symbols.tex

\documentclass[9pt,oneside]{amsart}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{longtable}
\usepackage{tabu}
\usepackage{colortbl}
%\usepackage{multicol}

% command from 9.4.1

\newcommand{\hcancel}[1]{%
    \tikz[baseline=(tocancel.base)]{
        \node[inner sep=0pt,outer sep=0pt] (tocancel) {#1};
        \draw[black] (tocancel.south west) -- (tocancel.north east);
    }%
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\newcommand{\reff}[1]{{\footnotesize #1}}
\newcommand{\weakhline}{\arrayrulecolor[gray]{0.9}\hline\arrayrulecolor{black}}

\begin{document}

\noindent
state transaction functions - (transaction) $\Upsilon$ $\rightarrow$
 (give rewards) $\Omega$ $\rightarrow$ (block) $\Pi$ \\
$\boldsymbol{\sigma}$ $\rightarrow$ $\boldsymbol{\sigma}_0$ $\rightarrow$
 $\boldsymbol{\sigma}_{P}$ $\rightarrow$ $\boldsymbol{\sigma}^*$ $\rightarrow$
 $\boldsymbol{\sigma}'$ \\
$\boldsymbol{\sigma}$ $\rightarrow$ $\boldsymbol{\sigma}_1'$ $\rightarrow$
 $\boldsymbol{\sigma}_1$ $\rightarrow$ $\boldsymbol{\sigma}^{**}$ $\rightarrow$
 $\boldsymbol{\sigma}'$

\begin{longtabu}{X[1.2lm] X[3] X}

\multicolumn3{c}{Greek Alphabets} \\\hline

$\mathbf{\alpha}$ &
stack items added &
\reff{9.4.1, 9.5} \\\hline

$\mathbf{\alpha}_w$ &
!!! &
\reff{9.4.2, 9.5} \\\hline

$\Delta$ &
!!! &
\reff{\textbf{9.5}} \\\hline

$\mathbf{\delta}$ &
stack items removed &
\reff{9.4.1, 9.5} \\\hline

$\delta$ &
number of stack items for a given operation &
\reff{3, 9.4.2} \\\hline

$\mathbf{\delta}_w$ &
!!! &
\reff{9.4.2, 9.5} \\\hline

$\epsilon$ &
exponential difficulty symbol for difficulty bomb (or ice age) &
\reff{\textbf{4.3.4}(4.4.4)} \\\hline

$\Gamma()$ &
function that maps a block to its initiation state &
\reff{\textbf{11.4}} \\\hline

$\boldsymbol{\mu}$ &
machine-state &
\reff{3, 9.4.0, 9.4.1, 9.4.2, 9.5} \\\hline

$\boldsymbol{\mu}'$ &
resultant machine state &
\reff{9.4.0(), 9.5} \\\weakhline

$\boldsymbol{\mu}_{\mathrm{g}}$ &
!!! &
\reff{9.4.0, 9.4.2} \\\weakhline

$\boldsymbol{\mu}_{\mathrm{i}}$ &
!!! &
\reff{9.4.0} \\\weakhline

$\boldsymbol{\mu}'_{\mathrm{i}}$ &
!!! &
\reff{9.5} \\\weakhline

$\boldsymbol{\mu}_{\mathbf{m}}$ &
machine's memory &
\reff{3, 9.4.0, 9.4.1} \\\weakhline

$\boldsymbol{\mu}'_{\mathbf{m}}$ &
!!! &
\reff{9.5} \\\hline

$\boldsymbol{\mu}_{\mathbf{o}}$ &
!!! &
\reff{9.4.0, 9.4.2()} \\\hline

$\boldsymbol{\mu}_{\mathrm{pc}}$ &
!!! ($\mathbb{N}_{256}$) &
\reff{9.4.0, 9.4.1, 9.5} \\\hline

$\boldsymbol{\mu}'_{\mathrm{pc}}$ &
!!! &
\reff{9.5} \\\hline

$\boldsymbol{\mu}_{\mathbf{s}}$ &
machine's stack &
\reff{3, 9.4.0, 9.4.2, 9.5} \\\hline

