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2 changes: 1 addition & 1 deletion holochain.tex
Original file line number Diff line number Diff line change
Expand Up @@ -505,7 +505,7 @@ \section{Complexity In Distributed Systems}
\subsection{Bitcoin}
Let $\Omega_{Bitcoin}$ be the Bitcoin network, $n$ be the number of transactions and $m$ be the number full validating nodes (i.e., \textit{miners}\footnote{For the sake of simplicity and focusing on a lower bound of the system's complexity, we are neglecting all nodes that are not crucial for the operation of the network, such as light-clients and clients not involved in the process of validation}) within $\Omega_{Bitcoin}$.

For every new transaction being issued, any given node will have to check the transaction's signature (among other checks, see. \cite{bitcoin-protocol}) and especially check if this transaction's output is not used in any other transaction to reject double-spendings, resulting in a time complexity of
For every new transaction being issued, any given node will have to check the transaction's signature (among other checks, see \cite{bitcoin-protocol}) and especially check if this transaction's output is not used in any other transaction to reject double-spendings, resulting in a time complexity of
\begin{equation}
c+n
\end{equation}
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