Question

Let Σ= {a, b}. Construct a regular expression defining each of the following languages over Σ.

All words that contain exactly 2 b's or exactly 3 b's, not more

Answer 1

To construct a regular expression defining the language with exactly 2 b's or exactly 3 b's, we use separate regular expressions for each case.

Step-by-step explanation:

To construct a regular expression defining the language of all words that contain exactly 2 b's or exactly 3 b's, we can break it down into two parts: one for words with exactly 2 b's and one for words with exactly 3 b's, not more.

For words with exactly 2 b's, we can use the regular expression (a*b*a*)b(a*b*a*)b(a*b*). This expression allows any number of a's before, between, and after the two b's.

For words with exactly 3 b's, we can use the regular expression (a*b*a*)b(a*b*a*)b(a*b*a*)b(a*b*). This expression allows any number of a's before, between, and after the three b's.