Computability and Logic

34 TURING COMPUTABILITY
Problems
3.1 Consider a tape containing a block of n strokes, followed by a space, followed
by a block of m strokes, followed by a space, followed by a block of k strokes,
and otherwise blank. Design a Turing machine that when started on the leftmost
stroke will eventually halt, having neither printed nor erased anything ...
(a) ...on the leftmost stroke of the second block.
(b) ...on the leftmost stroke of the third block.
3.2 Continuing the preceding problem, design a Turing machine that when started
on the leftmost stroke will eventually halt, having neither printed nor erased
anything ...
(a) ...on the rightmost stroke of the second block.
(b) ...on the rightmost stroke of the third block.
3.3 Design a Turing machine that, starting with the tape as in the preceding problems,
will eventually halt on the leftmost stroke on the tape, which is now to contain a
block of n strokes, followed by a blank, followed by a block of m + 1 strokes,
followed by a blank, followed by a block of k strokes.
3.4 Design a Turing machine that, starting with the tape as in the preceding problems,
will eventually halt on the leftmost stroke on the tape, which is now to contain a
block of n strokes, followed by a blank, followed by a block of m − 1 strokes,
followed by a blank, followed by a block of k strokes.
3.5 Design a Turing machine to compute the function min(x, y) = the smaller of x
and y.
3.6 Design a Turing machine to compute the function max(x, y) = the larger of
x and y.