TY - GEN

T1 - Satisfiability threshold for random regular nae-sat

AU - Ding, Jian

AU - Sly, Allan

AU - Sun, Nike

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

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 -