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We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant.
Convex analysis
R. T. Rockafellar · 1970
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Reducibility among combinatorial problems
R. M. Karp · 1972
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Solvable model of a spin-glass
D. Sherrington and S. Kirkpatrick · 1975
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Infinite number of order parameters for spin-glasses
G. Parisi · 1979
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A probabilistic proof of an asymptotic formula for the number of labelled regular graphs
B. Bollobás · 1980
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The order parameter for spin glasses: A function on the interval 0-1
G. Parisi · 1980
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A sequence of approximated solutions to the SK model for spin glasses
G. Parisi · 1980
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Probabilistic analysis of the Davis–Putnam procedure for solving the satisfiability problem
J. Franco and M. Paull · 1983
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Order parameter for spin-glasses
G. Parisi · 1983
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Replicas and optimization
M. Mézard and G. Parisi · 1985
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Average case complete problems
L. A. Levin · 1986
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Spin glass theory and beyond: An introduction to the replica method and its applications
M. Mézard, G. Parisi, and M. Virasoro · 1987
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Where the really hard problems are
P. Cheeseman, B. Kanefsky, and W. Taylor · 1991
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Mick gets some (the odds are on his side) [satisfiability]
V. Chvátal and B. Reed · 1992
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A threshold for unsatisfiability
A. Goerdt · 1992
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Hard and easy distributions of SAT problems
D. Mitchell, B. Selman, and H. Levesque · 1992
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Ergodic theory on Galton-Watson trees: speed of random walk and dimension of harmonic measure
R. Lyons, R. Pemantle, and Y. Peres · 1995
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Approximating the unsatisfiability threshold of random formulas
L. M. Kirousis, E. Kranakis, D. Krizanc, and Y. C. Stamatiou · 1998
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Sharp thresholds of graph properties, and the k k -SAT problem
E. Friedgut · 1999
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Models of random regular graphs
N. C. Wormald · 1999
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The phase transition in 1-in- k k -SAT and NAE-3-SAT
D. Achlioptas, A. Chtcherba, G. Istrate, and C. Moore · 2001
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The scaling window of the 2-SAT transition
B. Bollobás, C. Borgs, J. T. Chayes, J. H. Kim, and D. B. Wilson · 2001
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Recurrence of distributional limits of finite planar graphs
I. Benjamini and O. Schramm · 2001
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The asymptotic order of the random k k -SAT threshold
D. Achlioptas and C. Moore · 2002
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The thermodynamic limit in mean field spin glass models
F. Guerra and F. L. Toninelli · 2002
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Analytic and algorithmic solution of random satisfiability problems
M. Mézard, G. Parisi, and R. Zecchina · 2002
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The threshold for random k k -SAT is 2 k ln 2 − O ( k ) 2^{k}\ln 2-{O}(k)
D. Achlioptas and Y. Peres · 2003
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Replica bounds for optimization problems and diluted spin systems
S. Franz and M. Leone · 2003
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Broken replica symmetry bounds in the mean field spin glass model
F. Guerra · 2003
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Going after the k k -SAT threshold
A. Coja-Oghlan and K. Panagiotou · 2013
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Satisfiability threshold for random regular NAE-SAT
J. Ding, A. Sly, and N. Sun · 2013
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The Parisi ultrametricity conjecture
D. Panchenko · 2013
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The Sherrington–Kirkpatrick model
D. Panchenko · 2013
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Spin glass models from the point of view of spin distributions
D. Panchenko · 2013
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The condensation phase transition in random graph coloring
V. Bapst, A. Coja-Oghlan, S. Hetterich, F. Rassmann, and D. Vilenchik · 2014
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Limits of local algorithms over sparse random graphs
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Two solutions to diluted p p -spin models and xorsat
M. Mézard, F. Ricci-Tersenghi, and R. Zecchina · 2003
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Bounds for diluted mean-fields spin glass models
D. Panchenko and M. Talagrand · 2004
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Survey propagation: an algorithm for satisfiability
A. Braunstein, M. Mézard, and R. Zecchina · 2005
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On local equilibrium equations for clustering states
G. Parisi · 2005
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Constructing free-energy approximations and generalized belief propagation algorithms
J. S. Yedidia, W. T. Freeman, and Y. Weiss · 2005
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Threshold values of random k k -SAT from the cavity method
S. Mertens, M. Mézard, and R. Zecchina · 2006
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D. Gamarnik and M. Sudan · 2014
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Structure of 1-RSB asymptotic Gibbs measures in the diluted p p -spin models
D. Panchenko · 2014
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The Parisi formula has a unique minimizer
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Large deviations of empirical neighborhood distribution in sparse random graphs
C. Bordenave and P. Caputo · 2015
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Hierarchical exchangeability of pure states in mean field spin glass models
D. Panchenko · 2015
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The Legendre structure of the Parisi formula
A. Auffinger and W.-K. Chen · 2016
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The condensation phase transition in the regular k k -SAT model
V. Bapst and A. Coja-Oghlan · 2016
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The asymptotic k k -SAT threshold
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Maximum independent sets on random regular graphs
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Satisfiability threshold for random regular NAE-SAT
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A dynamic programming approach to the Parisi functional
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The satisfiability threshold for k k -XORSAT
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The number of solutions for random regular NAE-SAT
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Optimization of the Sherrington–Kirkpatrick Hamiltonian
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The SK model is infinite step replica symmetry breaking at zero temperature
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