Von Neumann Extractor - Which bit is retained?
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Which bit is retained in the Von Neumann debiasing algorithm? 00 and 11 are discarded and 10, 01 are retained but is the first or the second bit retained or does it matter?
In other words:
first: 10 -> 1 , 01 -> 0
second: 10 -> 0 , 01 -> 1
Original Paper (appears to be first but could be interpreted either way):
https://dornsifecms.usc.edu/assets/sites/520/docs/VonNeumann-ams12p36-38.pdf
Examples (first digit accept):
https://en.wikipedia.org/wiki/Hardware_random_number_generator#Software_whitening
https://en.wikipedia.org/wiki/Randomness_extractor
http://pit-claudel.fr/clement/blog/generating-uniformly-random-data-from-skewed-input-biased-coins-loaded-dice-skew-correction-and-the-von-neumann-extractor/#more-410
https://people.seas.harvard.edu/~salil/pseudorandomness/extractors.pdf
Examples (second digit accept):
https://www.researchgate.net/publication/38359648_Iterating_Von_Neumann's_Procedure_for_Extracting_Random_Bits
https://www.esat.kuleuven.be/cosic/publications/article-2628.pdf
Examples of the second are present in papers regarding an Iterated Von Neumann algorithm.
randomness entropy
asked 3 hours ago
bitbltbitblt
183
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add a comment |
$begingroup$
Which bit is retained in the Von Neumann debiasing algorithm? 00 and 11 are discarded and 10, 01 are retained but is the first or the second bit retained or does it matter?
In other words:
first: 10 -> 1 , 01 -> 0
second: 10 -> 0 , 01 -> 1
Original Paper (appears to be first but could be interpreted either way):
https://dornsifecms.usc.edu/assets/sites/520/docs/VonNeumann-ams12p36-38.pdf
Examples (first digit accept):
https://en.wikipedia.org/wiki/Hardware_random_number_generator#Software_whitening
https://en.wikipedia.org/wiki/Randomness_extractor
http://pit-claudel.fr/clement/blog/generating-uniformly-random-data-from-skewed-input-biased-coins-loaded-dice-skew-correction-and-the-von-neumann-extractor/#more-410
https://people.seas.harvard.edu/~salil/pseudorandomness/extractors.pdf
Examples (second digit accept):
https://www.researchgate.net/publication/38359648_Iterating_Von_Neumann's_Procedure_for_Extracting_Random_Bits
https://www.esat.kuleuven.be/cosic/publications/article-2628.pdf
Examples of the second are present in papers regarding an Iterated Von Neumann algorithm.
randomness entropy
asked 3 hours ago
bitbltbitblt
183
New contributor
bitblt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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2
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Does it matter? Hint: Write down the assumptions, and compute from the assumptions the probability distributions of the outcomes of both alternatives.
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– Squeamish Ossifrage
2 hours ago
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Why pick one when you can alternate?
$endgroup$
– Nat
12 mins ago
add a comment |
$begingroup$
Which bit is retained in the Von Neumann debiasing algorithm? 00 and 11 are discarded and 10, 01 are retained but is the first or the second bit retained or does it matter?
In other words:
first: 10 -> 1 , 01 -> 0
second: 10 -> 0 , 01 -> 1
Original Paper (appears to be first but could be interpreted either way):
https://dornsifecms.usc.edu/assets/sites/520/docs/VonNeumann-ams12p36-38.pdf
Examples (first digit accept):
https://en.wikipedia.org/wiki/Hardware_random_number_generator#Software_whitening
https://en.wikipedia.org/wiki/Randomness_extractor
http://pit-claudel.fr/clement/blog/generating-uniformly-random-data-from-skewed-input-biased-coins-loaded-dice-skew-correction-and-the-von-neumann-extractor/#more-410
https://people.seas.harvard.edu/~salil/pseudorandomness/extractors.pdf
Examples (second digit accept):
https://www.researchgate.net/publication/38359648_Iterating_Von_Neumann's_Procedure_for_Extracting_Random_Bits
https://www.esat.kuleuven.be/cosic/publications/article-2628.pdf
Examples of the second are present in papers regarding an Iterated Von Neumann algorithm.
randomness entropy
asked 3 hours ago
bitbltbitblt
183
New contributor
bitblt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Which bit is retained in the Von Neumann debiasing algorithm? 00 and 11 are discarded and 10, 01 are retained but is the first or the second bit retained or does it matter?
