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