Antunes, Fortnow, van Melkebeek and Vinodchandran captured the
notion of non-random information by computational depth, the
difference between the polynomial-time-bounded Kolmogorov
complexity and traditional Kolmogorov complexity We show how to
find satisfying assignments for formulas that have at least one
assignment of logarithmic depth. The converse holds under a
standard hardness assumptions though fails if BPP = UP = EXP.

We also show that under standard hardness assumptions one cannot
increase the depth of a string efficiently and that such
an assumption is required.