# Logical depth

tags
Complexity metrics
references
(Bennett 1995)

Logical depth can be defined as the run time of the Turing Machine that uses the minimal representation for an input $$x$$, $$M_{\min}(x)$$ — which is also its Kolmogorov complexity . It is therefore uncomputable (because the minimal representation is uncomputable).

## Bibliography

Bennett, Charles H. 1995. “Logical Depth and Physical Complexity.” In The Universal Turing Machine a Half-Century Survey, edited by Rolf Herken and Rolf Herken, 2:207–35. Vienna: Springer Vienna.