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Consider the following statements about L:
(i) L is accepted by multi-tape turing machine M1.
(ii) L is also accpted by a single tape turing machine M2.
Which of the following statement is correct?
(i) L is accepted by multi-tape turing machine M1.
(ii) L is also accpted by a single tape turing machine M2.
Which of the following statement is correct?
- a)Acceptance by M2 is slower by O(n2)
- b)Acceptance of M2 is slower by O(n)
- c)Acceptance of M2 is faster by O(n2)
- d)Acceptabce by M2 is faster by 0(n)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Consider the following statements about L:(i)L is accepted by multi-ta...
While simulating multi-tape TM on a single tape TM, the head has to move at least 2k cells per move, where k is the number of tracks on single tape TM. Thus for k moves, we get
which means quadratic slow down. Thus, acceptance by single-tape is slower by 0(n2).
which means quadratic slow down. Thus, acceptance by single-tape is slower by 0(n2).
Most Upvoted Answer
Consider the following statements about L:(i)L is accepted by multi-ta...
Statement: L is accepted by a multi-tape Turing machine M1.
Statement: L is also accepted by a single-tape Turing machine M2.
To determine the correctness of the given statements, let's analyze the implications of each statement individually.
Statement (i): L is accepted by a multi-tape Turing machine M1.
A multi-tape Turing machine has multiple tapes, which allows it to perform multiple operations simultaneously. This can potentially speed up the computation compared to a single-tape Turing machine.
Statement (ii): L is also accepted by a single-tape Turing machine M2.
A single-tape Turing machine has only one tape and can perform one operation at a time. It might seem slower than a multi-tape Turing machine because of its sequential nature.
To determine the correctness of the given options, we need to consider the time complexity of the acceptance by M1 and M2.
Option (a): Acceptance by M2 is slower by O(n^2).
This option states that the acceptance by M2 is slower than M1 by a quadratic time complexity, O(n^2). However, there is no evidence or information provided in the given statements to support this claim. Therefore, option (a) cannot be concluded as the correct answer.
Option (b): Acceptance of M2 is slower by O(n).
This option states that the acceptance by M2 is slower than M1 by a linear time complexity, O(n). Again, there is no evidence or information provided in the given statements to support this claim. Therefore, option (b) cannot be concluded as the correct answer.
Option (c): Acceptance of M2 is faster by O(n^2).
This option states that the acceptance by M2 is faster than M1 by a quadratic time complexity, O(n^2). However, this contradicts the given statements which suggest that both M1 and M2 accept the language L. Therefore, option (c) cannot be concluded as the correct answer.
Option (d): Acceptance by M2 is faster by O(n).
This option states that the acceptance by M2 is faster than M1 by a linear time complexity, O(n). This option is supported by the given statements and is consistent with the sequential nature of a single-tape Turing machine. Therefore, option (d) is the correct answer.
In conclusion, the correct answer is option (d) - Acceptance by M2 is faster by O(n).
Statement: L is also accepted by a single-tape Turing machine M2.
To determine the correctness of the given statements, let's analyze the implications of each statement individually.
Statement (i): L is accepted by a multi-tape Turing machine M1.
A multi-tape Turing machine has multiple tapes, which allows it to perform multiple operations simultaneously. This can potentially speed up the computation compared to a single-tape Turing machine.
Statement (ii): L is also accepted by a single-tape Turing machine M2.
A single-tape Turing machine has only one tape and can perform one operation at a time. It might seem slower than a multi-tape Turing machine because of its sequential nature.
To determine the correctness of the given options, we need to consider the time complexity of the acceptance by M1 and M2.
Option (a): Acceptance by M2 is slower by O(n^2).
This option states that the acceptance by M2 is slower than M1 by a quadratic time complexity, O(n^2). However, there is no evidence or information provided in the given statements to support this claim. Therefore, option (a) cannot be concluded as the correct answer.
Option (b): Acceptance of M2 is slower by O(n).
