"The meaning of token" is ambiguous. Do you intend to say the outcome of the token or what the machine is supposed to do with the token?

If you intend to say the "outcome", then yes we do disagree on the meaning of parsability. The meaning of the token isn't to play fortune teller; if you give a machine tape input, the machine doesn't pretend to somehow create a pipeline of the future, knowing the state of machine at time t+1. It only knows the state at execution t, where the reader is.

This isn't a perl problem. I know you know this. So what is this requirement on the parser that you are saying is a perl problem?

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