Even if something can change its semantics, you can still represent it as a state machine if you just make a copy of every state for every possible set of semantics. The semantic state can just be another part of the state machine's overall state.

> State machines cannot change the semantics of themselves.

That's not true at all. There are many, many state machine implementations where the machine's states and paths are altered by the machine itself. See for instance https://digitalcommons.trinity.edu/cgi/viewcontent.cgi?artic...