Question

Question 4. Let L1 be the language denoted by

ab∗ a ∗

and let L2 be the language denoted by

a ∗ b ∗ a

Write a regular expression that denotes the language L1 ∩ L2.

Answer 1

R.E.(L1) = ab*a

Therefore , L1 = { a, ab, aa, aba, aaa, abba, aaaa, abbaa, abbbaa, abbbaaa ....}

R.E.(L2) = a*b*a

Therefore , L2 = { a, ba, aa, aba, aaa, abba, aaaa, aabba, aaaaa, abbba, aabbba ....}

So, L1  ∩ L2= {a,aa, aaa aba,aaaa, abba, aaaaa, abbba .....}

Therefore,$R.E.(L1\cap L2 ) = a^++ab^*a=a(a^*+b^*a)$