An exposé exposes the research problem you are working on in your BA thesis. It serves as an agreement between you and the supervisors, so you both know what is expected from your thesis. It helps you to focus your research on a small set of questions, instead of exploring all directions. Therefore, to write an expose you need to have some understanding of the context of your research.
Now state your research questions, it should be 3 at maximum. They should be formulated clearly, concise, and related to your problem. If you answer your research questions you should be able to solve your research problem.
Describe your first ideas how you want to tackle the problem and answer your questions. Here you should reference related work that you will use, e.g. using finite state automata I will ..., if these are well-established approaches you do not need a citation, e.g. for Petri nets.
This section will most probably change during your research, as you will need to adapt your approach to the obstacles you will encounter. Or you have new great ideas.