Finite State Automata for recognising consecutive characters I'm currently working on this question as part of some homework, it has me stumped.



I'm familiar with finite state automata (FSA), I know how they work and I've read everything I can find on Google, but nothing's helped me come any closer to a solution.

If I don't know the length of the input string, or I'm not searching for a particular pattern, how can I design a machine that will always land on the final state? 

I've tried drawing some, but that always end up being a little off.
The FSA should have three states: 


$q_a$ represents:  last character was not a b, and no bb yet
$q_b$ represents:  last character was a b, and no bb yet
$q_{bb}$ represents:  there was already a bb


Clearly, you start with $q_a$ and you accept in $q_a$ and $q_b$. Now try to figure out how to connect the states.