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Normal number 
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#1
Apr214, 12:47 AM

P: 993

Wikipedia is not very clear on this. Is there a known computable normal number?
I found this paper: http://www.glyc.dc.uba.ar/santiago/papers/absnor.pdf But I'm not sure if it's been peer reviewed. 


#2
Apr214, 12:51 AM

Mentor
P: 18,240

What do you mean with "computable"?
Anyway, consider the Campernowne constant. It is just [tex]0.123456789101112131415161718192021222324...[/tex] This is known to be normal (one of the very few explicit numbers known to be normal, although it is also known that "most" numbers are normal). And it will probably also satisfy your criterium of computability. http://en.wikipedia.org/wiki/Champernowne_constant Now, your paper (which certainly is peerreviewed and correct!) shows the existence not only of a computable normal number, but of an computable absolutely normal number. This means that it is normal in any integer base ##\geq 2##. Champernowne's constant is only known to be normal in base ##10##. I don't think any other examples of absolutely normal computable numbers are known, but I'm not an expert. 


#3
Apr214, 02:08 AM

P: 993

Yes, I meant "absolutely normal". Computable means digits are enumerable by a Turing machine or uniform family of circuits. That paper presents a superexponentialtime algorithm for computing Sierpinski's construction.
Is there a known polynomialtime computable normal number? How many conjectures will the existence of such a number ruin? 


#4
Apr314, 07:58 AM

Sci Advisor
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P: 2,537

Normal number



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