In other words:
first: 10 -> 1 , 01 -> 0
second: 10 -> 0 , 01 -> 1
Original Paper (appears to be first but could be interpreted either way):
https://dornsifecms.usc.edu/assets/sites/520/docs/VonNeumann-ams12p36-38.pdf
Examples (first digit accept):
https://en.wikipedia.org/wiki/Hardware_random_number_generator#Software_whitening
https://en.wikipedia.org/wiki/Randomness_extractor
http://pit-claudel.fr/clement/blog/generating-uniformly-random-data-from-skewed-input-biased-coins-loaded-dice-skew-correction-and-the-von-neumann-extractor/#more-410
https://people.seas.harvard.edu/~salil/pseudorandomness/extractors.pdf
Examples (second digit accept):
https://www.researchgate.net/publication/38359648_Iterating_Von_Neumann's_Procedure_for_Extracting_Random_Bits
https://www.esat.kuleuven.be/cosic/publications/article-2628.pdf
Examples of the second are present in papers regarding an Iterated Von Neumann algorithm.
randomness entropy
randomness entropy
asked 3 hours ago
bitbltbitblt
183
New contributor
bitblt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 3 hours ago
bitbltbitblt
183
New contributor
bitblt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 3 hours ago
bitbltbitblt
183
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Check out our Code of Conduct.
asked 3 hours ago
bitbltbitblt
183
asked 3 hours ago
bitbltbitblt
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183
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bitblt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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bitblt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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2
$begingroup$
Does it matter? Hint: Write down the assumptions, and compute from the assumptions the probability distributions of the outcomes of both alternatives.
$endgroup$
– Squeamish Ossifrage
2 hours ago
$begingroup$
Why pick one when you can alternate?
$endgroup$
– Nat
12 mins ago
add a comment |
2
$begingroup$
Does it matter? Hint: Write down the assumptions, and compute from the assumptions the probability distributions of the outcomes of both alternatives.
$endgroup$
– Squeamish Ossifrage
2 hours ago
$begingroup$
Why pick one when you can alternate?
$endgroup$
– Nat
12 mins ago
2
2
$begingroup$
Does it matter? Hint: Write down the assumptions, and compute from the assumptions the probability distributions of the outcomes of both alternatives.
$endgroup$
– Squeamish Ossifrage
2 hours ago
$begingroup$
Does it matter? Hint: Write down the assumptions, and compute from the assumptions the probability distributions of the outcomes of both alternatives.
$endgroup$
– Squeamish Ossifrage
2 hours ago
$begingroup$
Why pick one when you can alternate?
$endgroup$
– Nat
12 mins ago
$begingroup$
Why pick one when you can alternate?
$endgroup$
– Nat
12 mins ago
add a comment |
1 Answer
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It doesn't matter at all, since both $01$ and $10$ have the same probability $p(1-p).$
answered 2 hours ago
kodlukodlu
9,45111332
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1
$begingroup$
Furthermore, using the second bit instead of the first (or vice versa) just has the effect of inverting the output. And a uniformly random bitstream is still uniform even if inverted.
$endgroup$
– Ilmari Karonen
2 hours ago
add a comment |
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1 Answer
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active
oldest
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$begingroup$
It doesn't matter at all, since both $01$ and $10$ have the same probability $p(1-p).$
answered 2 hours ago
kodlukodlu
9,45111332
$endgroup$
1
$begingroup$
Furthermore, using the second bit instead of the first (or vice versa) just has the effect of inverting the output. And a uniformly random bitstream is still uniform even if inverted.
$endgroup$
– Ilmari Karonen
2 hours ago
add a comment |
$begingroup$
It doesn't matter at all, since both $01$ and $10$ have the same probability $p(1-p).$
answered 2 hours ago
kodlukodlu
9,45111332
$endgroup$
1
$begingroup$
Furthermore, using the second bit instead of the first (or vice versa) just has the effect of inverting the output. And a uniformly random bitstream is still uniform even if inverted.
$endgroup$
– Ilmari Karonen
2 hours ago
add a comment |
$begingroup$
It doesn't matter at all, since both $01$ and $10$ have the same probability $p(1-p).$
answered 2 hours ago
kodlukodlu
9,45111332
$endgroup$
It doesn't matter at all, since both $01$ and $10$ have the same probability $p(1-p).$
answered 2 hours ago
kodlukodlu
9,45111332
answered 2 hours ago
kodlukodlu
9,45111332
answered 2 hours ago
kodlukodlu
9,45111332
answered 2 hours ago
kodlukodlu
9,45111332
9,45111332
1
$begingroup$
Furthermore, using the second bit instead of the first (or vice versa) just has the effect of inverting the output. And a uniformly random bitstream is still uniform even if inverted.
$endgroup$
– Ilmari Karonen
2 hours ago
add a comment |
1
$begingroup$
Furthermore, using the second bit instead of the first (or vice versa) just has the effect of inverting the output. And a uniformly random bitstream is still uniform even if inverted.
$endgroup$
– Ilmari Karonen
2 hours ago
1
1
$begingroup$
Furthermore, using the second bit instead of the first (or vice versa) just has the effect of inverting the output. And a uniformly random bitstream is still uniform even if inverted.
$endgroup$
– Ilmari Karonen
2 hours ago
$begingroup$
Furthermore, using the second bit instead of the first (or vice versa) just has the effect of inverting the output. And a uniformly random bitstream is still uniform even if inverted.
$endgroup$
– Ilmari Karonen
2 hours ago
add a comment |
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2
$begingroup$
Does it matter? Hint: Write down the assumptions, and compute from the assumptions the probability distributions of the outcomes of both alternatives.
$endgroup$
– Squeamish Ossifrage
2 hours ago
$begingroup$
Why pick one when you can alternate?
$endgroup$
– Nat
12 mins ago