2013/10/17 by Jian Ding, Ding, Jian, Allan Sly +3 · 2 citations
Computer Science · Decision Sciences · Engineering · #Educational Technology and Assessment #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Military Defense Systems Analysis #Multi-Criteria Decision Making #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1310.4784
openalex publication_date 2013/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 k0, we establish explicitly the satisfiability threshold d_*=d_*(k). We prove that for dd_* 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 Krzakala et al. (2007). Our proof verifies the one-step 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.