$\boldsymbol{\mu}'_{\mathbf{s}}$ &
!!! &
\reff{9.5} \\\hline

$\boldsymbol{\mu}_{\mathrm{g}}$ &
!!! &
\reff{9.4.0()} \\\hline

$\boldsymbol{\mu}'_{\mathrm{g}}$ &
remaining gas from the resultant machine state ($\boldsymbol{\mu}'$) &
\reff{9.4.0()} \\\hline

$\Lambda$ &
!!! &
\reff{(6.2), 7} \\\hline

$\Lambda_{4}$ &
!!! &
\reff{6.2()} \\\hline

$\Omega()$ &
block-finalisation state transition function that gives rewards &
\reff{2.0, 11.3, 11.4} \\\hline

$\Pi()$ &
block-level state transition function &
\reff{2.0, 4.3.2(4.4.2), 11.4} \\\hline

$\Phi$ &
block transition function which maps an incomplete block to a complete block &
\reff{\textbf{11.4}} \\\hline

$\boldsymbol{\sigma}, \boldsymbol{\sigma}_{t}$ &
world-state, global state, sequence of accounts &
\reff{2.0, 3, 4.3.2(4.4.2), 6.0, 7, 8, 9.3, 9.4.0, 9.4.2, 9.5, 11.3, 11.4} \\\hline

$\boldsymbol{\sigma}'$ &
final (post-transactional) state &
\reff{6.0, 6.2, 7, 8, 9.3, 9.4.0(), 9.5, 11.3} \\\hline

$\boldsymbol{\sigma}^*$ &
pre-final state &
\reff{\textbf{6.2}, \textbf{7}} \\\hline

$\boldsymbol{\sigma}^{**}$ &
resultant state &
\reff{7, 8} \\\hline

$\boldsymbol{\sigma}_0$ &
checkpoint state &
\reff{\textbf{6.2}, 11.4} \\\hline

$\boldsymbol{\sigma}_1$ &
first transitional state &
\reff{8} \\\hline

$\boldsymbol{\sigma}_1'$ &
!!! &
\reff{8} \\\hline

$\boldsymbol{\sigma}_{\mathrm{i}}$ &
!!! &
\reff{11.4} \\\hline

$\boldsymbol{\sigma}_{P}$ &
tuple of post-execution provisional state &
\reff{\textbf{6.2}} \\\hline

$\boldsymbol{\sigma}[a]$ &
account state &
\reff{4.1, 6.2, 11.3(), 11.4()} \\\hline

$\boldsymbol{\sigma}[a]_{\mathrm{b}}$ &
balance, number of Wei owned by this address ($\mathbb{N}_{256}$) &
\reff{4.1, 6.2, 7, 8, 11.3} \\\hline

$\boldsymbol{\sigma}[a]_{\mathrm{c}}$ &
codeHash, hash of the EVM code of this address ($\mathbb{N}_{32}$) &
\reff{4.1, 7, 8, 11.3()} \\\hline

$\boldsymbol{\sigma}[a]_{\mathrm{n}}$ &
nonce, (non-contract account) number of transactions sent from this address or (contract account) number of contract-creations made by this accout ($\mathbb{N}_{256}$) &
\reff{4.1, 6.2, 7, 8(), 11.3()} \\\hline

$\boldsymbol{\sigma}[a]_{\mathrm{s}}$ &
storageRoot, root node hash of a Merkle Patricia tree that encodes the storage contents of this accout ($\mathbb{N}_{32}$) &
\reff{4.1, 7(), 8(), 11.3()} \\\hline

$\varsigma_1$ &
pre-Homestead difficulty parameter &
\reff{(4.4.4)} \\\hline

$\varsigma_2$ &
Homestead difficulty parameter &
\reff{4.3.4(4.4.4)} \\\hline

$\Theta$ &
!!! &
\reff{8} \\\hline

$\Theta_{3}$ &
!!! &
\reff{(6.2)} \\\hline

$\Theta_{4}$ &
!!! &
\reff{6.2()} \\\hline

$\Upsilon$ &
transaction-level state transition function &
\reff{2.0, 3, 6.0, 11.4} \\\hline

$\Upsilon^{\mathrm{g}}()$ &
total gas used in the execution of a transaction &
\reff{6.0, 6.2, 11.4} \\\hline

$\Upsilon^{\mathbf{l}}()$ &
log items created by this transaction &
\reff{6.0, 6.2, 11.4} \\\hline

$\Upsilon^{\mathrm{z}}()$ &
status code resulting from the transaction &
\reff{6.0(), 6.2(), 11.4()} \\\hline

