### Abstract

It is proved that for every choice of positive integers c and k such that k ≥ 3 and c2^{-k} ≥ 0.7, there is a positive number ε such that, with probability tending to 1 as n tends to ∞, a randomly chosen family of cn clauses of size k over n variables is unsatisfiable, but every resolution proof of its unsatisfiability must generate at least (1 + ε)^{n} clauses. The proof makes use of random hypergraphs.

Original language | English |
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Pages (from-to) | 759-768 |

Number of pages | 10 |

Journal | Journal of the ACM |

Volume | 35 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 1988 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Graphics and Computer-Aided Design
- Hardware and Architecture
- Information Systems
- Software
- Theoretical Computer Science

### Cite this

*Journal of the ACM*,

*35*(4), 759-768. https://doi.org/10.1145/48014.48016

**Many hard examples for resolution.** / Chvatal, Vasek; Szemerédi, E.

Research output: Contribution to journal › Article

*Journal of the ACM*, vol. 35, no. 4, pp. 759-768. https://doi.org/10.1145/48014.48016

}

TY - JOUR

T1 - Many hard examples for resolution

AU - Chvatal, Vasek

AU - Szemerédi, E.

PY - 1988/10

Y1 - 1988/10

N2 - It is proved that for every choice of positive integers c and k such that k ≥ 3 and c2-k ≥ 0.7, there is a positive number ε such that, with probability tending to 1 as n tends to ∞, a randomly chosen family of cn clauses of size k over n variables is unsatisfiable, but every resolution proof of its unsatisfiability must generate at least (1 + ε)n clauses. The proof makes use of random hypergraphs.

AB - It is proved that for every choice of positive integers c and k such that k ≥ 3 and c2-k ≥ 0.7, there is a positive number ε such that, with probability tending to 1 as n tends to ∞, a randomly chosen family of cn clauses of size k over n variables is unsatisfiable, but every resolution proof of its unsatisfiability must generate at least (1 + ε)n clauses. The proof makes use of random hypergraphs.

UR - http://www.scopus.com/inward/record.url?scp=0024090265&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024090265&partnerID=8YFLogxK

U2 - 10.1145/48014.48016

DO - 10.1145/48014.48016

M3 - Article

AN - SCOPUS:0024090265

VL - 35

SP - 759

EP - 768

JO - Journal of the ACM

JF - Journal of the ACM

SN - 0004-5411

IS - 4

ER -