# 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+…….. }