3-sat phase and hardness

http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.0217v1.pdf

It was observed early [4, 17] that plotting P[UNSAT]
against shows a sharp threshold behavior at some critical c. Furthermore,
around this c it also takes various algorithms the longest time to solve random
3-SAT problems, i.e., the problems are hard. To quantify the hardness, either
the number of distinct steps of the solving algorithm is counted, or simply the
time measured until the problem is solved. The divergence of the hardness together
with the sudden jump of P[UNSAT] at some critical resembles a phase
transition-like behavior [9, 21]. The numerical analysis of this sharp threshold
behavior resulted in c = 4.15 ± 0.05 [10].