$\Xi(), \Xi_{\mathtt{...}}()$ &
code execution function &
\reff{7, 8, 9.3, 9.4.0} \\

\\
\multicolumn3{c}{Mathematical Symbols} \\\hline

$\equiv$ &
defined to be &
... \\\hline

$\lVert ... \rVert$ &
sequence length &
... \\\hline

$| ... |$ &
size of the code &
\reff{7} \\\hline

$\wedge$ &
and &
... \\\hline

$\vee$ &
or &
... \\\hline

$\bigvee$ &
bitwise or &
\reff{4.3.1(4.4.1), 4.3.2(4.4.2)} \\\hline

$()$ &
empty string &
\reff{4.1, 6.1, 7, 9.4.0, 9.4.4} \\\hline

$\varnothing$ &
empty set &
... \\\hline

$\top$ &
!!! &
\reff{6.2()} \\\hline

$\neg$ &
not &
\reff{9.4.2()} \\

\\
\multicolumn3{c}{Latin Alphabets} \\\hline

% AA
$A$ &
transaction substate &
\reff{6.1, 6.2, 7, 8, 9.3(), 9.4.0, 9.5} \\\hline

$A'$ &
!!! &
\reff{9.5} \\\hline

$A^0$ &
empty substate &
\reff{\textbf{6.1}, 9.4.0} \\\hline

$A_{\mathbf{l}}$ &
log series, series of archived and indexable 'checkpoints' &
\reff{6.1} \\\hline

$A_{\mathrm{r}}$ &
refund balance which increases through using the {\small SSTORE} instruction in order to reset contract storage &
\reff{6.1, 6.2} \\\hline

$A_{\mathbf{s}}$ &
self-destruct (suicide) set: a set of accounts that will be discarded &
\reff{6.1, 6.2} \\\hline

$A_{\mathbf{t}}$ &
set of touched empty accounts which are deleted at the end of a transaction &
\reff{6.1(), 6.2()} \\\hline

$a$ &
address of the new account &
\reff{7} \\\hline

$\mathbf{a}'$ &
!!! &
\reff{11.3()} \\\hline

$\mathbf{a}^*$ &
updated contract creation sender (see also $s$) &
\reff{7} \\\hline

$\mathbf{a}_1$ &
!!! &
\reff{8()} \\\hline

$\mathbf{a}_1'$ &
!!! &
\reff{8()} \\\hline

$\mathbf{a}_1$ &
!!! &
\reff{8()} \\\hline

$\mathbf{a}_1'$ &
!!! &
\reff{8()} \\\hline

{\small ADD} &
!!! &
\reff{9.4.1} \\\hline

% BB
$B$ &
this block &
\reff{2.0, 4.3.0(4.4.0), 4.3.2(4.4.2), 4.3.3(4.4.3), 6.2, 10, 11.3, 11.4} \\\hline

$B_{H}$ &
block header (see $H$) &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4), 11.1} \\\hline

${B_{H}}_{\mathrm{c}}$ &
beneficiary ($H_{\mathrm{c}}$) &
\reff{6.2} \\\hline

$B_{\mathrm{d}}$ &
block's difficulty &
\reff{10} \\\hline

${\mathbf{B}_{H}}_{\mathrm{c}}$ &
!!! &
\reff{11.3} \\\hline

${B_{H}}_{\mathrm{g}}$ &
total gas used in the block ($H_{\mathrm{g}}$) &
\reff{11.2} \\\hline

${B_{H}}_{\mathrm{i}}$ &
!!! ($H_{\mathrm{i}}$) &
\reff{11.3} \\\hline

${B_{H}}_{\mathrm{l}}$ &
block's gasLimit ($H_{\mathrm{l}}$) &
\reff{6.2} \\\hline

$B_{\mathbf{R}}$ &
transaction receipts in this block &
\reff{4.3.1(4.4.1), 4.3.2(4.4.2), 6.2} \\\hline

$B_{\mathbf{T}}$ &
a series of the transactions in this block &
\reff{4.3.0(4.4.0), 4.3.2(4.4.2), 4.3.3(4.4.3), 11.4} \\\hline

