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: e, aba, bbabba would be in this language. Then write down this automata formally using our 5-tuple notation. 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