i didn't understand the part that explained the search operation: where the head keeps moving right until it reaches a'' or the end of the tape.
when you say "end of the tape" do you mean the end of the input? or the end of the infinite tape?!
and if it is the first option, then how does it know where the input stops, as there can be blank symbols in the middle of the left side of the tape during a run of the machine.