1.
Let us consider the NSA (the non-self-accepting Turing machines) and SA (the self-accepting
Turing machines). Which of the following statements is true?
a) The NSA is recursive, but not recursively enumerable, and SA is recursively enumerable;
b) The NSA is recursively enumerable, but not recursive, and SA is recursive;
c) Both NSA and SA are recursively enumerable;
d) The NSA is not recursively enumerable (like the set of reals), and SA is recursively
enumerable, but not recursive (like the set of positive integers);
e) None of the above.
Solution
The stetement D is correct
The NSA is not recursively enumerable and SA is recursively enumerable, but not recursive.