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Complexity of counting the optimal solutions

Miki Hermann, Reinhard Pichler
2009 Theoretical Computer Science  
In particular, the classes #·Π k P with k ≥ 1 corresponding to all levels of the polynomial hierarchy have thus been studied.  ...  We prove several important properties of these new classes, like closure properties and the relationship with the #·Π k P-classes.  ...  Acknowledgment: We thank Arnaud Durand and Yann Strozecki for their remarks and for the discussion on the proof of Theorem 9.  ... 
doi:10.1016/j.tcs.2009.05.025 fatcat:64qcmnafzjdt7pgq2vf4umtgsu


Deepika Rai
2018 International Journal of Advanced Research in Computer Science  
Thus, we have obtained polynomial 3-SAT reduction of Sudoku Puzzle (n x n) as well as total number of 3-SAT clauses and new variables generated in 3-SAT reduction are 4 [n 4 -2n 2 + m] and 2 [n 2 {n 2  ...  3-Satisfiability (3-SAT) reduction has always been remarkable asset in proving the NP-Completeness of other problems. 3-SAT problem is an NP-Complete problem used as a starting point to prove the hardness  ...  By using equation(1)and table 1, we get the total number of 3-SAT clauses (say |C|) and new variables (say |V|) used in 3-SAT reduction of Sudoku Puzzle: depicts the results of our implementation on  ... 
doi:10.26483/ijarcs.v9i3.6096 fatcat:p2z34m3thrglxhofkgwmrujkde

Positive 1-in-3-SAT admits a non-trivial Kernel [article]

Valentin Bura
2020 arXiv   pre-print
We obtain an upper bound for the complexity of counting, O(2κ r 2^(1-κ) r) for number of variables r and clauses to variables ratio κ.  ...  Any such instance of |V| variables and |C| clauses can be polynomial-time reduced to an instance of 0/1 Integer Programming with Equality, of size at most 2/3|V| variables and at most |C| clauses.  ...  Jansen and Pieterse are not primarily interested in reduction of the number of variables, only in reduction of number of constraints. They do not tackle the associated counting problem.  ... 
arXiv:1808.02821v6 fatcat:5p4olgashbb6ho4xxwwtqrurje

Hard satisfiable 3-SAT instances via autocorrelation

Srinivasan Arunachalam, Ilias Kotsireas
2016 Journal on Satisfiability, Boolean Modeling and Computation  
We generated a family of 3-SAT instances from the D-optimal matrices problem with the motivation to solve interesting cases using the power of SAT solvers.  ...  Our reduction techniques is fairly straightforward and can be adapted to various other problems that are defined via autocorrelation.  ...  During the workshop we were able to discuss, clarify and finalize several key aspects of this paper.  ... 
doi:10.3233/sat190111 fatcat:4nhqvae34bcpnnpzvangax7tsi

A Comparison of Local Reduction and Sat-Solver Based Algebraic Cryptanalysis of Jh And Keccak

Peter Adamček, Marek Loderer, Pavol Zajac
2012 Tatra Mountains Mathematical Publications  
We also compare the results based on the local reduction with the attack based on the use of SAT-solvers PrecoSAT, and CryptoMiniSAT, respectively.  ...  In the article we show the application of this method to evaluate the strength of (reduced versions of) two chosen SHA-3 candidates: JH, and Keccak, respectively.  ...  The authors are grateful to an anonymous referee for helpful comments.  ... 
doi:10.2478/v10127-012-0036-6 fatcat:s6teywqgirciho6ixcxg4ke5zy

On Moderately Exponential Time for SAT [chapter]

Evgeny Dantsin, Alexander Wolpert
2010 Lecture Notes in Computer Science  
In this paper, we relate the question of moderately exponential complexity of sat to the question of moderately exponential complexity of problems defined by existential second-order sentences.  ...  Can sat be solved in "moderately exponential" time, i.e., in time p(|F |) 2 cn for some polynomial p and some constant c < 1, where F is a CNF formula of size |F | over n variables?  ...  Acknowledgment We are grateful to the anonymous referees for their careful analysis and valuable suggestions. We implemented most of the suggestions in the final version.  ... 
doi:10.1007/978-3-642-14186-7_27 fatcat:vwu4po4v7jac7n4ifktf3wqctu

Improved SAT-based Reachability Analysis with Observability Don't Cares

Sean Safarpour, Andreas Veneris, Rolf Drechsler, Miroslav N. Velev
2008 Journal on Satisfiability, Boolean Modeling and Computation  
Since ODCs represent variables whose values do not affect the outcome of a problem, it is possible to satisfy a problem with fewer assigned variables.  ...  This work proposes to use the ODCs to improve the quality and performance of SATbased reachability analysis frameworks.  ...  The score for each variable is calculated in a quick linear time pre-processing step with respect to the problem size.  ... 
doi:10.3233/sat190050 fatcat:clfuhzj4wbbufmn22xn3rhlmxa

On the Subexponential Time Complexity of CSP [article]

Iyad Kanj, Stefan Szeider
2013 arXiv   pre-print
We first establish relations between the subexponential-time complexity of CSP and that of other problems, including CNF-Sat.  ...  For several natural CSP parameters, we obtain threshold functions that precisely dictate the subexponential-time complexity of CSP with respect to the parameters under consideration.  ...  In the case of CSP and CNF-SAT, µ and µ ′ will be the number of variables in the instances of these problems.  ... 
arXiv:1304.1996v1 fatcat:6lg37c6elrdbfl24dh3bm2x3ju

