1. If doable, find a regular expression for the following languages over alphabet T:{a , b}. In either case, provide a brief explanation for your response.

i. { , a, b, c, aa, bb, cc, ..., a^n, b^n, c^n,...} (Over alphabet {a,b,c})

ii. Strings that do not end with bb

iii. Strings which contains even number of a's

iv. Strings which do not contain the substring ab

2. Verify whether or not the following regular expressions generate (represent) the same language. Explain your answers.

i. a*(b + ab*) = b + aa*b*

ii. (a + b)* = a*(ba*)

3. Construct a DFA for each of the languages generated by regular expressions in Question 1

(briefly explain your answer)

4. Construct an NFA for the following languages (briefly explain your answer)

i. (a + b)*a

ii. (ab + abc)*