Recursively Enumerable Language - Closure Properties

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.