$B_{\mathrm{t}}$ &
total difficulty of block &
\reff{10} \\\hline

$B'_{\mathrm{t}}$ &
total difficulty of the parent block &
\reff{10} \\\hline

$B_{\mathbf{U}}$ &
list of ommer (uncle) block headers &
\reff{4.3.0(4.4.0), 4.3.2(4.4.2), 4.3.3(4.4.3), 4.3.4(4.4.4), 11.1, 11.3} \\\hline

$B'$ &
parent block &
\reff{\textbf{10}} \\\hline

$B'$ &
!!! complete block &
\reff{11.4} \\\hline

$B'_{\mathrm{n}}$ &
!!! &
\reff{11.4} \\\hline

$B'_{\mathrm{m}}$ &
!!! &
\reff{11.4} \\\hline

$B^*$ &
!!! &
\reff{11.4} \\\hline

$B^*_{\hcancel{n}}$ &
!!! &
\reff{11.4} \\\hline

$B^*_{\mathrm{r}}$ &
!!! &
\reff{11.4} \\\hline

$\mathbb{B}, \mathbb{B}_{number}$ &
byte sequence, of length $number$ &
\reff{3, 4.1, 4.2(4.3), 4.3.1(4.4.1), 4.3.3(4.4.3)} \\\hline

$\mathcal{B}_{\mathrm{j}}(), \mathcal{B}_{a..b}()$ &
bit of index $j$ or bits of indices in the range $[a, b]$ in the byte array &
\reff{\textbf{4.3.1}(4.4.1), 7} \\\hline

$\mathbf{b}$ &
EVM code &
\reff{4.1} \\\hline

{\small BLOCKHASH} &
!!! &
\reff{12.2} \\\hline

$C, C_\text{OPERATION}$ &
cost function &
\reff{3, 9.4.1} \\\hline

$C()$ &
!!! &
\reff{9.4.0, 9.4.2, 9.5} \\\hline

$\mathbf{c}$ &
!!! &
\reff{9.4.3} \\\hline

$c$ &
code-deposit cost &
\reff{\textbf{7}} \\\hline

$c$ &
account whose code is to be executed (the same as message call recipient) &
\reff{8} \\\hline

{\small CALL} &
!!! &
\reff{9.2, 9.3, 9.4.2()} \\\hline

{\small CALLCODE} &
!!! &
\reff{9.2, 9.4.2()} \\\hline

{\small CREATE} &
!!! &
\reff{9.2, 9.3, 9.4.2()} \\\hline

$D()$ &
canonical difficulty of a block of the given header (see $H_{\mathrm{d}}$) &
\reff{\textbf{4.3.4}(4.4.4)} \\\hline

$D()$ &
function to determine the set of valid jump destinations given the code that is being run &
\reff{9.4.2, \textbf{9.4.3}} \\\hline

$D_{J}()$ &
!!! &
\reff{\textbf{9.4.3}} \\\hline

$D_0$ &
difficulty of the genesis block &
\reff{\textbf{4.3.4}(4.4.4)} \\\hline

\DH{} &
Ether, {\small ETH} &
\reff{2.1} \\\hline

$\mathbf{d}$ &
current DAG for computing the mix-hash &
\reff{4.3.4(4.4.4), 11.4, 11.5.0} \\\hline

$\mathbf{d}$ &
input data of the call &
\reff{8} \\\hline

$\mathtt{\tiny DEAD}()$ &
whether an account is dead, when its account state is non-existent or empty ($\mathtt{\tiny EMPTY}()$) &
\reff{(\textbf{4.1}, 6.2, 7)} \\\hline

{\small DELEGATECALL} &
!!! &
\reff{8} \\\hline

$e$ &
present depth of the message-call/contract-creation stack &
\reff{7, 8} \\\hline

$\mathtt{\tiny EMPTY}()$ &
whether an account is empty, when it has no code, zero nonce and zero balance &
\reff{(\textbf{4.1})} \\\hline

$F$ &
out-of-gas exception condition &
\reff{(7)} \\\hline

$G_{\mathrm{...}}$ &
specific gas cost &
\reff{6.2} \\\hline

$g$ &
!!! ($\boldsymbol{\mu}_{\mathrm{g}}$) &
\reff{9.4.1} \\\hline

$g$ &
amount of gas remaining after deducting the basic amount, $T_{\mathrm{g}} - g_0$ &
\reff{\textbf{6.2}, 7, 8, 9.3, 9.4.0} \\\hline

