# User:IssaRice/Computability and logic/Least search operator

From Machinelearning

The **least search operator**, **minimzation operator**, or **μ-operator** is used in computability theory to define new functions.

The least search operator allows us to move from primitive recursive functions to general recursive (total or partial) functions.

## Definition

- note: the least search operator may run into an "infinite loop". This means that partial recursive functions are not in general total.

## Notation

Most texts seem to write the least search operator was as in or maybe (like the operator for defining anonymous functions).

Boolos/Burgess/Jeffrey use (for "minimization").

## Intuition

bounded search vs unbounded search; bounded for-loop vs while-loop.