
%bitcoin.tex: A Probabilistic Analysis of Bitcoin attacks
%%a Plain TeX file by Evangelos Georgiadis and Doron Zeilberger (x pages)

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\centerline
{\bf A Probabilistic Analysis of Bitcoin attacks }
\bigskip
\centerline
{\it Evangelos GEORGIADIS and Doron ZEILBERGER}
\bigskip


$$
{\frac { ( q-1 )  ( 4
\,{q}^{2}-3\,q-2 ) }{ ( 2\,q-1 ) ^{4}}}-{\frac {
( q-1 )  ( 4\,{q}^{2}+2\,q-7 ) }{ ( 2\,q-1
 ) ^{6}n}}-{\frac { ( q-1 )  ( 24\,{q}^{4}-12\,{q
}^{3}-58\,{q}^{2}+29\,q+18 ) }{ ( 2\,q-1 ) ^{8}{n}^{2}
}}
$$
$$
-{\frac { ( q-1 )  ( 144\,{q}^{6}-216\,{q}^{5}-348\,{
q}^{4}+444\,{q}^{3}+328\,{q}^{2}-312\,q-41 ) }{ ( 2\,q-1
 ) ^{10}{n}^{3}}}
$$
$$
-{\frac { ( q-1 )  ( 864\,{q}^{8
}-2160\,{q}^{7}-1704\,{q}^{6}+4956\,{q}^{5}+4632\,{q}^{4}-9972\,{q}^{3}
+1586\,{q}^{2}+1711\,q+88 ) }{ ( 2\,q-1 ) ^{12}{n}^{4}
}} \, + \, O(\frac{1}{n^5})
$$

\end
