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Certifying Unsatisfiability of Random 2k-SAT Formulas Using Approximation Techniques
[chapter]

2003
*
Lecture Notes in Computer Science
*

This argument does not give

doi:10.1007/978-3-540-45077-1_3
fatcat:k2ceyyoo5fgp3l4pdfhe72dv24
*us*an efficient algorithm*certifying*the*unsatisfiability**of*a given*random*instance. ... It is known that*random*k-*SAT**formulas*with at least (2 k · ln 2) · n*random*clauses are*unsatisfiable*with high probability. ... Hence, Feiges results emphasize the intimate relationship between*approximation**techniques*and*random*k-*SAT*. ...##
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Strong Refutation Heuristics for Random k-SAT
[chapter]

2004
*
Lecture Notes in Computer Science
*

In this paper, we deal with the corresponding algorithmic strong refutation problem: given a

doi:10.1007/978-3-540-27821-4_28
fatcat:zvmoreg3vvd2fjaswigpxqjsqa
*random*k-*SAT**formula*, can we find a certificate that the fraction*of*satisfiable clauses is 1 − 2 −k + o(1) ... A simple first moment argument shows that in a randomly chosen k-*SAT**formula*with m clauses over n boolean variables, the fraction*of*satisfiable clauses is 1 − 2 −k + o(1) as m/n → ∞ almost surely. ... For instance, in order to refute a*random*4-*SAT**formula*, [10, Section 2] combines somewhat intricate spectral methods with the*use**of**approximation*algorithms for NP-hard problems such as MAX CUT or MIN ...##
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Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k-SAT

2004
*
Theoretical Computer Science
*

We apply

doi:10.1016/j.tcs.2004.07.017
fatcat:utrbprsyxfcedevefv7bfkpetu
*techniques*from the theory*of**approximation*algorithms to the problem*of*deciding whether a*random*k-*SAT**formula*is satisfiable. ...*Using*known*approximation*algorithms for MAX CUT or MIN BISECTION, we show how to*certify*that Form n,4,m is*unsatisfiable*efficiently, provided that m Cn 2 for a sufficiently large constant C > 0. ... Thus, as we*use**approximation**techniques*to derive improved algorithms for*random*k-*SAT*, in a sense our work complements the relations between*approximation*algorithms and*random*k-*SAT*established in ...##
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Computer-Aided Proof of Erdos Discrepancy Properties
[article]

2014
*
arXiv
*
pre-print

We show that by encoding the problem into Boolean satisfiability and applying the state

arXiv:1405.3097v2
fatcat:vfkh65uysreg7iuhmzixn2wuhe
*of*the art*SAT*solvers, one can obtain a discrepancy 2 sequence*of*length 1160 and a proof*of*the Erdős discrepancy ... For the particular case*of*C=1 a human proof*of*the conjecture exists; for C=2 a bespoke computer program had generated sequences*of*length 1124*of*discrepancy 2, but the status*of*the conjecture remained ... the preliminary version*of*this paper [Konev and Lisitsa, 2014a] . ...##
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How to Refute a Random CSP

2015
*
2015 IEEE 56th Annual Symposium on Foundations of Computer Science
*

When P is the 3-ary Boolean OR predicate, this is the well studied problem

doi:10.1109/focs.2015.48
dblp:conf/focs/AllenOW15
fatcat:vfva5hlhc5hfdbaapgozys5aue
*of*refuting*random*3-*SAT**formulas*; in this case, an efficient algorithm is known only when m n 3/2 . ... This last result is new even in the context*of**random*k-*SAT*. ... Acknowledgments The authors would like to thank Amin Coja-Oghlan for help with the literature, and Boaz Barak and Ankur Moitra for permission to reprint the proof*of*the strong k-XOR refutation result. ...##
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The Phase Transition Analysis for Random Regular Exact (s,c,k)-SAT Problem

2021
*
IEEE Access
*

That is to say, when k ≥ 3 and s > s * ,

doi:10.1109/access.2021.3057858
fatcat:sq3qppkjfjftxf4b2wrndqmwvq
*random*regular exact (s, c, k) −*SAT*instance*unsatisfiable*with high probability. Lemma 1 has been*certified*. ... For the classic*random*3-*SAT*problem, the researchers*used*the cavity domain method [7] in statistical physics to give an*approximate*value α d = 4.267*of*the satisfiable phase transition point, and ... He is also the director*of*Guizhou Key Laboratory*of*Intelligent Medical Imaging and Accurate Diagnosis. He is the author*of*more than 120 articles. ...##
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How to refute a random CSP
[article]

2015
*
arXiv
*
pre-print

When P is the 3-ary OR predicate, this is the well studied problem

arXiv:1505.04383v3
fatcat:pzthjtxtdvhqlif7yurbb5djfa
*of*refuting*random*3-*SAT**formulas*, and an efficient algorithm is known only when m ≫ n^3/2. ... This last result is new even in the context*of**random*k-*SAT*. ... Acknowledgments The authors would like to thank Amin Coja-Oghlan for help with the literature, and Boaz Barak and Ankur Moitra for permission to reprint the proof*of*the strong k-XOR refutation result. ...##
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The threshold for SDP-refutation of random regular NAE-3SAT
[article]

