Final answer:
The problem of determining if a two-tape Turing machine writes a nonblank symbol on the second tape is undecidable. It can be formulated as a language L and shown to be undecidable by relating it to the undecidable halting problem. The assumption of a decider leads to a contradiction, proving L's undecidability.
Step-by-step explanation:
The question asks about the decidability of a problem related to a two-tape Turing machine. Specifically, the problem is to determine whether such a machine ever writes a nonblank symbol on its second tape during its computation on any input string. We can formulate this as a language L where each string in L represents the encoding of a two-tape Turing machine M that does write a nonblank symbol on its second tape for some input. The decidability of this problem can be related to the halting problem, which is a well-known undecidable problem.
To show that our language L is undecidable, we can assume that there exists a Turing machine H that decides L. If H exists, then we could use H to decide the halting problem by constructing a modified machine M' which uses its second tape to simulate the computation of another machine on a given input and writes a nonblank symbol if and only if the simulated machine halts. However, since the halting problem is undecidable, such a machine H cannot exist, hence our original problem is also undecidable.
The correct answer to the question is therefore (c) Undecidable.