  Depth of an object concerns a tradeoff between computation time and excess of
program length over the shortest program length required to obtain the object.
It gives an unconditional lower bound on the computation time from a given
program in absence of auxiliary information. Variants known as logical depth
and computational depth are expressed in Kolmogorov complexity theory.
  We derive quantitative relation between logical depth and computational depth
and unify the different depth notions by relating them to A. Kolmogorov and L.
Levin's fruitful notion of randomness deficiency. Subsequently, we revisit the
computational depth of infinite strings, introducing the notion of super deep
sequences and relate it with other approaches.
