User:IssaRice/Computability and logic/Least search operator

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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 \mu as in \mu y[f(y) = 0] or maybe \mu y.f(y) = 0 (like the \lambda operator for defining anonymous functions).

Boolos/Burgess/Jeffrey use \mathrm{Mn} (for "minimization").

Intuition

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