On the maximum satisfiability of random formulas

Dimitris Achlioptas; Assaf Naor; Yuval Peres

doi:10.1145/1219092.1219098

On the maximum satisfiability of random formulas

Dimitris Achlioptas
, Assaf Naor
, Yuval Peres

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

Say that a k-CNF a formula is p-satisfiable if there exists a truth assignment satisfying a fraction 1 - 2^-k +p 2^-k of its clauses (note that every k-CNF formula is 0-satisfiable). Let F_k(n, m) denote a random k-CNF formula on n variables with m clauses. For every k2 and every r>0 we determine p and Δ=Δ(k)=O(k2^-k/2) such that with probability tending to 1 as n→, a random k-CNF formula F _k(n, rn) is p-satisfiable but not (p+Δ)-satisfiable.

Original language	English (US)
Article number	1219098
Journal	Journal of the ACM
Volume	54
Issue number	2
DOIs	https://doi.org/10.1145/1219092.1219098
State	Published - Apr 1 2007
Externally published	Yes

All Science Journal Classification (ASJC) codes

Software
Control and Systems Engineering
Information Systems
Hardware and Architecture
Artificial Intelligence

Keywords

Maximum satisfiability

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10.1145/1219092.1219098

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abstract = "Say that a k-CNF a formula is p-satisfiable if there exists a truth assignment satisfying a fraction 1 - 2-k +p 2-k of its clauses (note that every k-CNF formula is 0-satisfiable). Let Fk(n, m) denote a random k-CNF formula on n variables with m clauses. For every k2 and every r>0 we determine p and Δ=Δ(k)=O(k2-k/2) such that with probability tending to 1 as n→, a random k-CNF formula F k(n, rn) is p-satisfiable but not (p+Δ)-satisfiable.",

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AU - Naor, Assaf

AU - Peres, Yuval

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N2 - Say that a k-CNF a formula is p-satisfiable if there exists a truth assignment satisfying a fraction 1 - 2-k +p 2-k of its clauses (note that every k-CNF formula is 0-satisfiable). Let Fk(n, m) denote a random k-CNF formula on n variables with m clauses. For every k2 and every r>0 we determine p and Δ=Δ(k)=O(k2-k/2) such that with probability tending to 1 as n→, a random k-CNF formula F k(n, rn) is p-satisfiable but not (p+Δ)-satisfiable.

AB - Say that a k-CNF a formula is p-satisfiable if there exists a truth assignment satisfying a fraction 1 - 2-k +p 2-k of its clauses (note that every k-CNF formula is 0-satisfiable). Let Fk(n, m) denote a random k-CNF formula on n variables with m clauses. For every k2 and every r>0 we determine p and Δ=Δ(k)=O(k2-k/2) such that with probability tending to 1 as n→, a random k-CNF formula F k(n, rn) is p-satisfiable but not (p+Δ)-satisfiable.

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On the maximum satisfiability of random formulas

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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