recursively enumerable
For a language , TFAE:
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•
There exists a Turing machine such that .
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There exists a total recursive function which is onto.
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There exists a total recursive function which is one-to-one and onto.
A language fulfilling any (and therefore all) of the above conditions is called recursively enumerable.
Examples
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1.
Any recursive language.
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2.
The set of encodings of Turing machines which halt when given no input.
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3.
The set of encodings of theorems of Peano arithmetic.
- 4.
Title | recursively enumerable |
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Canonical name | RecursivelyEnumerable |
Date of creation | 2013-03-22 12:44:32 |
Last modified on | 2013-03-22 12:44:32 |
Owner | ariels (338) |
Last modified by | ariels (338) |
Numerical id | 6 |
Author | ariels (338) |
Entry type | Definition |
Classification | msc 03D25 |
Synonym | semi-recursive |
Related topic | HaltingProblem |
Related topic | TuringComputable |
Defines | semi-recursive |
Defines | recursively enumerable function |