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recursively enumerable set
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Definitions of recursively enumerable set in various dictionaries:
RECURSIVELY ENUMERABLE SET - In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, s...
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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 such that the set of input numbers for which the algorithm halts is exactly 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. * In computational complexity theory, the complexity class containing all recursively enumerable sets is RE. In recursion theory, the lattice of r.e. sets under inclusion is denoted * * * * * * E * * * * * {\displaystyle {\mathcal {E}}} * . |