### Abstract

We study the complexity of approximating Max NM-E3SAT, a variant of Max 3SAT when the instances are guaranteed to not have any mixed clauses, i.e., every clause has either all its literals unnegated or all of them negated. This is a natural special case of Max 3SAT introduced in [7], where the question of whether this variant can be approximated within a factor better than 7/8 was also posed. We prove that it is NP-hard to approximate Max NM-E3SAT within a factor of 7/8 + ∈ for arbitrary ∈ > 0, and thus this variant is no easier to approximate than general Max 3SAT. The proof uses the technique of multilayered PCPs, introduced in [3], to avoid the technical requirement of folding of the proof tables. Circumventing this requirement means that the PCP verifier can use the bits it accesses without additional negations, and this leads to a hardness for Max 3SAT without any mixed clauses.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual IEEE Conference on Computational Complexity |

Pages | 154-162 |

Number of pages | 9 |

State | Published - 2005 |

Event | 20th Annual IEEE Conference on Computational Complexity - San Jose, CA, United States Duration: Jun 11 2005 → Jun 15 2005 |

### Other

Other | 20th Annual IEEE Conference on Computational Complexity |
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Country | United States |

City | San Jose, CA |

Period | 6/11/05 → 6/15/05 |

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### ASJC Scopus subject areas

- Computational Mathematics

### Cite this

*Proceedings of the Annual IEEE Conference on Computational Complexity*(pp. 154-162)

**Hardness of Max 3SAT with no mixed clauses.** / Guruswami, Venkatesan; Khot, Subhash.

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

*Proceedings of the Annual IEEE Conference on Computational Complexity.*pp. 154-162, 20th Annual IEEE Conference on Computational Complexity, San Jose, CA, United States, 6/11/05.

}

TY - GEN

T1 - Hardness of Max 3SAT with no mixed clauses

AU - Guruswami, Venkatesan

AU - Khot, Subhash

PY - 2005

Y1 - 2005

N2 - We study the complexity of approximating Max NM-E3SAT, a variant of Max 3SAT when the instances are guaranteed to not have any mixed clauses, i.e., every clause has either all its literals unnegated or all of them negated. This is a natural special case of Max 3SAT introduced in [7], where the question of whether this variant can be approximated within a factor better than 7/8 was also posed. We prove that it is NP-hard to approximate Max NM-E3SAT within a factor of 7/8 + ∈ for arbitrary ∈ > 0, and thus this variant is no easier to approximate than general Max 3SAT. The proof uses the technique of multilayered PCPs, introduced in [3], to avoid the technical requirement of folding of the proof tables. Circumventing this requirement means that the PCP verifier can use the bits it accesses without additional negations, and this leads to a hardness for Max 3SAT without any mixed clauses.

AB - We study the complexity of approximating Max NM-E3SAT, a variant of Max 3SAT when the instances are guaranteed to not have any mixed clauses, i.e., every clause has either all its literals unnegated or all of them negated. This is a natural special case of Max 3SAT introduced in [7], where the question of whether this variant can be approximated within a factor better than 7/8 was also posed. We prove that it is NP-hard to approximate Max NM-E3SAT within a factor of 7/8 + ∈ for arbitrary ∈ > 0, and thus this variant is no easier to approximate than general Max 3SAT. The proof uses the technique of multilayered PCPs, introduced in [3], to avoid the technical requirement of folding of the proof tables. Circumventing this requirement means that the PCP verifier can use the bits it accesses without additional negations, and this leads to a hardness for Max 3SAT without any mixed clauses.

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M3 - Conference contribution

SP - 154

EP - 162

BT - Proceedings of the Annual IEEE Conference on Computational Complexity

ER -