Computability and Logic

30 TURING COMPUTABILITY
Example 3.4. The object is to erase the leftmost stroke, fill the gap between the
two blocks of strokes, and halt scanning the leftmost stroke that remains on the tape.
Here is one way of doing it, in quadruple notation: q 1 S 1 S 0 q 1 ; q 1 S 0 Rq 2 ; q 2 S 1 Rq 2 ;
q 2 S 0 S 1 q 3 ; q 3 S 1 Lq 3 ; q 3 S 0 Rq 4 .
Example 3.5. A flow chart for a machine is shown in Figure 3-7.
Figure 3-7. Multiplication machine.
Here is how the machine works. The first block, of p strokes, is used as a counter,
to keep track of how many times the machine has added q strokes to the group at the
right. To start, the machine erases the leftmost of the p strokes and sees if there are
any strokes left in the counter group. If not, pq = q, and all the machine has to do is
position itself over the leftmost stroke on the tape, and halt.