A language is considered regular if it can be recognized by a finite state machine. Non-regular languages require memory or the ability to count strings. Examples of non-regular languages include L={anbn} where n can vary, as counting is required. Regular languages can be defined in terms of finite state machines and are closed under operations like union, intersection, concatenation, and Kleene closure.

1. Regular Languages
A language is said to be Regular Language if and only if
some
Finite State Machine(FSM) recognizes it.
Which languages are not Regular?
The languages
which are not recognized by any FSM
which require memory

2. Finite State Machine
FSM has the limited memory
It cannot store or count strings
Example for Non-regular languages
L={an
bn
}
if n=3 then aaabbb
Eg if n=4 then aaaabbbb
count is required so cannot
recognized by FSM

3. Examples of Regular Languages

4. Operations on Regular
Languages
Some of the operations on regular languages are
as follows
Union
Intersection
Difference
Concatenation
kleen * closure

5. Union
If Ll and If L2 are two regular
languages, their union Ll u L2 will
also be regular.
For example, Ll = {an
I n > O}
and
L2 = {bn
I n > O}
L3 = Ll U L2 = {an
U bn
I n > O}
is also regular

6. Intersection
If Ll and If L2 are two regular
languages, their intersection Ll n
L2 will also be regular.
For example,
Ll = {am
bn
I n > 0 and m > O}
and
L2 = {am
bn
U bn
am
I n > 0 and m
> O}
L3 = Ll n L2 = {am
bn
I n > 0 and
m > O} is also regular.

7. Concatenation
If Ll and If L2 are two regular
languages, their concatenation
L1.L2 will also be regular.
For example,
Ll = {an
I n > 0} and L2 = {bn
I n
> O}
L3 = L1.L2 = {am
. bn
I m > 0 and
n > O} is also regular.

8. Kleene Closure
If Ll is a regular language, its
Kleene closure Ll* will also be
regular.
For example, Ll = (a U b ), Ll* =
(a U b)*

9. Compliment
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.
For example,
L(G) = {an
I n > 3}
L'(G) = {an
I n <= 3}

10. Thank You!