All the questions that saw about languages of TMs that can move only right, there were decidable, even polynomial languages.
Is there a rule that says that Atm, Htm for TMs that can move only right are decidable problems?
And another question about it:
In solutions, there were an assumption that if TM can move only right and it reaches the empty side of the tape, after each step in this part of tape it changes it state, so after |Q|+1 steps we can check if it enters same configuration twice.
I can't understand why is it right, why can't it use the following transition formula:
delta(_, q0) = (letter, R, q0) - meaning, right something and go right…
OK, during writing the question, i understood it :)
If transition function doesn't change it's state when it sees " ", you can bravely say that this machine won't halt. because this is what it will always do.
So you should check if it changed more than |Q| states, if it, you will get same configuration at least once ==> loop.
So the first question is still open.