Yes there is. You may want to look into Deterministic and Non-Deterministic Finite Automata. They are foundational to computability and Turing machines.

https://en.wikipedia.org/wiki/Deterministic_finite_automaton...

You are designing a "prefix code". It is a collection of strings of button presses such as {A, BA, BBAA, BBABA, BBB, ...}. Each string maps to an action.

Ideally no string is a prefix of another string. Even more ideally any infinite sequence of As and Bs can be decoded into a sequence of actions.