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

Amin Coja-Oghlan, Andreas Goerdt, André Lanka, Frank Schädlich
2003 Lecture Notes in Computer Science  
This argument does not give 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.  ... 
doi:10.1007/978-3-540-45077-1_3 fatcat:k2ceyyoo5fgp3l4pdfhe72dv24

Strong Refutation Heuristics for Random k-SAT [chapter]

Amin Coja-Oghlan, Andreas Goerdt, André Lanka
2004 Lecture Notes in Computer Science  
In this paper, we deal with the corresponding algorithmic strong refutation problem: given a 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  ... 
doi:10.1007/978-3-540-27821-4_28 fatcat:zvmoreg3vvd2fjaswigpxqjsqa

Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k-SAT

Amin Coja-Oghlan, Andreas Goerdt, André Lanka, Frank Schädlich
2004 Theoretical Computer Science  
We apply 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  ... 
doi:10.1016/j.tcs.2004.07.017 fatcat:utrbprsyxfcedevefv7bfkpetu

Computer-Aided Proof of Erdos Discrepancy Properties [article]

Boris Konev, Alexei Lisitsa
2014 arXiv   pre-print
We show that by encoding the problem into Boolean satisfiability and applying the state 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] .  ... 
arXiv:1405.3097v2 fatcat:vfkh65uysreg7iuhmzixn2wuhe

How to Refute a Random CSP

Sarah R. Allen, Ryan ODonnell, David Witmer
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 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.  ... 
doi:10.1109/focs.2015.48 dblp:conf/focs/AllenOW15 fatcat:vfva5hlhc5hfdbaapgozys5aue

The Phase Transition Analysis for Random Regular Exact (s,c,k)-SAT Problem

Xiaoling Mo, Daoyun Xu, Xi Wang
2021 IEEE Access  
That is to say, when k ≥ 3 and s > s * , 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.  ... 
doi:10.1109/access.2021.3057858 fatcat:sq3qppkjfjftxf4b2wrndqmwvq

How to refute a random CSP [article]

Sarah R. Allen, Ryan O'Donnell, David Witmer
2015 arXiv   pre-print
When P is the 3-ary OR predicate, this is the well studied problem 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.  ... 
arXiv:1505.04383v3 fatcat:pzthjtxtdvhqlif7yurbb5djfa

The threshold for SDP-refutation of random regular NAE-3SAT [article]

Yash Deshpande, Andrea Montanari, Ryan O'Donnell, Tselil Schramm, Subhabrata Sen
2018 arXiv   pre-print
But do these methods work immediately above the "satisfiability threshold", or is there still a range 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  ... 
arXiv:1804.05230v1 fatcat:7g245eqz7vh7zg22bk7rbx2ome

The SDP Value for Random Two-Eigenvalue CSPs

Sidhanth Mohanty, Ryan O'Donnell, Pedro Paredes, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
Our 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.  ... 
doi:10.4230/lipics.stacs.2020.50 dblp:conf/stacs/MohantyO020 fatcat:ay2heso6hbcm3nyl6tdr2cdqo4

On the Hardness and Easiness of Random 4-SAT Formulas [chapter]

Andreas Goerdt, André Lanka
2004 Lecture Notes in Computer Science  
We extend this result in that we show that 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] .  ... 
doi:10.1007/978-3-540-30551-4_42 fatcat:ky2pzp3ktree7gwzxgz35icvje

Circuit lower bounds in bounded arithmetics

Ján Pich
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.  ... 
doi:10.1016/j.apal.2014.08.004 fatcat:5h55o7tvk5h3hm4xscug5x54oa

Strongly Refuting Random CSPs Below the Spectral Threshold [article]

Prasad Raghavendra, Satish Rao, Tselil Schramm
2016 arXiv   pre-print
Additionally, we extend our 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.  ... 
arXiv:1605.00058v2 fatcat:izqpdlwsffc6ji42dfkxit6czq

Narrow Proofs May Be Maximally Long

Albert Atserias, Massimo Lauria, Jakob Nordström
2016 ACM Transactions on Computational Logic  
In [FLN + 12] the 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  ... 
doi:10.1145/2898435 fatcat:fyixt7jbinastnhcaltahbrjmi

On Percolation and NP-Hardness [article]

Daniel Reichman, Igor Shinkar
2015 arXiv   pre-print
We consider the robustness 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.  ... 
arXiv:1508.02071v1 fatcat:aatotozrfbfmfauxbpu3cmgfey

Communication Lower Bounds via Critical Block Sensitivity [article]

Mika Göös, Toniann Pitassi
2016 arXiv   pre-print
We 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.  ... 
arXiv:1311.2355v2 fatcat:xhrth42o2nbqbaytaol2e34gt4
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