TY - GEN
T1 - The Number of Solutions for Random Regular NAE-SAT
AU - Sly, Allan
AU - Sun, Nike
AU - Zhang, Yumeng
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/12/14
Y1 - 2016/12/14
N2 - Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems (CSPs). In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming predictions from the statistical physics literature. Here we revisit one of these models, random regular 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.
AB - Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems (CSPs). In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming predictions from the statistical physics literature. Here we revisit one of these models, random regular 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.
KW - Condensation transition
KW - Free energy
KW - One-step replica symmetry breaking
KW - Random constraint satisfaction problem
KW - Replica symmetry
KW - Satisfiability threshold
UR - http://www.scopus.com/inward/record.url?scp=85009381609&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85009381609&partnerID=8YFLogxK
U2 - 10.1109/FOCS.2016.82
DO - 10.1109/FOCS.2016.82
M3 - Conference contribution
AN - SCOPUS:85009381609
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 724
EP - 731
BT - Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016
PB - IEEE Computer Society
T2 - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016
Y2 - 9 October 2016 through 11 October 2016
ER -