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The execution function X returns remaining gas instead of a state #240

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The execution function X returns remaining gas instead of a state #240

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6 changes: 3 additions & 3 deletions Paper.tex
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Original file line number Diff line number Diff line change
Expand Up @@ -854,16 +854,16 @@ \subsection{Execution Overview}
\end{eqnarray}
\begin{equation}
X\big( (\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I) \big) \equiv \begin{cases}
\big(\varnothing, \boldsymbol{\mu}, A^0, I, ()\big) & \text{if} \quad Z(\boldsymbol{\sigma}, \boldsymbol{\mu}, I)\\
O(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I) \cdot \mathbf{o} & \text{if} \quad \mathbf{o} \neq \varnothing\\
\big(\varnothing, \boldsymbol{\mu}_g, A^0, I, ()\big) & \text{if} \quad Z(\boldsymbol{\sigma}, \boldsymbol{\mu}, I)\\
O(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I) \boxplus \mathbf{o} & \text{if} \quad \mathbf{o} \neq \varnothing\\
X\big(O(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I)\big) & \text{otherwise}\\
\end{cases}
\end{equation}

where
\begin{eqnarray}
\mathbf{o} & \equiv & H(\boldsymbol{\mu}, I) \\
(a, b, c) \cdot d & \equiv & (a, b, c, d)
(a, b, c, d) \boxplus e & \equiv & (a, b_g, c, d, e)
\end{eqnarray}

Note that we must drop the fourth value in the tuple returned by $X$ to correctly evaluate $\Xi$, hence the subscript $X_{0,1,2,4}$.
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