Question

Give a regular expression for the set of strings over {a, b, c} such that the sum of the number of a’s and the number of b’s is equal to 3.

Answer 1

Solution for the regular expression is provided below. If any doubt please comment below.

Need to find the regular expression for which the sum of number of a and number of b is three. The input alphabet is{a, b, c}.

There are 8 possibilities for the sum of number of a and b as 3 (excluding c).

• aaa
• aab
• aba
• abb
• baa
• bab
• bba
• bbb

Now include c in all these possibilities. There is no restriction on number of c.

Required regular expression:

c*ac*ac*ac* + c*ac*ac*bc* + c*ac*bc*ac* + c*ac*bc*bc* + c*bc*ac*ac* + c*bc*ac*bc* + c*bc*bc*ac* + c*bc*bc*bc*

Here c* denotes zero or more occurrence of c.