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Time taken by one tape TM to simulate n moves of k-tape TM is
- a)O(n)
- b)0(nk)
- c)O(n2)
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Time taken by one tape TM to simulate n moves of k-tape TM isa)O(n)b)0...
Single tape turing machine can simulate n-moves of k-tape TM in O(n2).
Most Upvoted Answer
Time taken by one tape TM to simulate n moves of k-tape TM isa)O(n)b)0...
Explanation:
To simulate n moves of k-tape TM, we need to simulate each move of the k-tape TM n times. Let's assume that the maximum number of moves required by the k-tape TM is m.
So, the time taken by one tape TM to simulate n moves of k-tape TM would be:
n * m
As the maximum number of moves required by the k-tape TM is m, we can assume that the time complexity of simulating one move of the k-tape TM is O(m).
Therefore, the time complexity of simulating n moves of the k-tape TM would be:
n * O(m) = O(nm)
Now, as per the question, we are given that the k-tape TM has k tapes. Let's assume that the maximum length of the input on each tape is l.
So, the maximum number of moves required by the k-tape TM is:
O(l^k)
Therefore, the time taken by one tape TM to simulate n moves of k-tape TM would be:
n * O(l^k)
= O(n * l^k)
= O(n^2) (as l is a constant)
Hence, option (c) is the correct answer.
To simulate n moves of k-tape TM, we need to simulate each move of the k-tape TM n times. Let's assume that the maximum number of moves required by the k-tape TM is m.
So, the time taken by one tape TM to simulate n moves of k-tape TM would be:
n * m
As the maximum number of moves required by the k-tape TM is m, we can assume that the time complexity of simulating one move of the k-tape TM is O(m).
Therefore, the time complexity of simulating n moves of the k-tape TM would be:
n * O(m) = O(nm)
Now, as per the question, we are given that the k-tape TM has k tapes. Let's assume that the maximum length of the input on each tape is l.
So, the maximum number of moves required by the k-tape TM is:
O(l^k)
Therefore, the time taken by one tape TM to simulate n moves of k-tape TM would be:
n * O(l^k)
= O(n * l^k)
= O(n^2) (as l is a constant)
Hence, option (c) is the correct answer.
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