Logical depth

Complexity metrics
(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).


  1. . . "Logical Depth and Physical Complexity". In The Universal Turing Machine a Half-Century Survey, edited by Rolf Herken, 2:207–35. Vienna: Springer Vienna. DOI.

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