$g'$ &
remaining gas &
\reff{6.2, \textbf{7}, 8, 9.3} \\\hline

$g^*$ &
amount of gas to be refunded &
\reff{\textbf{6.2}} \\\hline

$g^{**}$ &
available gas remaining &
\reff{7} \\\hline

$g_0$ &
intrinsic gas, the amount of gas this transaction requires to be paid prior to execution &
\reff{\textbf{6.2}} \\\hline

% HH
$H()$ &
function which specifies the output data of the instruction if and only if the present state is a normal halting state of the machine (cf. $Z()$) &
\reff{9.4.0, 9.4.1, 9.4.4} \\\hline

$H$ &
block header &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4), 11.5.0} \\\hline

$H_{\mathrm{b}}$ &
logsBloom, Bloom filter for each log entry from the each transaction receipt &
\reff{4.3.0(4.4.0), 4.3.2(4.4.2), 4.3.3(4.4.3)} \\\hline

$H_{\mathrm{c}}$ &
beneficiary, address to which all fees collected be transferred &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 11.3} \\\hline

$H_{\mathrm{d}}$ &
difficulty, difficulty level of this block &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4), 11.4, 11.5.0} \\\hline

$H_{\mathrm{e}}$ &
receiptRoot, root node hash of each transaction receipt &
\reff{4.3.0(4.4.0), 4.3.1(4.4.1), 4.3.2(4.4.2), 4.3.3(4.4.3)} \\\hline

$H_{\mathrm{g}}$ &
gasUsed, total gas used in transactions in this block &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4)} \\\hline

$H_{\mathrm{i}}$ &
number, number of ancestor blocks, block number &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4), (6.2), (7), 11.3} \\\hline

$H'_{\mathrm{i}}$ &
fake block number to delay the ice age &
\reff{(\textbf{4.3.4})} \\\hline

$H_{\mathrm{l}}$ &
gasLimit, current limit of gas expenditure per block &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4)} \\\hline

$H_{\mathrm{m}}$ &
mixHash, hash which proves a sufficient amount of computation &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4), 11.5.0} \\\hline

$H_{\mathrm{n}}$ &
nonce, value which proves a sufficient amount of computation &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4), 11.5.0} \\\hline

$H_{\hcancel{n}}$ &
block's header without the nonce ($H_{\mathrm{n}}$) and mix-hash ($H_{\mathrm{m}}$) components &
\reff{4.3.4(4.4.4), 11.5.0} \\\hline

$H_{\mathrm{o}}$ &
ommersHash, hash of the ommers (uncles) list &
\reff{4.3.0(4.4.0), 4.3.2(4.4.2), 4.3.3(4.4.3)} \\\hline

$H_{\mathrm{p}}$ &
parentHash, hash of the parent block's header &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4)} \\\hline

$H_{\mathrm{r}}$ &
stateRoot, root node hash of the state trie &
\reff{4.3.0(4.4.0), 4.3.2(4.4.2), 4.3.3(4.4.3), 11.4} \\\hline

$H_{\mathrm{s}}$ &
timstamp, block creation time in seconds &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4)} \\\hline

$H_{\mathrm{t}}$ &
transactionsRoot, root node hash of each transaction &
\reff{4.3.0(4.4.0), 4.3.2(4.4.2), 4.3.3(4.4.3)} \\\hline

$H_{\mathrm{x}}$ &
extraData, arbitrary data relevant to this block &
\reff{4.3.0(4.4.0), 4.3.3(4.4.3), 4.3.4(4.4.4)} \\\hline

$H_{\text{\tiny RETURN}}$ &
special function for {\small RETURN} and {\small REVERT} &
\reff{9.4.4} \\\hline

% II
$I$ &
parameters of the execution environment &
\reff{7, 8, 9.3, 9.4.0, 9.4.2, 9.5} \\\hline

$I_{\mathrm{a}}$ &
address of the account which owns the code that is executing ($a$) &
\reff{7, 8, 9.3} \\\hline

$I_{\mathbf{b}}$ &
byte array that is the machine code to be executed ($\mathbf{i}$) &
\reff{7, 8, 9.3, 9.4.1, 9.4.2} \\\hline

$I_{\mathbf{d}}$ &
!!! empty tuple as there is no input data to this call ($()$), byte array that is the input data to this execution; if the execution agent is a transaction, this would be the transaction data &
\reff{7, 8, 9.3} \\\hline

