Semicomputable function


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.