The Threshold for Random k-SAT is 2^k ln2 - O(k)
| dc.creator | Achlioptas, Dimitris | |
| dc.creator | Peres, Yuval | |
| dc.date | 2003-05-14 | |
| dc.date | 2003-09-08 | |
| dc.date.accessioned | 2026-07-07T03:19:39Z | |
| dc.date.available | 2026-07-07T03:19:39Z | |
| dc.description | Let F be a random k-SAT formula on n variables, formed by selecting uniformly and independently m = rn out of all possible k-clauses. It is well-known that if r>2^k ln 2, then the formula F is unsatisfiable with probability that tends to 1 as n tends to infinity. We prove that there exists a sequence t_k = O(k) such that if r < 2^k ln 2 - t_k, then the formula F is satisfiable with probability that tends to 1 as n tends to infinity. Our technique yields an explicit lower bound for the random k-SAT threshold for every k. For k>3 this improves upon all previously known lower bounds. For example, when k=10 our lower bound is 704.94 while the upper bound is 708.94. | |
| dc.description | Added figures and explained the intuition behind our approach. Made a correction following comments of Chris Calabro | |
| dc.identifier | https://arxiv.org/abs/cs/0305009 | |
| dc.identifier | http://arxiv.org/abs/cs/0305009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/31549 | |
| dc.subject | Computational Complexity | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Probability | |
| dc.subject | F.2.2 | |
| dc.title | The Threshold for Random k-SAT is 2^k ln2 - O(k) | |
| dc.type | text |