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+…….. }