On the maximum satisfiability of random formulas

@article{Achlioptas2007OnTM,
  title={On the maximum satisfiability of random formulas},
  author={D. Achlioptas and A. Naor and Y. Peres},
  journal={J. ACM},
  year={2007},
  volume={54},
  pages={10}
}
Say that a <i>k</i>-CNF a formula is <i>p-satisfiable</i> if there exists a truth assignment satisfying a fraction 1 − 2<sup>−<i>k</i></sup> +<i>p</i> 2<sup>−<i>k</i></sup> of its clauses (note that every <i>k</i>-CNF formula is 0-satisfiable). Let <i>F</i><sub><i>k</i></sub>(<i>n</i>, <i>m</i>) denote a random <i>k</i>-CNF formula on <i>n</i> variables with <i>m</i> clauses. For every <i>k</i>≥2 and every <i>r</i>>0 we determine <i>p</i> and Δ=Δ(<i>k</i>)=<i>O</i>(<i>k</i>2<sup>−<i>k</i>/2… Expand
19 Citations
Bounds on thresholds related to maximum satisfiability of regular random formulas
  • 1
  • PDF
Limit Theorems for Random MAX-2-XORSAT
  • 3
The phase transition in random regular exact cover
  • C. Moore
  • Mathematics, Computer Science
  • ArXiv
  • 2015
  • 6
  • PDF
Bounds on Threshold of Regular Random k-SAT
  • 13
  • PDF
On the lower bounds of random Max 3 and 4-SAT
On the Lower Bounds of Random Max 3 and 4-SAT
  • 1
Random k-SAT: Two Moments Suffice to Cross a Sharp Threshold
  • 139
  • PDF
On the max-cut of sparse random graphs
  • 5
  • PDF
...
1
2
...

References

SHOWING 1-2 OF 2 REFERENCES
Approximation Algorithms for Combinatorial Problems
  • D. Johnson
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1974
  • 2,401
  • Highly Influential
  • PDF
Some optimal inapproximability results
  • 1,706
  • Highly Influential
  • PDF