Is it possible to construct a Turing Machine such that given any finite input on a tape $s$, it clears the tape in a finite amount of time?
I have used such a TM as an intermediate step to show a reduction from the State Entry Problem to is $w \in L(M)$ problem but I don't know if it is feasible to construct one.
Even if we assume that the head of the TM always starts at the leftmost character on the tape and keep moving write, clearing each symbol we encounter, if the tape is infinite, how will we know when to stop moving right?