Consider a problem Z, in it-“Suppose there is a Turing Machine L over the input alphabet ∑ any state of L and a word s € ∑, does the computation of L on s visit the state q?Choose the correct statement about Z?a)Z is partially decidableb)Z is decidablec)Z is undecidabled)Z is undecidable but partially decidableCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Z is undecidable.

Explanation:

To determine whether problem Z is decidable or undecidable, we need to analyze the problem and its properties.

1. Problem Definition:
The problem Z is defined as follows:
Given a Turing Machine L, a state q, and a word s, we need to determine whether the computation of L on s visits the state q.

2. Decidability:
A problem is decidable if there exists an algorithm that can always provide a correct yes/no answer for every instance of the problem.

3. Partial Decidability:
A problem is partially decidable if there exists an algorithm that can provide a correct yes answer for every instance of the problem. However, if the answer is no, the algorithm may either provide a correct no answer or run indefinitely without halting.

4. Analysis of Problem Z:
To determine whether the computation of L on s visits the state q, we can simulate the execution of L on s and check if the state q is ever visited. There are two possible cases:

- If the state q is visited during the execution, we can answer yes.
- If the state q is never visited, we cannot answer no since the simulation can potentially run forever. This is because L may never halt or may go into an infinite loop without visiting the state q.

5. Conclusion:
Since there is no algorithm that can always provide a correct answer for every instance of problem Z, we can conclude that problem Z is undecidable. The algorithm for problem Z can provide a correct yes answer, but it may not halt for instances where the answer is no.

Therefore, the correct answer is option 'C': Z is undecidable.

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Which of the following languages are undecidable? Note that M indicates encoding of the Turing machine M.L1 = {ML(M) = φ]L2 = {M, w, qM on input w reaches state q in exactly 100 steps}L3 = {ML(M) is not recursiv e)L4 = {ML(M) contains at least 21 members)

Let A, B, C and D are problems. Consider the following polynomial reductions to know about the problem B.(i) AB (A is reducible to B)(ii) C D(iii) B DFind the correct statement from the following.

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