Closure Properties
Recursively enumerable languages are closed under the following operations. That is, if L and P are two recursively enumerable languages, then the following languages are recursively enumerable as well:
- the Kleene star of L
- the concatenation of L and P
- the union
- the intersection .
Note that recursively enumerable languages are not closed under set difference or complementation. The set difference L - P may or may not be recursively enumerable. If L is recursively enumerable, then the complement of L is recursively enumerable if and only if L is also recursive.
Read more about this topic: Recursively Enumerable Language
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