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) $aba$
My Answer
Are multiple completion states allowed?