# Examples of Finite Regular Expressions

Finite Regular expressions are used to represent the finite regular languages. As we know, finite regular languages have a finite number of strings. So, the length of finite regular expressions is always limited.

## Examples of Finite Regular Expressions

Following are the various examples of finite regular expressions

### Example 01

Write the regular expression for the language which has no string.

Solution:

Language for the given example is given below

L = { } //empty string

Regular expression for the above language is given below

L(R) = Φ

### Example 02

Write the regular expression for the language with a string with zero length.

Solution

Language for the given example is given below

L = { ε } //single string

Regular expression for the above language is given below

L(R) = ε

### Example 03

Write the regular expression for the language with a string with a single length over ∑ = {a, b}.

Solution

Language for the given example is given below

L = { a,b } //string with single length

A regular expression for the above language is given below

L(R) = (a+b)

### Example 04

Write the regular expression for the language with a string with the length of two over ∑ = {a, b}.

Solution

Language for the given example is given below

L =  (a,b).(a,b) = { aa,ab,ba,bb } //string with length of two

A regular expression for the above language is given below

L(R) = (aa+ab+ba+bb)

### Example 05

Write the regular expression for the language with a string of three over ∑ = {a, b}.

Solution

Language for the given example is given below

L = (a,b).(a,b). (a,b) = { aaa,abb,aab,baa……..,bbb } //string with length of three

Regular expression for the above language is given below

L(R) = (aaa + abb + aab + baa+……..+ bbb)

### Example 06

Write the regular expression for the language with strings with an at-most length of 2 over ∑ = {a, b}.

Solution

Language for the given example is given below

L = (ε,a,b).( ε,a,b) = { ε, a ,b, aa,ba……..,bb } // strings with at-most length of 2

Regular expression for the above language is given below

L(R) = (ε+a+b).( ε+a+b)

### Example 07

Write the regular expression for the language with strings “Not More than two a’s and one b” over ∑ = {a, b}.

Solution

Language for the given example is given below

L = { ε, a ,b, aa,aba, aab…….. } // strings with Not More than two a’s and one b

Regular expression for the above language is given below

L(R) = { ε + a + b + aa +aba + aab+…….. }