Recall that LR is the language consisting of the inverses of all strings in a language L.

Let L be the language over {a,b,c} given by the regular expression (a+b+c)(a+b+c)(b+c)(a+b)*

Draw the state diagram for a DFA M1 with four states (not counting the dead state) which accepts L.

Give a regular expression for LR.

Draw the state diagram for an NFA M2 with four states which accepts LR.

Give the transition function, in tabular form, of a DFA M3 with 16 states (counting the dead state) which accepts LR. (The state diagram of M3 has 16 states and 48 transitions, making it too cumbersome to grade.)

Is M3 a minimal DFA? Explain your answer.