Formal Languages Questions Medium
The closure properties of recursively enumerable languages refer to the properties that are preserved under certain operations on these languages. The closure properties of recursively enumerable languages are as follows:
1. Union: The union of two recursively enumerable languages is also recursively enumerable. In other words, if L1 and L2 are recursively enumerable languages, then their union L1 ∪ L2 is also recursively enumerable.
2. Intersection: The intersection of two recursively enumerable languages is also recursively enumerable. In other words, if L1 and L2 are recursively enumerable languages, then their intersection L1 ∩ L2 is also recursively enumerable.
3. Concatenation: The concatenation of a recursively enumerable language with any language is also recursively enumerable. In other words, if L1 is a recursively enumerable language and L2 is any language, then their concatenation L1L2 is also recursively enumerable.
4. Kleene Star: The Kleene star of a recursively enumerable language is also recursively enumerable. In other words, if L is a recursively enumerable language, then its Kleene star L* is also recursively enumerable.
5. Complementation: The complement of a recursively enumerable language is not necessarily recursively enumerable. In other words, if L is a recursively enumerable language, then its complement L' may or may not be recursively enumerable.
It is important to note that these closure properties apply specifically to recursively enumerable languages, which are a subset of formal languages.