# Logical depth

Formally, in the context of some universal computer ${\displaystyle U}$ the logical depth of a string ${\displaystyle x}$ to significance level ${\displaystyle s}$ is given by ${\displaystyle {\text{min}}\{T(p):(|p|-|p^{*}| the running time of the fastest program that produces ${\displaystyle x}$ and is no more than ${\displaystyle s}$ longer than the minimal program.