The idea of a read-only right-moving Turing Machine already exists . Is there a relaxed version of this where an input-reading head only moves right to read inputs as needed? There may be other heads doing the computation on work tapes; the movement of these heads is unrestricted.
Of course the right-moving head could simply copy the contents to another unrestricted TM tape and start that; I'm trying to study TM configurations where the TM works as much as possible before requesting another input character.
I'm assuming this machine is Turing complete; correct me if I'm wrong.
References with your answer would be helpful. Thanks