This option states that the acceptance by M2 is slower than M1 by a linear time complexity, O(n). Again, there is no evidence or information provided in the given statements to support this claim. Therefore, option (b) cannot be concluded as the correct answer.
Option (c): Acceptance of M2 is faster by O(n^2).
This option states that the acceptance by M2 is faster than M1 by a quadratic time complexity, O(n^2). However, this contradicts the given statements which suggest that both M1 and M2 accept the language L. Therefore, option (c) cannot be concluded as the correct answer.
Option (d): Acceptance by M2 is faster by O(n).
This option states that the acceptance by M2 is faster than M1 by a linear time complexity, O(n). This option is supported by the given statements and is consistent with the sequential nature of a single-tape Turing machine. Therefore, option (d) is the correct answer.
In conclusion, the correct answer is option (d) - Acceptance by M2 is faster by O(n).
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Consider the following statements about L:(i)L is accepted by multi-tape turing machine M1.(ii)L is also accpted by a single tape turing machine M2.Which of the following statement is correct?a)Acceptance by M2 is slower by O(n2)b)Acceptance of M2 is slower by O(n)c)Acceptance of M2 is faster by O(n2)d)Acceptabce by M2 is faster by 0(n)Correct answer is option 'A'. Can you explain this answer?
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Consider the following statements about L:(i)L is accepted by multi-tape turing machine M1.(ii)L is also accpted by a single tape turing machine M2.Which of the following statement is correct?a)Acceptance by M2 is slower by O(n2)b)Acceptance of M2 is slower by O(n)c)Acceptance of M2 is faster by O(n2)d)Acceptabce by M2 is faster by 0(n)Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following statements about L:(i)L is accepted by multi-tape turing machine M1.(ii)L is also accpted by a single tape turing machine M2.Which of the following statement is correct?a)Acceptance by M2 is slower by O(n2)b)Acceptance of M2 is slower by O(n)c)Acceptance of M2 is faster by O(n2)d)Acceptabce by M2 is faster by 0(n)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements about L:(i)L is accepted by multi-tape turing machine M1.(ii)L is also accpted by a single tape turing machine M2.Which of the following statement is correct?a)Acceptance by M2 is slower by O(n2)b)Acceptance of M2 is slower by O(n)c)Acceptance of M2 is faster by O(n2)d)Acceptabce by M2 is faster by 0(n)Correct answer is option 'A'. Can you explain this answer?.
Consider the following statements about L:(i)L is accepted by multi-tape turing machine M1.(ii)L is also accpted by a single tape turing machine M2.Which of the following statement is correct?a)Acceptance by M2 is slower by O(n2)b)Acceptance of M2 is slower by O(n)c)Acceptance of M2 is faster by O(n2)d)Acceptabce by M2 is faster by 0(n)Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following statements about L:(i)L is accepted by multi-tape turing machine M1.(ii)L is also accpted by a single tape turing machine M2.Which of the following statement is correct?a)Acceptance by M2 is slower by O(n2)b)Acceptance of M2 is slower by O(n)c)Acceptance of M2 is faster by O(n2)d)Acceptabce by M2 is faster by 0(n)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements about L:(i)L is accepted by multi-tape turing machine M1.(ii)L is also accpted by a single tape turing machine M2.Which of the following statement is correct?a)Acceptance by M2 is slower by O(n2)b)Acceptance of M2 is slower by O(n)c)Acceptance of M2 is faster by O(n2)d)Acceptabce by M2 is faster by 0(n)Correct answer is option 'A'. Can you explain this answer?.
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ample number of questions to practice Consider the following statements about L:(i)L is accepted by multi-tape turing machine M1.(ii)L is also accpted by a single tape turing machine M2.Which of the following statement is correct?a)Acceptance by M2 is slower by O(n2)b)Acceptance of M2 is slower by O(n)c)Acceptance of M2 is faster by O(n2)d)Acceptabce by M2 is faster by 0(n)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
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