$I_{\mathrm{e}}$ &
depth of the present message-call or contract-creation ($e$) &
\reff{7, 8, 9.3} \\\hline

$I_{H}$ &
block header of the present block &
\reff{7, 9.3} \\\hline

$I_{\mathrm{o}}$ &
sender address of the transaction that originated this execution ($o$) &
\reff{7, 8, 9.3} \\\hline

$I_{\mathrm{p}}$ &
price of gas in the transaction that originated this execution ($p$) &
\reff{7, 8, 9.3} \\\hline

$I_{\mathrm{s}}$ &
address of the account which caused the code to be executing; if the execution agent is a transaction, this would be transaction sender ($s$) &
\reff{7, 8, 9.3} \\\hline

$I_{\mathrm{v}}$ &
value in Wei passed to this account as part of the same procedure as execution ($v$) &
\reff{7, 8, 9.3} \\\hline

$I_{\mathrm{w}}$ &
permission to make modifications to the state ($w$) &
\reff{(7, 8, 9.3, 9.4.2)} \\\hline

$I'$ &
dropped fourth element from $X()$ &
\reff{9.4.0()} \\\hline

$\mathbf{i}$ &
initialisation EVM code for creating a contract &
\reff{7} \\\hline

$i$ &
!!! ($\boldsymbol{\mu}_{\mathrm{i}}$) &
\reff{9.4.1} \\\hline

$J, J_{\text{JUMP}}, J_{\text{JUMPI}}$ &
!!! &
\reff{9.5} \\\hline

$J_{cacheinit}, J_{datasetinit}, J_{epoch}$ &
!!! &
\reff{11.5.1} \\\hline

{\small JUMP} &
!!! &
\reff{9.4.2} \\\hline

{\small JUMPDEST} &
!!! &
\reff{9.4.3} \\\hline

{\small JUMPI} &
!!! &
\reff{9.4.2} \\\hline

$k()$ &
check ``is-kin'' property &
\reff{11.1} \\\hline

$\mathtt{\small KEC}()$ &
Keccak-256 hash function, plain Keccak &
\reff{3, 4.1, 4.3.1(4.4.1), 4.3.2(4.4.2), 4.3.4(4.4.4), 7, 8} \\\hline

$\mathtt{\small KEC512}()$ &
Keccak 512 hash function &
\reff{3} \\\hline

$L_{B}()$ &
preparation function for a block &
\reff{4.3.3(4.4.3)} \\\hline

$L_{H}()$ &
preparation function for a block header &
\reff{4.3.3(4.4.3)} \\\hline

$L_{H}^*()$ &
!!! &
\reff{4.3.2(4.4.2), 4.3.3(4.4.3)} \\\hline

$L_{I}()$ &
collapse function for a key/value pair in the trie, $L_{I}\big( (k, v) \big) \equiv \big(\texttt{\small KEC}(k), \texttt{\small RLP}(v)\big)$ &
\reff{4.1} \\\hline

$L_{I}^*()$ &
element-wise transformation of $L_{I}$ (see $\boldsymbol{\sigma}[a]_{\mathbf{s}}$) &
\reff{4.1} \\\hline

$L_{R}()$ &
function that converts a transaction receipt into an RLP-serialised byte array &
\reff{4.3.1(4.4.1), 4.3.2(4.4.2)} \\\hline

$L_{S}()$ &
world-state collapse function &
\reff{4.1, (4.4.1), 4.3.2(4.4.2), 11.4} \\\hline

$L_{T}()$ &
!!! &
\reff{4.2(4.3), 4.3.2(4.4.2)} \\\hline

$L_{T}^*()$ &
!!! &
\reff{4.3.3(4.4.3)} \\\hline

$\mathbf{l}$ &
log series ($A_{\mathbf{l}}$) &
\reff{9.3} \\\hline

$\ell()$ &
last item in the sequence &
\reff{\textbf{3}, 11.2, 11.4} \\\hline

{\small LOG0} &
!!! &
\reff{9.4.2()} \\\hline

{\small LOG4} &
!!! &
\reff{9.4.2()} \\\hline

$M()$ &
Bloom filter function to reduce a log entry into a single 256-byte hash &
\reff{4.3.1(4.4.1)} \\\hline

