Q 7. Let M be the DFA over {a, b} shown below.

(a) What are the initial and accepting states of M?

(b) Write out a table for δ, the transition function of M. Use □ for undefined entries.

(c) Show how M processes the input abbababba, indicating whether it is accepted or rejected.

(d) Let ∆ denote the extended transition function of M. Calculate each of the following states, writing □ if the state is undefined. (You do not need to show working.)

(i) ∆(baaba, q0)        (ii) ∆(ababb, q1)

(iii) ∆(bbaab, q2)      (iv) ∆(bbbbbbbbba, q0

(e) What is the shortest word in {a, b} ∗ accepted by M?

(f) Give a regular expression over {a, b} for the language of M,