3. For we {a,b), let T(w) denote the processing time of machine M on word w....

  

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3. For we {a,b), let T(w) denote the processing time of machine M on word w. (a) Give a word w,, of length n> 0 such that T(w) is linear in n. Justify your answer by giving T(w) as a function of n and showing that it is in O(n). [3 marks] (b) Give a word , of length n > 0 (you may assume n is even) such that T() is quadratic in n. Justify your answer by giving T(vn) as a function of n and showing that it is in O(n²). [3 marks] 3. For we {a,b), let T(w) denote the processing time of machine M on word w. (a) Give a word w,, of length n> 0 such that T(w) is linear in n. Justify your answer by giving T(w) as a function of n and showing that it is in O(n). [3 marks] (b) Give a word , of length n > 0 (you may assume n is even) such that T() is quadratic in n. Justify your answer by giving T(vn) as a function of n and showing that it is in O(n²). [3 marks]

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a To find a word w such that Tw is linear in n we can consider a simple wordprocessing task that inv... View the full answer