Proof of the satisfiability conjecture for large k
STOC(2016)
摘要
We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_*(k)$ such that a random $k$-SAT formula of clause density $\alpha$ is with high probability satisfiable for $\alpha<\alpha_*$, and unsatisfiable for $\alpha>\alpha_*$. We show that the threshold $\alpha_*(k)$ is given explicitly by the one-step replica symmetry breaking prediction from statistical physics. The proof develops a new analytic method for moment calculations on random graphs, mapping a high-dimensional optimization problem to a more tractable problem of analyzing tree recursions. We believe that our method may apply to a range of random CSPs in the 1-RSB universality class.
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关键词
random constraint satisfaction problem,boolean satisfiability,spin glasses,replica symmetry breaking,warning propagation
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