# Examples of Finite Regular Expressions

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

**Examples of Finite Regular Expressions**

**Example 01**

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

**Solution:**

Language for given example is given below

L = { } //empty string

Regular expression for above language is given below

L(R) = Φ

**Example 02**

Write the regular expression for the language **which has string with zero length.**

**Solution**

Language for given example is given below

L = { ε } //single string

Regular expression for above language is given below

L(R) = ε

**Example 03**

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

**Solution**

Language for given example is given below

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

Regular expression for above language is given below

L(R) = (a+b)

**Example 04**

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

**Solution**

Language for given example is given below

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

Regular expression for above language is given below

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

**Example 05**

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

**Solution**

Language for 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 above language is given below

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

**Example 06**

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

**Solution**

Language for 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 above language is given below

L(R) = (ε+a+b).( ε+a+b)

**Example 07**

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

**Solution**

Language for 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 above language is given below

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