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25th Annual Symposium on Foundations of Computer Science (FOCS 1984)
Singer Island, FL
October 24October 26
ISBN: 081860591X
ASCII Text  x  
M. Blum, "Independent Unbiased Coin Flips From A Correlated Biased Source: A Finite State Markov Chain," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 425433, 25th Annual Symposium on Foundations of Computer Science (FOCS 1984), 1984.  
BibTex  x  
@article{ 10.1109/SFCS.1984.715944, author = {M. Blum}, title = {Independent Unbiased Coin Flips From A Correlated Biased Source: A Finite State Markov Chain}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {1984}, isbn = {081860591X}, pages = {425433}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.1984.715944}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Independent Unbiased Coin Flips From A Correlated Biased Source: A Finite State Markov Chain SN  081860591X SP425 EP433 A1  M. Blum, PY  1984 VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
von Neumann's trick for generating an absolutely unbiased coin from a biased one is this: 1. Toss the biased coin twice, getting 00, 01, 10, or 11. 2. If 00 or 11 occur, go back to step 1; else 3. Call 10 a H, 01 a T. Since p[H] = p[1]*p[0] = p[T], the output is unbiased. Example: 00 10 11 01 01 /spl I.oarr/ H T T. Peter Elias gives an algorithm to generate an independent unbiased sequence of Hs and Ts that nearly achieves the Entropy of the onecoin source. His algorithm is excellent, but certain difficulties arise in trying to use it (or the original von Neumann scheme) to generate bits in expected linear time from a Markov chain. In this paper, we return to the original onecoin von Neumann scheme, and show how to extend it to generate an independent unbiased sequence of Hs and Ts from any Markov chain in expected linear time. We give a right and wrong way to do this. Two algorithms A and B use the simple von Neumann trick on every state of the Markov chain. They differ in the time they choose to announce the coin flip. This timing is crucial.
Citation:
M. Blum, "Independent Unbiased Coin Flips From A Correlated Biased Source: A Finite State Markov Chain," focs, pp.425433, 25th Annual Symposium on Foundations of Computer Science (FOCS 1984), 1984
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