Does automata theory have many interesting open questions?

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I’m studying Automata Theory and I love it. My question is, is there much more research to discover in automata theory, aside from quantum automata? Also, as a side question, are quantum automata the place to be for research in this field?

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You will find a series of open problems in

J.-É. Pin, Open problems about regular languages, 35 years later, The Role of Theory in Computer Science, Essays Dedicated to Janusz Brzozowski, World Scientific (2017), 153-176.

Another famous open problem in automata theory is Cerny's conjecture.