$M_{3:2048}()$ &
specialised Bloom filter that sets three bits out of 2048 &
\reff{\textbf{4.3.1}(4.4.1)} \\\hline

$\mathbf{m}$ &
!!! ($\boldsymbol{\mu}_{\mathbf{m}}$) &
\reff{9.4.1} \\\hline

$m$ &
beneficiary (miner, $H_{\mathrm{c}}$) &
\reff{\textbf{6.2}} \\\hline

$m()$ &
fetch the given index after hashing &
\reff{\textbf{4.3.1}(4.4.1)} \\\hline

% NN
$N()$ &
next valid instruction position in the code &
\reff{9.4.3, 9.5} \\\hline

$\mathbb{N}, \mathbb{N}_{number}$ &
positive integer, smaller than $2^{number}$ &
\reff{3(), 4.1() \textbf{4.2}(), 4.3.1(), 4.3.3()} \\\hline

$N_H$ &
block number between the Frontier and Homestead phases ($1,150,000$) &
\reff{(\textbf{4.2}), 4.3.4(4.4.4), (6.2), (7)} \\\hline

$n$ &
transaction nonce (see $T_{\mathrm{n}}$) &
\reff{3} \\\hline

$O()$ &
iterator function which defines the result of a single cycle of the state machine &
\reff{9.4.0, 9.4.1, 9.5} \\\hline

$O, O_{number}$ &
log entry created through execution of the transaction (see $R_{\mathbf{l}}$) &
\reff{4.3.1(4.4.1)} \\\hline

$O_{\mathrm{a}}$ &
logger's address ($\mathbb{B}_{20}$) &
\reff{4.3.1(4.4.1)} \\\hline

$O_{\mathbf{d}}$ &
number of bytes of data ($\mathbb{B}$) &
\reff{4.3.1(4.4.1)} \\\hline

$O_{\mathbf{t}}$ &
series of log topics &
\reff{4.3.1(4.4.1)} \\\hline

${O_{\mathbf{t}}}_{number}$ &
log topic ($\mathbb{B}_{32}$) &
\reff{4.3.1(4.4.1)} \\\hline

$\mathbf{o}$ &
output data of a message call or created contract's code (the resultant byte sequence from the execution of the initialisation code) &
\reff{3, 7(), 8, 9.3} \\\hline

$o$ &
(contract creation or transaction) originator (see also $T_{\mathrm{o}}$) &
\reff{7, 8} \\\hline

% PP
$\mathbb{P}, \mathbb{P}_{number}$ &
positive integer, smaller than $2^{number}$ &
\reff{(3, 4.1, \textbf{4.3}, 4.4.1, 4.4.3)} \\\hline

$P(B_H), P(H)$ &
parent block of $B$ (see $H_{\mathrm{p}}$) &
\reff{4.3.2(4.4.2), \textbf{4.3.4}(4.4.4), 10, 11.1, 11.4} \\\hline

$p$ &
(contract creation or message call) gas price &
\reff{7, 8} \\\hline

$p()$ &
per-account collapse function (see $L_{S}()$) &
\reff{4.1} \\\hline

$p()$ &
pairwise RLP transformation &
\reff{4.3.2(4.4.2)} \\\hline

$pc$ &
!!! ($\boldsymbol{\mu}_{\mathrm{pc}}$) &
\reff{9.4.1} \\\hline

$\mathtt{PoW}$ &
proof-of-work function &
\reff{4.3.4(4.4.4), 11.5.0} \\\hline

{\small PUSH1} &
!!! &
\reff{9.4.3} \\\hline

{\small PUSH32} &
!!! &
\reff{9.4.3} \\\hline

% RR
$\mathbf{R}$ &
!!! &
\reff{11.2} \\\hline

$R$ &
transaction receipt &
\reff{4.3.1(4.4.1)} \\\hline

$R$ &
!!! &
\reff{11.3()} \\\hline

$R_{\boldsymbol{\sigma}}$ &
post-transaction state &
\reff{(4.4.1, 11.4)} \\\hline

$\mathbf{R}[n]_{\boldsymbol{\sigma}}$ &
!!! ($\boldsymbol{\sigma}[n]$) &
\reff{(11.4)} \\\hline

$R_{\mathrm{b}}$ &
Bloom filter composed from information in those logs ($\mathbb{B}_{256}$) &
\reff{4.3.1(4.4.1), 11.4} \\\hline

