The number of solutions for random regular NAE-SAT

• 成果类型: Article
• 署名作者: Sly, Allan; Sun, Nike; Zhang, Yumeng
• 署名单位: Princeton University; Massachusetts Institute of Technology (MIT); Stanford University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01029-5
• 发表日期: 2022
• 页码: 1-109
• 关键词: random k-sat; PHASE-TRANSITION; bounds; reconstruction; propagation; threshold; LIMITS

摘要

Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems. In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming predictions of statistical physics. Here we revisit one of these models, random regular k-nae-sat: knowing the satisfiability threshold, it is natural to study, in the satisfiable regime, the number of solutions in a typical instance. We prove here that these solutions have a well-defined free energy (limiting exponential growth rate), with explicit value matching the one-step replica symmetry breaking prediction. The proof develops new techniques for analyzing a certain survey propagation model associated to this problem. We believe that these methods may be applicable in a wide class of related problems.