a) Draw a deterministic finite automata which accepts string over the alphabet {a,b} which don't contain the substring aa. So for example the strings: , aba, bbabba would be in this language. Then write down this automata formally using 5-tuple notation.

b) Argue using the pigeonhole principle, that any time your automata above accepts a string longer than some fixed length, it must repeat a state. For the automata you drew, what is this fixed length?

Mostly looking for an answer on b) ! Please explain. Thank you very much.