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Pull in the changes from #616 that are from #151 #636

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Feb 22, 2018
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Pull in the changes from #616 that are from #151 #636

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Pull in the changes from #616 that are from #151
jamesray1 Feb 22, 2018
08debbd
Merge branch 'master' into patch-191
pirapira Feb 22, 2018
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21 changes: 12 additions & 9 deletions Paper.tex
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Original file line number Diff line number Diff line change
Expand Up @@ -959,24 +959,27 @@ \subsubsection{Machine State}
\subsubsection{Exceptional Halting}\hypertarget{Exceptional_Halting_function_Z}{}\linkdest{zhalt}

The exceptional halting function $Z$ is defined as:
\begin{equation}
\begin{equation}
Z(\boldsymbol{\sigma}, \boldsymbol{\mu}, I) \equiv
\begin{array}[t]{l}
\boldsymbol{\mu}_{\mathrm{g}} < C(\boldsymbol{\sigma}, \boldsymbol{\mu}, I) \quad \vee \\
\mathbf{\delta}_{w} = \varnothing \quad \vee \\
\lVert\boldsymbol{\mu}_{\mathbf{s}}\rVert < \mathbf{\delta}_{w} \quad \vee \\
( w \in \{ \text{\small JUMP}, \text{\small JUMPI} \} \quad \wedge \\ \quad \boldsymbol{\mu}_{\mathbf{s}}[0] \notin D(I_{\mathbf{b}}) ) \quad \vee \\
\boldsymbol{\mu}_g < C(\boldsymbol{\sigma}, \boldsymbol{\mu}, I) \quad \vee \\
\mathbf{\delta}_w = \varnothing \quad \vee \\
\lVert\boldsymbol{\mu}_\mathbf{s}\rVert < \mathbf{\delta}_w \quad \vee \\
( w = \text{\small JUMP} \quad \wedge \quad \boldsymbol{\mu}_\mathbf{s}[0] \notin D(I_\mathbf{b}) ) \quad \vee \\
( w = \text{\small JUMPI} \quad \wedge \quad \boldsymbol{\mu}_\mathbf{s}[1] \neq 0 \quad \wedge \\
\quad \boldsymbol{\mu}_\mathbf{s}[0] \notin D(I_\mathbf{b}) ) \quad \vee \\
( w = \text{\small RETURNDATACOPY} \wedge \\ \quad \boldsymbol{\mu}_{\mathbf{s}}[1] + \boldsymbol{\mu}_{\mathbf{s}}[2] > \lVert\boldsymbol{\mu}_{\mathbf{o}}\rVert) \quad \vee \\
\lVert\boldsymbol{\mu}_{\mathbf{s}}\rVert - \mathbf{\delta}_{w} + \mathbf{\alpha}_{w} > 1024 \quad \vee \\
\lVert\boldsymbol{\mu}_\mathbf{s}\rVert - \mathbf{\delta}_w + \mathbf{\alpha}_w > 1024
\neg I_{\mathrm{w}} \wedge W(w, \boldsymbol{\mu})
\end{array}
\end{equation}
where
\begin{equation}
W(w, \boldsymbol{\mu}) \equiv \begin{array}[t]{l}
w \in \{\text{\small CREATE}, \text{\small SSTORE}, \text{\small SELFDESTRUCT}\} \quad \vee \\
\text{\small LOG0} \le w \wedge w \le \text{\small LOG4} \quad \vee \\
w \in \{\text{\small CALL}, \text{\small CALLCODE}\} \wedge \boldsymbol{\mu}_{\mathbf{s}}[2] \neq 0
w \in \{\text{\small CREATE}, \, \text{\small SSTORE}, \\
\text{\small SELFDESTRUCT}\} \quad \vee \\
(\text{\small LOG0} \le w \wedge w \le \text{\small LOG4}) \quad \vee \\
(w \in \{\text{\small CALL}, \text{\small CALLCODE}\} \wedge \boldsymbol{\mu}_{\mathbf{s}}[2] \neq 0)
\end{array}
\end{equation}

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