers for useful comments*on*the first version of this paper. ...##
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The Boolean Satisfiability Problem
[article]

2020
*
Figshare
*

The Boolean Satisfiability

doi:10.6084/m9.figshare.12331172.v1
fatcat:ky6vwo7gm5h3vfovcrpoknfovm
*Problem*is also the first*problem*proven to be NP-complete. ... (Thus being able to solve a NP-complete*problem*is equivalent to being able to solve every*problem*in NP). ... 13 3-*SAT**Hardness**As*n increases*hardness*transition grows sharper m / n 14 Transition at m/n ' 4.3 m / n Threshold Conjecture • For every k, there exists a c* such that -For m/n < ...##
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Backdoors to Satisfaction
[article]

2011
*
arXiv
*
pre-print

We also discuss recent results

arXiv:1110.6387v2
fatcat:4k2qifbdyvd6hi5qvhlp6w2uaq
*on*backdoor sets for*problems*that are beyond NP. ... 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. ... Acknowledgment We thank Ryan Williams for his comments*on*an earlier version of this survey. ...##
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Symmetry Breaking for Maximum Satisfiability
[article]

2008
*
arXiv
*
pre-print

In

arXiv:0804.0599v1
fatcat:ztpiet5xkvcddmx55lpwbd7zha
*SAT*, the identification of symmetry breaking predicates (SBPs) is a well-known, often effective, technique for solving*hard**problems*. ...*As*with*SAT*and PB, symmetry breaking predicates for MaxSAT and variants are shown to be effective for a representative number of*problem*domains, allowing solving*problem*instances that current state ... For the weighted partial MaxSAT*problem*, the formula is the conjunction of a weighted*CNF*formula (soft clauses) and a classical*CNF*formula (*hard*clauses). ...
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