eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2008-12-05
163
174
10.4230/LIPIcs.FSTTCS.2008.1750
article
A new upper bound for 3-SAT
Diaz, Josep
Kirousis, Lefteris
Mitsche, Dieter
Perez-Gimenez, Xavier
We show that a randomly chosen
$3$-CNF formula over $n$ variables with clauses-to-variables
ratio at least $4.4898$ is asymptotically almost surely unsatisfiable.
The previous best such bound,
due to Dubois in 1999, was $4.506$.
The first such bound, independently
discovered by many groups of researchers since 1983,
was $5.19$. Several decreasing values between
$5.19$ and $4.506$ were published in the years between.
The probabilistic techniques we use for the proof are, we believe, of independent interest.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol002-fsttcs2008/LIPIcs.FSTTCS.2008.1750/LIPIcs.FSTTCS.2008.1750.pdf
Satisfiability
3-SAT
random
threshold