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Unformatted text preview: (c) 0 n 1 followed by any arbitrary sequence. (d) (Optional) ω 1 ω 2 ...ω n followed by any arbitrary sequence, where Ω = ∑ U ( p ) halts 2l ( p ) , Ω = .ω 1 ω 2 ..., where Ω is the probability that the computer halts. 4. Image Complexity. Consider two binary subsets A and B (of an n × n grid). For example, ¶ ± ‡ · ¤ § ¥ ƒ Find general upper and lower bounds, in terms of K ( A  n ) and K ( B  n ), for (a) K ( A c  n ) . (b) K ( A ∪ B  n ) . (c) K ( A ∩ B  n ) . 5. Random program Suppose that a random program (symbols i.i.d. uniform over the symbol set) is fed into the nearest available computer. To our surprise the ﬁrst n bits of the binary expansion of 1 / √ 2 are printed out. Roughly what would you say the probability is that the next output bit will agree with the corresponding bit in the expansion of 1 / √ 2 ? 2...
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 Spring '05
 TomCover
 Binary numeral system, arbitrary sequence

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