Recursively Enumerable Set
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High Quality Content by WIKIPEDIA articles! 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: There is an algorithm that, when given an input number, eventually halts if and only if the input is an element of S. Or, equivalently, there is an algorithm that enumerates the members of S. That means that its output is simply a list of the members of S: s1, s2, s3, ... . If necessary, this algorithm may run forever. The first condition suggests why the…mehr

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High Quality Content by WIKIPEDIA articles! 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: There is an algorithm that, when given an input number, eventually halts if and only if the input is an element of S. Or, equivalently, there is an algorithm that enumerates the members of S. That means that its output is simply a list of the members of S: s1, s2, s3, ... . If necessary, this algorithm may run forever. 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.