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Pasted title into question, deleted erroneous tag. –  Gerry Myerson Apr 3 '12 at 7:39
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Changed BPP to BBP. –  Robert Israel Apr 4 '12 at 0:29
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up vote 5 down vote accepted

Nobody has done it yet, and it hasn't been for lack of trying. However, Bailey and Crandall have some interesting results showing that there may be some connection there: see e.g. http://www.scribd.com/doc/54635409/Random-Generators-and-Normal-Numbers-Bailey-e-Crandall-2003

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