Question

Let L 1be the language denoted by ab ∗ a ∗ and let L 2 be the language denoted by a ∗ b ∗ a Write a regular expression that denotes the language L 1 ∩ L 2 .

Answer 1

1.

• For the language L1, the regular expression is R1 = ab*a*
• Now expanding the language L1 = {a , ab ,aba , aaaaa , ......}

2.

• For the language L2, the regular expression is R2 = a*b*a
• Now expanding the language L2 = {a , aba ,aaabbba , aaaaa , ......}

3.

• Based on this expanding, the intersection of L1 and L2 will include all the strings that are common in both the languages i.e  
• L 1 ∩ L 2 = { a , abs , abbba , abbbaaaa , ..... }
• L 1 ∩ L 2 = {w | w belongs to (a+b)* , w starts and ends with a and have b*a* as a substring }

4.

• The regular expression based on these statements will be :
• R 1 ∩ R 2 = ab*a*a