Closure properties of REGULAR Language

1. The union of two regular languages is regular.
2. The intersection of two regular languages is regular
3. The complement of a regular languages is regular
4. The difference of two regular languages is regular
5. The reversal of a regular languages is regular
6. The concatenation of two regular languages is regular
7. A homomorphism (substitution of strings for symbols) of a regular languages is regular
8. The inverse homomorphism of a regular languages is regular
9. If a language L is recursive, then it is recursively enumerable languages.

 

Recursively Enumerable & Recursive language

When a Turing Machine executes an input, there are 4 possible outcomes of execution.

Then the turning machine

i)                    Halts and accept the input

ii)                   Halts & rejects the input

iii)                 Never halts (fall into loop)

iv)                 Crash

The language accepted by Turning Machine is known as recursively enumerable.

A language is recursive if there exists a turning machine that accepts every string of the language & rejects every string that is not in the language.