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What are the closure properties of Regular languages?
In an automata theory, there are different closure properties for regular languages. They are as follows −
- Union
- Intersection
- concatenation
- Kleene closure
- Complement
Let see one by one with an example
Union
If L1 and If L2 are two regular languages, their union L1 U L2 will also be regular.
Example
L1 = {an | n > O} and L2 = {bn | n > O}
L3 = L1 U L2 = {an U bn | n > O} is also regular.
Intersection
If L1 and If L2 are two regular languages, their intersection L1 ∩ L2 will also be regular.
Example
L1= {am bn | n > 0 and m > O} and
L2= {am bn U bn am | n > 0 and m > O}
L3 = L1 ∩ L2 = {am bn | n > 0 and m > O} are also regular.
Concatenation
If L1 and If L2 are two regular languages, their concatenation L1.L2 will also be regular.
Example
L1 = {an | n > 0} and L2 = {bn | n > O}
L3 = L1.L2 = {am . bn | m > 0 and n > O} is also regular.
Kleene Closure
If L1 is a regular language, its Kleene closure L1* will also be regular.
Example
L1 = (a U b )
L1* = (a U b)*
Complement
If L(G) is a regular language, its complement L'(G) will also be regular. Complement of a language can be found by subtracting strings which are in L(G) from all possible strings.
Example
L(G) = {an | n > 3} L'(G) = {an | n <= 3}
Note − Two regular expressions are equivalent, if languages generated by them are the same. For example, (a+b*)* and (a+b)* generate the same language. Every string which is generated by (a+b*)* is also generated by (a+b)* and vice versa.
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