Examples of Regular Expression

Example 1:

Write the regular expression for the language accepting all the string which are starting with 1 and ending with 0, over ∑ = {0, 1}.

Solution:

In a regular expression, the first symbol should be 1, and the last symbol should be 0. The r.e. is as follows:

R = 1 (0+1)* 0  

Example 2:

Write the regular expression for the language starting and ending with a and having any combination of b's in between.

Solution:

The regular expression will be:

R = a b* a  

Example 3:

Write the regular expression for the language starting with a but not having consecutive b's.

Solution: The regular expression has to be built for the language:

L = {a, aab, ab, aaa, abab, .....}  

The regular expression for the above language is:

R = {a + ab}*  

Example 4:

Write the regular expression for the language accepting all the string in which any number of a's is followed by any number of b's is followed by any number of c's.

Solution: As we know, any number of a's means a* any number of b's means b*, any number of c's means c*. Since as given in problem statement, b's appear after a's and c's appear after b's. So the regular expression could be:

R = a* b* c*  

Example 5:

Write the regular expression for the language over ∑ = {0} having even length of the string.

Solution:

The regular expression has to be built for the language:

L = {ε, 00, 0000, 000000, ......}  

The regular expression for the above language is:

R = (00)*  

Example 6:

Write the regular expression for the language having a string which should have atleast one 0 and alteast one 1.

Solution:

The regular expression will be:

R = [(0 + 1)* 0 (0 + 1)* 1 (0 + 1)*] + [(0 + 1)* 1 (0 + 1)* 0 (0 + 1)*]  

Example 7:

Describe the language denoted by following regular expression

r.e. = (b* (aaa)* b*)*  

Solution:

The language can be predicted from the regular expression by finding the meaning of it. We will first split the regular expression as:

r.e. = (any combination of b's) (aaa)* (any combination of b's)

L = {The language consists of the string in which a's appear triples, there is no restriction on the number of b's}

Example 8:

Write the regular expression for the language L over ∑ = {0, 1} such that all the string do not contain the substring 01.

Solution:

The Language is as follows:

L = {ε, 0, 1, 00, 11, 10, 100, .....}  

The regular expression for the above language is as follows:

R = (1* 0*)  

Example 9:

Write the regular expression for the language containing the string over {0, 1} in which there are at least two occurrences of 1's between any two occurrences of 1's between any two occurrences of 0's.

Solution: At least two 1's between two occurrences of 0's can be denoted by (0111*0)*.

Similarly, if there is no occurrence of 0's, then any number of 1's are also allowed. Hence the r.e. for required language is:

R = (1 + (0111*0))*  

Example 10:

Write the regular expression for the language containing the string in which every 0 is immediately followed by 11.

Solution:

The regular expectation will be:

R = (011 + 1)*