Question: [15] Let x satisfy C(x) n O(1), where n = l(x). (a) Show that C(y), C(z) 1 2n O(1) for x
[15] Let x satisfy C(x) ≥ n − O(1), where n = l(x).
(a) Show that C(y), C(z) ≥ 1 2n − O(1) for x = yz and l(y) = l(z).
(b) Show that C(y) ≥ n/3 − O(1) and C(z) ≥ 2n/3 − O(1) for x = yz and l(z)=2l(y).
(c) Let x = x1 ...xlog n with l(xi) = n/ log n for all 1 ≤ i ≤ log n. Show that C(xi) ≥ n/ log n − O(log log n) for all 1 ≤ i ≤ log n.
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