closure properties of regular language - Mind Map

closure properties of regular language

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.

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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.

KLEEN CLOSURE

Example

L1 = (a U b )

L1* = (a U b)*

If L1 is a regular language, its Kleene closure L1* will also be regular.

COMPLEMENT

Example

L(G) = {an | n > 3} L'(G) = {an | n <= 3}

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.

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