That's such a large field, and it's very new. You have plenty of room to make contributions, but I can't really list problems for you to solve. In order to identify the most pressing issues in your area of interest, I would have to be an expert in that area. That's why you need to make a contribution like this in order to become an expert. Writing a thesis or dissertation is only 10% of the work. The other 90% is reading enough RECENT articles by others so that you know what problems have been tackled and what has been done about them. You'll find your own research question when you look at the next logical step that should be taken after the steps that are being taken now (i.e. you build off of another recent article). So Google around for "automata language" to find articles about it, and read one that has a literature review.
The trick is to read an excellent, recent literature review. : )