(2+f(n))-SAT and its properties

Yunlei Zhao, Xiaotie Deng, C.H Lee, Hong Zhu
2004 Discrete Applied Mathematics  
Consider a formula that contains n variables with the form = 2 ∧ 3, where 2 is an instance of 2-SAT containing m2 2-clauses and 3 is an instance of 3-SAT containing m3 3-clauses. is an instance of (2 ,  ...  Most interestingly, we give a candidate, (2 + (log n) k =n 2 )-SAT (k ¿ 2), for natural problems in NP − NPC − P (denoted as NPI) with respect to this (2 + f(n))-SAT model.  ...  Acknowledgements The authors are grateful to the anonymous referees for their many valuable suggestions and constructive criticism that has improved former versions of this paper greatly.  ... 
doi:10.1016/s0166-218x(03)00194-x fatcat:rwhorgzlgncw5a2caf7cbiqova

On the Subexponential-Time Complexity of CSP

Ronald De Haan, Iyad Kanj, Stefan Szeider
2015 The Journal of Artificial Intelligence Research  
Not all NP-complete problems share the same practical hardness with respect to exact computation.  ...  We provide tight characterizations of the subexponential-time complexity of the aforementioned problems with respect to several natural structural parameters, which allows us to draw a detailed landscape  ...  In the case of CSP and CNF-SAT, µ and µ will be the number of variables in the instances of these problems.  ... 
doi:10.1613/jair.4540 fatcat:kr5w2c53vnd6laa6xbpdnk5ryy

Planar 3-SAT with a Clause/Variable Cycle

Alexander Pilz, Marc Herbstritt
2018 Scandinavian Workshop on Algorithm Theory  
The problem remains hard for monotone formulas and instances with exactly three distinct variables per clause.  ...  In the Planar 3-SAT problem, we are given a 3-SAT formula together with its incidence graph, which is planar, and are asked whether this formula is satisfiable.  ...  However, with the right perspective on the Linked Planar 3-SAT problem, it will be easy to observe that there are formulas whose incidence graph has a grid minor with a linear number of vertices (and thus  ... 
doi:10.4230/lipics.swat.2018.31 dblp:conf/swat/Pilz18 fatcat:7lbtmoksengo7es2h2oseadnke

The complexity of counting solutions to Generalised Satisfiability Problems modulo k [article]

John Faben
2008 arXiv   pre-print
In 1979, Valiant introduced the complexity class parity P, the problem of counting the number of solutions to NP problems modulo two.  ...  We give a dichotomy theorem for the complexity of counting the number of solutions to Generalised Satisfiability Problems modulo integers.  ...  We proceed by reduction from # p -SAT. Given a SAT formula F with clauses {C 1 , . . . C m } and variables {x 1 , . . . x n } and a prime number p, we construct a graph as described below.  ... 
arXiv:0809.1836v1 fatcat:kuigcxlghjdfxcwxtopswq3eny

On planar variants of the monotone satisfiability problem with bounded variable appearances [article]

Andreas Darmann, Janosch Döcker, Britta Dorn
2016 arXiv   pre-print
We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances.  ...  Hence, a planar and orthogonal drawing for these graphs can be computed efficiently, which may turn out to be useful in reductions using these variants as a starting point for proving some decision problem  ...  We present hardness proofs for planar and monotone variants of the satisfiability problem with bounds on the number of variable appearances.  ... 
arXiv:1604.05588v1 fatcat:72otsflwxrb35eorur3q573x4a

Mapping NP-Hard Problems to Restricted Adiabatic Quantum Architectures [article]

Gary J. Mooney, Sam U.Y. Tonetto, Charles D. Hill, Lloyd C.L. Hollenberg
2019 arXiv   pre-print
Separating the mapping into two distinct stages, we introduce problem-specific reductions for both quadratic unconstrained binary optimisation (QUBO) and satisfiability (SAT) and develop the subdivision-embedding  ...  For each of the problem mapping methods presented, we examine how the physical qubit count scales with problem size on architectures of varying connectivity.  ...  For an arbitrary SAT instance where the number of variables per clause is not constant, Ck may be replaced with the total number of variable appearances.  ... 
arXiv:1911.00249v2 fatcat:d4c4r3gaqbc7pk3jjlusngnz6u

Strong partial clones and the time complexity of SAT problems

Peter Jonsson, Victor Lagerkvist, Gustav Nordh, Bruno Zanuttini
2017 Journal of computer and system sciences (Print)  
In this article we study the complexity of SAT(S) with reductions increasing the amount of variables by a constant (CV-reductions) or a constant factor (LV-reductions).  ...  Hence, using clone theory, we obtain a solid understanding of the complexity of SAT(S) with CV-and LV-reductions.  ...  Acknowledgments We thank Magnus Wahlström for helpful discussions on the topic of this article, and in particular for suggesting the proof strategy in Lemma 17.  ... 
doi:10.1016/j.jcss.2016.07.008 fatcat:ydgat5j4f5errokt7zrdpn2yqi
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