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‎rlp_txn_v2/generalities/phase_end.tex

Lines changed: 21 additions & 21 deletions
Original file line numberDiff line numberDiff line change
@@ -4,24 +4,24 @@
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\begin{array}{l}
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\locValidPhaseTransition _{i} \define \vspace{2mm} \\
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\left[ \begin{array}{clcl}
7-
+ & \phaseRlpPrefix _{i} & \cdot \typeZeroTx _{i} & \cdot \phaseNonce _{i + 1} \\
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+ & \phaseRlpPrefix _{i} & \cdot (\typeOneTx _{i} + \typeTwoTx _{i}) & \cdot \phaseChainId _{i + 1} \\
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+ & \phaseChainId _{i} & & \cdot \phaseNonce _{i + 1} \\
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+ & \phaseNonce _{i} & \cdot (\typeZeroTx _{i} + \typeOneTx _{i}) & \cdot \phaseGasPrice _{i + 1} \\
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+ & \phaseNonce _{i} & \cdot \typeTwoTx _{i} & \cdot \phaseMaxPriorityFeePerGas_{i + 1} \\
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+ & \phaseGasPrice _{i} & & \cdot \phaseGasLimit _{i + 1} \\
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+ & \phaseMaxPriorityFeePerGas_{i} & & \cdot \phaseMaxFeePerGas _{i + 1} \\
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+ & \phaseMaxFeePerGas _{i} & & \cdot \phaseGasLimit _{i + 1} \\
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+ & \phaseGasLimit _{i} & & \cdot \phaseTo _{i + 1} \\
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+ & \phaseTo _{i} & & \cdot \phaseValue _{i + 1} \\
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+ & \phaseValue _{i} & & \cdot \phaseData _{i + 1} \\
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+ & \phaseData _{i} & \cdot \typeZeroTx _{i} & \cdot \phaseBeta _{i + 1} \\
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+ & \phaseData _{i} & \cdot (\typeOneTx{} + \typeTwoTx{}) & \cdot \phaseAccessList _{i + 1} \\
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+ & \phaseAccessList _{i} & & \cdot \phaseY _{i + 1} \\
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+ & \phaseBeta _{i} & & \cdot \phaseR _{i + 1} \\
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+ & \phaseY _{i} & & \cdot \phaseR _{i + 1} \\
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+ & \phaseR _{i} & & \cdot \phaseS _{i + 1} \\
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+ & \phaseS _{i} & & \cdot \phaseRlpPrefix _{i + 1} \\
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+ & \phaseRlpPrefix _{i} & \cdot \typeZeroTx _{i} & \cdot \phaseNonce _{i + 1} \\
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+ & \phaseRlpPrefix _{i} & \cdot (\typeOneTx _{i} + \typeTwoTx _{i}) & \cdot \phaseChainId _{i + 1} \\
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+ & \phaseChainId _{i} & & \cdot \phaseNonce _{i + 1} \\
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+ & \phaseNonce _{i} & \cdot (\typeZeroTx _{i} + \typeOneTx _{i}) & \cdot \phaseGasPrice _{i + 1} \\
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+ & \phaseNonce _{i} & \cdot \typeTwoTx _{i} & \cdot \phaseMaxPriorityFeePerGas _{i + 1} \\
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+ & \phaseGasPrice _{i} & & \cdot \phaseGasLimit _{i + 1} \\
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+ & \phaseMaxPriorityFeePerGas _{i} & & \cdot \phaseMaxFeePerGas _{i + 1} \\
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+ & \phaseMaxFeePerGas _{i} & & \cdot \phaseGasLimit _{i + 1} \\
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+ & \phaseGasLimit _{i} & & \cdot \phaseTo _{i + 1} \\
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+ & \phaseTo _{i} & & \cdot \phaseValue _{i + 1} \\
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+ & \phaseValue _{i} & & \cdot \phaseData _{i + 1} \\
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+ & \phaseData _{i} & \cdot \typeZeroTx _{i} & \cdot \phaseBeta _{i + 1} \\
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+ & \phaseData _{i} & \cdot (\typeOneTx _{i} + \typeTwoTx _{i}) & \cdot \phaseAccessList _{i + 1} \\
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+ & \phaseAccessList _{i} & & \cdot \phaseY _{i + 1} \\
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+ & \phaseBeta _{i} & & \cdot \phaseR _{i + 1} \\
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+ & \phaseY _{i} & & \cdot \phaseR _{i + 1} \\
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+ & \phaseR _{i} & & \cdot \phaseS _{i + 1} \\
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+ & \phaseS _{i} & & \cdot \phaseRlpPrefix _{i + 1} \\
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\end{array} \right]
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\end{array}
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\]
@@ -32,12 +32,12 @@
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\item \label{rlp txn v2: generalities: PHASE_END constraints}
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$\phaseEnd_{i} = \locValidPhaseTransition_{i}$
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\end{enumerate}
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In other words, a phase transition happens if and only if $\phaseEnd_{i} = 1$ and means $\phase{p}_{i} = 1$ and $\phase{q}_{i + 1} = 1$ with the only given possibility for p and q, depending of $\rlpTxnTransactionColumnTxType$:
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\saNote{}
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The above constraint~(\ref{rlp txn v2: generalities: PHASE_END constraints})
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must be understood as follows: rather than \textbf{constraining} \phaseEnd{},
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the constraints will often times \textbf{set} the value of \phaseEnd{} and thereby forcing a phase transition.
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the constraints will often times \textbf{set} the value of \phaseEnd{} and thereby force a phase transition upon the module.
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40+
In other words, a phase transition happens if and only if $\phaseEnd_{i} = 1$ and means $\phase{p}_{i} = 1$ and $\phase{q}_{i + 1} = 1$ with the only given possibility for p and q, depending of $\rlpTxnTransactionColumnTxType$:
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\begin{table}[h]
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\centering
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\renewcommand{\arraystretch}{1.5}

‎rlp_utils/_local.tex

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -10,7 +10,7 @@
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\def\locWeightedFlagSum {\loc{wght\_flag\_sum}}
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% INTEGER instruction
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\def\integerCtMax {\redm{2}}
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\def\integerCtMax {\numConst{2}}
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\def\locInputInteger {\loc{in/integer}}
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\def\locInputIntegerHi {\locInputInteger\loc{\_hi}}
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\def\locInputIntegerLo {\locInputInteger\loc{\_lo}}
@@ -38,8 +38,8 @@
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\def\locBaseRlpPrefixShort {\loc{base\_rlp\_prefix\_short}}
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\def\locBaseRlpPrefixLong {\loc{base\_rlp\_prefix\_long}}
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\def\bytestringEmptyCtMax {\redm{0}}
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\def\bytestringNonEmptyCtMax {\redm{2}}
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\def\bytestringEmptyCtMax {\numConst{0}}
42+
\def\bytestringNonEmptyCtMax {\numConst{2}}
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\def\locInputBytestringLength {\loc{in/byte\_string\_length}}
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\def\locInputFirstByte {\loc{in/first\_byte}}

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