### Abstract

Maximum satisfiability is a canonical NP-complete problem that appears empirically hard for random instances. At the same time, it is rapidly becoming a canonical problem for statistical physics. In both of these realms, evaluating new ideas relies crucially on knowing the maximum number of clauses one can typically satisfy in a random k-CNF formula. In this paper we give asymptotically tight estimates for this quantity. Our result gives very tight bounds for the fraction of satisfiable clauses in a random k-CNF. In particular, for k > 2 it improves upon all previously known such bound.

Original language | English (US) |
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Title of host publication | Proceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003 |

Publisher | IEEE Computer Society |

Pages | 362-370 |

Number of pages | 9 |

Volume | 2003-January |

ISBN (Print) | 0769520405 |

DOIs | |

State | Published - 2003 |

Event | 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003 - Cambridge, United States Duration: Oct 11 2003 → Oct 14 2003 |

### Other

Other | 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003 |
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Country | United States |

City | Cambridge |

Period | 10/11/03 → 10/14/03 |

### Fingerprint

### Keywords

- Benchmark testing
- Computer science
- Glass
- H infinity control
- Mathematics
- NP-complete problem
- Operations research
- Physics
- Stationary state
- Statistics

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Proceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003*(Vol. 2003-January, pp. 362-370). [1238210] IEEE Computer Society. https://doi.org/10.1109/SFCS.2003.1238210

**On the maximum satisfiability of random formulas.** / Achlioptas, D.; Naor, A.; Peres, Y.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003.*vol. 2003-January, 1238210, IEEE Computer Society, pp. 362-370, 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003, Cambridge, United States, 10/11/03. https://doi.org/10.1109/SFCS.2003.1238210

}

TY - GEN

T1 - On the maximum satisfiability of random formulas

AU - Achlioptas, D.

AU - Naor, A.

AU - Peres, Y.

PY - 2003

Y1 - 2003

N2 - Maximum satisfiability is a canonical NP-complete problem that appears empirically hard for random instances. At the same time, it is rapidly becoming a canonical problem for statistical physics. In both of these realms, evaluating new ideas relies crucially on knowing the maximum number of clauses one can typically satisfy in a random k-CNF formula. In this paper we give asymptotically tight estimates for this quantity. Our result gives very tight bounds for the fraction of satisfiable clauses in a random k-CNF. In particular, for k > 2 it improves upon all previously known such bound.

AB - Maximum satisfiability is a canonical NP-complete problem that appears empirically hard for random instances. At the same time, it is rapidly becoming a canonical problem for statistical physics. In both of these realms, evaluating new ideas relies crucially on knowing the maximum number of clauses one can typically satisfy in a random k-CNF formula. In this paper we give asymptotically tight estimates for this quantity. Our result gives very tight bounds for the fraction of satisfiable clauses in a random k-CNF. In particular, for k > 2 it improves upon all previously known such bound.

KW - Benchmark testing

KW - Computer science

KW - Glass

KW - H infinity control

KW - Mathematics

KW - NP-complete problem

KW - Operations research

KW - Physics

KW - Stationary state

KW - Statistics

UR - http://www.scopus.com/inward/record.url?scp=84943395381&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943395381&partnerID=8YFLogxK

U2 - 10.1109/SFCS.2003.1238210

DO - 10.1109/SFCS.2003.1238210

M3 - Conference contribution

SN - 0769520405

VL - 2003-January

SP - 362

EP - 370

BT - Proceedings - 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003

PB - IEEE Computer Society

ER -