(A) Undecidable.
The problem of determining whether two Turing machines accept the same language is known as the language equivalence problem for Turing machines. This problem is undecidable because it would require deciding, for every possible input string, whether both machines behave identically. This problem can be reduced from the halting problem, which is undecidable. Hence, option (A) is undecidable.
(B) Undecidable.
Deciding whether the language accepted by a given Turing machine is regular is an undecidable problem. There is no algorithm that can examine an arbitrary Turing machine and determine whether its language can be recognized by a finite automaton. This follows from Rice’s Theorem, since regularity is a non-trivial semantic property of the language recognized by a Turing machine. Therefore, option (B) is undecidable.
(C) Undecidable.
The problem of deciding whether a Turing machine accepts all possible strings over its input alphabet is undecidable. This problem is equivalent to the universality problem for Turing machines, which can be reduced from the halting problem. Since the halting problem is undecidable, option (C) is also undecidable.
(D) Decidable.
For a fixed constant number of steps, it is possible to decide whether a Turing machine takes more than that many steps on every input string. This is because the behavior of a Turing machine for a bounded number of steps can be fully simulated, and only a finite number of configurations need to be examined. Hence, option (D) is decidable.