Satisfiability threshold for random regular NAE-SAT

We consider the random regular k -nae-sat problem with n variables each appearing in exactly d clauses. For all k exceeding an absolute constant k 0 , we establish explicitly the satisfiability threshold d * ∈ d * ( k ). We prove that for d d * the problem is unsatisfiable with high probability. If the threshold d * lands exactly on an integer, we show that the problem is satisfiable with probability bounded away from both zero and one. This is the first result to locate the exact satisfiability threshold in a random constraint satisfaction problem exhibiting the condensation phenomenon identified by Krzakał a et al. (2007). Our proof verifies the onestep replica symmetry breaking formalism for this model. We expect our methods to be applicable to a broad range of random constraint satisfaction problems and combinatorial problems on random graphs.

Authors

• Jian Ding
• Allan Sly
• Nike Sun

Keywords

• condensation
• constraint satisfaction problem
• replica symmetry breaking
• satisfiability threshold
• survey propagation