quality:correction
Definitions

A Blum complexity measure is a pair (φ, Φ) {\displaystyle (\varphi,\Phi)} with φ {\displaystyle \varphi } a numbering of the partial computable functions P (1) {\displaystyle \mathbf {P} ^{(1)}} and a computable function

which satisfies the following Blum axioms. We write φ i {\displaystyle \varphi _{i}} for the i -th partial computable function under the Gödel numbering φ {\displaystyle \varphi }, and Φ i {\displaystyle \Phi _{i}} for the partial computable function Φ (i) {\displaystyle \Phi (i)}.