Exam 12: Theory of Computation

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List the following complexity classes in order of increasing complexity. Θ(n3)Θ(2n)Θ(log2n)Θ(n)\Theta \left( n ^ { 3 } \right) \quad \Theta \left( 2 ^ { n } \right) \quad \Theta \left( \log _ { 2 } n \right) \quad \Theta ( n )

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The precise time complexity of which of the following problems has not yet been established by researchers?

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Are all problems in P solvable in a reasonable amount of time? Explain your answer.

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Is a problem in O(n³)more complex than a problem in O(n²)? Explain your answer.

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A _______________ is a relationship between input and output values such that any input is associated with only one output.If the output can be determined algorithmically from the input,the relationship is said to be _______________ .

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Which of the following algorithms represents an optimal solution (in terms of time complexity)for sorting a list?

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A.Give an example of an algorithm for sorting a list with time complexity in Θ\Theta (n2). B.Give an example of an algorithm for sorting a list with time complexity in Θ\Theta (n lg n).

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What action is performed by the Turing machine described below? Current Current Value Direction New START * * left X X 1 0 left X X 0 0 right Y 0 0 right Y Y * * no move HALT

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Complete the following sentence. An NP-complete problem is a problem in NP for which ___________________________.

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Which of the following questions has not yet been answered by researchers?

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Which of the following statements is false?

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