Recursively enumerable set

Recursive enumeration of the set of all Turing machines halting on a fixed input: Simulate all Turing machines (enumerated on vertical axis) step by step (horizontal axis), using the shown diagonalization scheduling. If a machine terminates, print its number. This way, the number of each terminating machine is eventually printed. In the example, the algorithm prints

In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing-recognizable if:

Or, equivalently,

The first condition suggests why the term semidecidable is sometimes used; the second suggests why computably enumerable is used. The abbreviations r.e. and c.e. are often used, even in print, instead of the full phrase.

单词	Enumerability
释义	Enumerability 英语百科 Recursively enumerable set In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing-recognizable if: Or, equivalently, The first condition suggests why the term semidecidable is sometimes used; the second suggests why computably enumerable is used. The abbreviations r.e. and c.e. are often used, even in print, instead of the full phrase.
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Enumerability

Recursively enumerable set