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. Ideal

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.