# Finite state automata, multiple completion states?

I'm currently studying for an exam for a course where some of the material covered included finite state automata, I've completed a question and I'm not sure about my answer.

Exercise

Explain what is meant by a Finite State Automaton (FSA) by drawing an FSA to recognise strings of the form $$a^rb^s$$, where $$r\gt0$$ and $$s\ge0$$ and with an alphabet of $$\{a,b\}$$, i.e., there must be at least one $$a$$, zero or more $$b$$'s and all occurrences of $$a$$ must precede any occurrence of $$b$$. Illustrate, how your FSA works given the following sample strings:
$$\quad$$(i) $$abbb$$
$$\quad$$(ii) $$aaaa$$
$$\quad$$(iii) $$aba$$

Your DFA is close, but not quite right. Note that the description requires the strings in the language to have at least one $$a$$, whereas your DFA will accept the empty string. The fix is simple of course: