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modify (136) equation #324

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Aug 7, 2017
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modify (136) equation #324

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2 changes: 1 addition & 1 deletion Paper.tex
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Expand Up @@ -937,7 +937,7 @@ \subsection{The Execution Cycle}
O\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I)\big) & \equiv & (\boldsymbol{\sigma}', \boldsymbol{\mu}', A', I) \\
\Delta & \equiv & \mathbf{\alpha}_w - \mathbf{\delta}_w \\
\lVert\boldsymbol{\mu}'_\mathbf{s}\rVert & \equiv & \lVert\boldsymbol{\mu}_\mathbf{s}\rVert + \Delta \\
\quad \forall x \in [\mathbf{\alpha}_w, \lVert\boldsymbol{\mu}'_\mathbf{s}\rVert): \boldsymbol{\mu}'_\mathbf{s}[x] & \equiv & \boldsymbol{\mu}_\mathbf{s}[x+\Delta]
\quad \forall x \in [\mathbf{\alpha}_w, \lVert\boldsymbol{\mu}'_\mathbf{s}\rVert): \boldsymbol{\mu}'_\mathbf{s}[x] & \equiv & \boldsymbol{\mu}_\mathbf{s}[x-\Delta]
\end{eqnarray}

The gas is reduced by the instruction's gas cost and for most instructions, the program counter increments on each cycle, for the three exceptions, we assume a function $J$, subscripted by one of two instructions, which evaluates to the according value:
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