Finite automata and languages question

Question

I have attempted these few simple questions, can someone let me know if this is correct please? If not please provide the answer as I learn better that way and if possible explain.

i) FA1 Start = -X1 and FA1 End = +X2

FA2 Start = -Y1 and FA2 End = +Y3

ii) FA1 NOT ACCEPTED and FA2 ACCEPTED

iii) In FA1 the string must begin with 'a' and this is in a loop, the next string is a 'b' followed by another 'b' in a loop. it can then go back round through 'a' and start again but must end with a 'b'

In FA2 it must start with a 'b' and is in a loop, then it is followed by an 'a' and go back through 'b' or continue onto 'a' and then end or go through 'a' in a loop or start the cycle again through 'b' back to the start but must end with an 'a' at y3.

Answer 1

That's not quite right. Here's a hint:

• What are the necessary suffixes for $L_1$ and $L_2$?
• Suppose $w_1 \in L_1$. Does $\mathtt{a}w_1$ or $\mathtt{b}w_1$ belong to $L_1$?
• Suppose $w_2 \in L_2$. Does $\mathtt{a}w_2$ or $\mathtt{b}w_2$ belong to $L_2$?

I hope this helps $\ddot\smile$

Answer 2

Your answers:
(i) is OK
(ii) There are four questions, you need to give four answers.
(iii) Hint. Give a regular expression for the languages accepted by $FA_1$ and $FA_2$ and then convert them to plain English.