Semicomputable function

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In computability theory, a semicomputable function is a partial function that can be approximated either from above or from below by a computable function.

More precisely a partial function is upper semicomputable, meaning it can be approximated from above, if there exists a computable function , where is the desired parameter for and is the level of approximation, such that:

Completely analogous a partial function is lower semicomputable iff is upper semicomputable or equivalently if there exists a computable function such that

If a partial function is both upper and lower semicomputable it is called computable.

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References[edit]

  • Ming Li and Paul Vitányi, An Introduction to Kolmogorov Complexity and Its Applications, pp 37–38, Springer, 1997.