Question: [15] Consider the following proof for Exercise 6.10.20 without using Kolmogorov complexity: Assume that a PRAM M adds n numbers in o(log n) time. Take

[15] Consider the following ‘proof’ for Exercise 6.10.20 without using Kolmogorov complexity: Assume that a PRAM M adds n numbers in o(log n) time. Take any input x1,...,xn. Then there is an input xk that is ‘not useful’ as in the hint in Exercise 6.10.20.

If we change xk to xk + 1, then the output should still be the same, since xk is not useful, a contradiction. What is wrong with this proof?

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