TY - GEN
T1 - Satisfiability threshold for random regular nae-sat
AU - Ding, Jian
AU - Sly, Allan
AU - Sun, Nike
PY - 2014
Y1 - 2014
N2 - We consider the random regular κ-nae-sat problem with n variables each appearing in exactly d clauses. For all κ exceeding an absolute constant κ0, we establish explicitly the satisfiability threshold d* ≡ d*pkq. We prove that for d < d* the problem is satisfiable with high probability while 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 Krzakała 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.
AB - We consider the random regular κ-nae-sat problem with n variables each appearing in exactly d clauses. For all κ exceeding an absolute constant κ0, we establish explicitly the satisfiability threshold d* ≡ d*pkq. We prove that for d < d* the problem is satisfiable with high probability while 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 Krzakała 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.
KW - Condensation
KW - Constraint satisfaction problem
KW - Replica symmetry breaking
KW - Satisfiability threshold
KW - Survey propagation
UR - http://www.scopus.com/inward/record.url?scp=84904348861&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84904348861&partnerID=8YFLogxK
U2 - 10.1145/2591796.2591862
DO - 10.1145/2591796.2591862
M3 - Conference contribution
AN - SCOPUS:84904348861
SN - 9781450327107
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 814
EP - 822
BT - STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing
PB - Association for Computing Machinery
T2 - 4th Annual ACM Symposium on Theory of Computing, STOC 2014
Y2 - 31 May 2014 through 3 June 2014
ER -