2018
*
arXiv
*
pre-print

But do these methods work immediately above the "satisfiability threshold", or is there still a range

arXiv:1804.05230v1
fatcat:7g245eqz7vh7zg22bk7rbx2ome
*of*constraint densities for which*random*NAE-3SAT instances are*unsatisfiable*but hard to refute? ... More precisely, whereas a*random*d-regular instance*of*NAE-3SAT is easily shown to be*unsatisfiable*(whp) once d ≥ 8, we establish the following sharp threshold result regarding efficient refutation: If ... Acknowledgments This work began at the American Institute*of*Mathematics workshop "Phase transitions in*randomized*computational problems"; the authors would like to thank AIM, as well as the organizers ...##
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The SDP Value for Random Two-Eigenvalue CSPs

2020
*
Symposium on Theoretical Aspects of Computer Science
*

Our

doi:10.4230/lipics.stacs.2020.50
dblp:conf/stacs/MohantyO020
fatcat:ay2heso6hbcm3nyl6tdr2cdqo4
*techniques*include new generalizations*of*the nonbacktracking operator, the Ihara-Bass*Formula*, and the Friedman/Bordenave proof*of*Alon's Conjecture. ... We precisely determine the SDP value (equivalently, quantum value)*of*large*random*instances*of*certain kinds*of*constraint satisfaction problems, "two-eigenvalue 2CSPs". ... Acknowledgements We thank Yuval Peled for emphasizing the bipartite graph view*of*additive lifts, and Tselil Schramm for helpful discussions surrounding the trace method on graphs. ...##
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On the Hardness and Easiness of Random 4-SAT Formulas
[chapter]

2004
*
Lecture Notes in Computer Science
*

We extend this result in that we show that

doi:10.1007/978-3-540-30551-4_42
fatcat:ky2pzp3ktree7gwzxgz35icvje
*approximating*max bipartite clique is hard under the weaker assumption, that*random*4-*SAT**formulas*are hard to refute with high probability. ... Assuming 3-*SAT**formulas*are hard to refute with high probability, Feige showed*approximation*hardness results, among others for the max bipartite clique. ... assignments in a*random*3-*SAT**formula*[8] . ...##
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Circuit lower bounds in bounded arithmetics

2015
*
Annals of Pure and Applied Logic
*

*of*size n 4kc where k ≥ 1, c ≥ 2 unless each function f ∈ SIZE(n k ) can be

*approximated*by

*formulas*{F n } ∞ n=1

*of*subexponential size 2 O(n 1/c ) with subexponential advantage: P x∈{0,1} n [F n (x) ... Unconditionally, V 0 cannot prove that for sufficiently large n,

*SAT*does not have circuits

*of*size n log n . ... This is the main

*technique*we

*use*. We show that it works in our context as well and allows

*us*to

*use*the S-T protocol to compute f by subexponential

*formulas*with a subexponential advantage. ...

##
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Strongly Refuting Random CSPs Below the Spectral Threshold
[article]

2016
*
arXiv
*
pre-print

Additionally, we extend our

arXiv:1605.00058v2
fatcat:izqpdlwsffc6ji42dfkxit6czq
*techniques*to give new results for*certifying*upper bounds on the injective tensor norm*of**random*tensors. ... Strong refutation is the problem*of**certifying*that no variable assignment satisfies more than a constant fraction*of*clauses; this is the natural algorithmic problem in the*unsatisfiable*regime (when ... Acknowledgements T.S. thanks Sam Hopkins for helpful conversations, and Jonah Brown-Cohen for helpful comments in the preparation*of*this manuscript. ...##
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Narrow Proofs May Be Maximally Long

2016
*
ACM Transactions on Computational Logic
*

In [FLN + 12] the

doi:10.1145/2898435
fatcat:fyixt7jbinastnhcaltahbrjmi
*techniques*in [ABRW02] were adapted to prove space lower bounds also for*formulas**of*constant width, and optimal (linear) lower bounds on space were finally obtained in [BG13] . ... Moreover, Lasserre's method is the strongest*of*all three in the sense that, level by level, it provides the tightest*of*all three*approximations**of*the integer linear program. ... We want to acknowledge the input from participants*of*the Dagstuhl workshop 15171 Theory and Practice*of**SAT*Solving in April 2015, in particular from Paul Beame, that helped*us*to correct some details ...##
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On Percolation and NP-Hardness
[article]

2015
*
arXiv
*
pre-print

We consider the robustness

arXiv:1508.02071v1
fatcat:aatotozrfbfmfauxbpu3cmgfey
*of*computational hardness*of*problems whose input is obtained by applying independent*random*deletions to worst-case instances. ... at*random*. ... Acknowledgements We thank Itai Benjamini, Huck Bennett, Uri Feige and Sam Hopkins for*useful*discussions. ...##
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Communication Lower Bounds via Critical Block Sensitivity
[article]

2016
*
arXiv
*
pre-print

We

arXiv:1311.2355v2
fatcat:xhrth42o2nbqbaytaol2e34gt4
*use*critical block sensitivity, a new complexity measure introduced by Huynh and Nordström (STOC 2012), to study the communication complexity*of*search problems. ... a certain two-party lift*of*S requires Ω(b) bits*of*communication. ... Thanks to Nathan Grosshans for e-mail correspondence, which clarified our presentation*of*the monotone CSP-*SAT*function. ...
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