We consider Boolean formulas with three literals per clause,
or 3-SAT formulas. For random formulas with m clauses over n variables,
such as r = m=n is a constant, it has been experimentally observed
that, asymptotically as r crosses the threshold value 4:2 (approximately)
the probability that Á is satis¯able falls abruptly from nearly 1 to 0.
Moreover, as n increases towards larger and larger values, the transition
of the probability becomes sharper. The purpose of this paper is to simply
outline a connection between the problem of determining bounds to the
threshold value and the concept of Kolmogorov complexity.