If language

L = ɸ = { } then r (regular expression) = ɸ

L = {λ} the r = λ

L = {a} then r = a

L = {a, b} then r = a + b

L = {a, b, aa, bb} then r = a + b + aa + bb

L = {λ, a, b} then r = λ + a + b

If the language is finite then we write a regular expression for it. Language finite means it has finite no. of strings.


One language has more than one Regular Expression



But one Regular Expression has a unique Regular Language.

Now one language has many machines.



Same as a Regular Expression has many machines.




L = ɸ   ∑ = {a, b}     RE = ɸ



So, one Regular Expression (RE) may have several machines (DFA or NFA) or one machine may several RE.





RE = (a + b)*



So, some RE may more than one machine.





For one machine may more than one Regular Expression.


RE1 = (a + ba*b)*ba*   and RE2 = a*b(a + ba*b)* 

We can write another regular expression for this machine RE3 = a*b(a + ba*b)*a*

So, one machine may one or more regular expressions.



But one Regular Expression has one unique language.



Because we know L = {a, b} RE = a + b and L = {a, ab, ba} RE = a + ab + ba

Because the language is finite and we can write a RE for it then it is a regular language.


String length wise ordering is called proper ordering. Another way we can order is alphabetically ordering. = {λ, a, aa, aaa, ab,….. , bbb}