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 if and only if 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.