### Abstract

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 κ_{0}, 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.

Original language | English (US) |
---|---|

Title of host publication | STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing |

Publisher | Association for Computing Machinery |

Pages | 814-822 |

Number of pages | 9 |

ISBN (Print) | 9781450327107 |

DOIs | |

State | Published - Jan 1 2014 |

Externally published | Yes |

Event | 4th Annual ACM Symposium on Theory of Computing, STOC 2014 - New York, NY, United States Duration: May 31 2014 → Jun 3 2014 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
---|---|

ISSN (Print) | 0737-8017 |

### Other

Other | 4th Annual ACM Symposium on Theory of Computing, STOC 2014 |
---|---|

Country | United States |

City | New York, NY |

Period | 5/31/14 → 6/3/14 |

### All Science Journal Classification (ASJC) codes

- Software

### Keywords

- Condensation
- Constraint satisfaction problem
- Replica symmetry breaking
- Satisfiability threshold
- Survey propagation

## Fingerprint Dive into the research topics of 'Satisfiability threshold for random regular nae-sat'. Together they form a unique fingerprint.

## Cite this

*STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing*(pp. 814-822). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/2591796.2591862