Consider a single-tape Turing machine that cannot write on its tape, but does have three pebbles on the tape. The pebbles are colored red, green, and blue, and all three are initially on the leftmost tape cell. Each move of this Turing machine works like a standard one (except it cannot write on the tape) with the additional operation of determining which pebbles (if any) are on the tape cell currently being scanned by the head, and optionally moving each of these pebbles one cell to the left or right (pebbles do not have to move in the same direction that the head does, and if there is more than one pebble on the current tape cell, they do not have to more in the same direction). A. Describe how any r. e. set can be accepted by such a Turing Machine. HINT: Simulate a two-counter machine.
B. Suppose that the pebbles are not colored and one cannot tell them apart; is it still possible to accept any r. e. set?