$R_b$ &
!!! &
\reff{(11.3)} \\\hline

$R_{\mathrm{block}}$ &
block's beneficiary account &
\reff{11.3()} \\\hline

$R_{\mathbf{l}}$ &
a series of log entries ($O$) created through execution of the transaction &
\reff{4.3.1(4.4.1), 11.4} \\\hline

$R_{\mathrm{u}}$ &
cumulative gas used immediately after the transaction has happended ($\mathbb{N}$) &
\reff{4.3.1(4.4.1), 11.2, 11.4} \\\hline

$R_{\mathrm{z}}$ &
status code of the transaction ($\mathbb{N}$) &
\reff{4.3.1(), 11.4()} \\\hline

$r$ &
message call recipient &
\reff{8} \\\hline

$r$ &
refunds ($A_{\mathrm{r}}$) &
\reff{9.3} \\\hline

$r()$ &
!!! &
\reff{11.4} \\\hline

$\mathbf{r}_{\mathrm{b}}$ &
Bloom filter of a receipt (see $O$) &
\reff{4.3.2(4.4.2)} \\\hline

{\small RETURN} &
!!! &
\reff{9.4.4} \\\hline

{\small RETURNDATACOPY} &
!!! &
\reff{9.4.2()} \\\hline

{\small REVERT} &
!!! &
\reff{9.4.0(), 9.4.4()} \\\hline

$\texttt{RLP}()$ &
!!! RLP transformation &
\reff{4.1, 4.3.2(4.4.2), 4.3.3(4.4.3), 4.3.4(4.4.4), 7} \\\hline

$S(T)$ &
transaction sender &
\reff{4.2(4.3), 6.2} \\\hline

$\mathbf{s}$ &
suicides set ($A_{\mathbf{s}}$) &
\reff{9.3} \\\hline

$\mathbf{s}$ &
!!! ($\boldsymbol{\mu}_{\mathbf{s}}$) &
\reff{9.4.1} \\\hline

$s$ &
(contract creation or message call) sender &
\reff{7, 8} \\\hline

$s()$ &
check ``is-sibling'' property &
\reff{11.1} \\\hline

{\small SELFDESTRUCT} &
!!! &
\reff{6.1(), 9.4.2(), 9.4.4()} \\\hline

{\small SSTORE} &
!!! &
\reff{6.1, 9.4.2()} \\\hline

{\small STOP} &
!!! &
\reff{6.1, 9.4.1, 9.4.4} \\\hline

{\small SUICIDE} &
!!! &
\reff{(6.1, 9.4.4)} \\\hline

% TT
$\mathbf{T}$ &
transactions in the given block &
\reff{4.3.0(4.4.0)} \\\hline

$T, T_{number}$ &
a transaction &
\reff{2.0, 4.2(4.3), 6.0, 6.2} \\\hline

$T_{\mathbf{d}}$ &
data, input data of the message call ($\mathbb{B}$) &
\reff{4.2(4.3), 6.2} \\\hline

$T_{\mathrm{g}}$ &
gasLimit, maximum amount of gas used in this transaction ($\mathbb{N}_{256}$) &
\reff{4.2(4.3), 6.2} \\\hline

$T_{\mathbf{i}}$ &
init, EVM-code for the account initialisation procedure, executed only once at account creation ($\mathbb{B}$) &
\reff{4.2(4.3), 6.2} \\\hline

$T_{\mathrm{n}}$ &
transaction nonce, number of transactions sent by the sender ($\mathbb{N}_{256}$) &
\reff{3, 4.2(4.3)} \\\hline

$T_{\mathrm{o}}$ &
original transactor, which can differ from the sender ($S(T)$) &
\reff{6.2} \\\hline

$T_{\mathrm{p}}$ &
gasPrice, number of Wei to be paid per unit of gas ($\mathbb{N}_{256}$) &
\reff{4.2(4.3), 6.2} \\\hline

$T_{\mathrm{r}}$ &
one of transaction signature values ($\mathbb{N}_{256}$) &
\reff{4.2(4.3)} \\\hline

$T_{\mathrm{s}}$ &
one of transaction signature values ($\mathbb{N}_{256}$) &
\reff{4.2(4.3)} \\\hline

$T_{\mathrm{t}}$ &
to, message call' recipient address ($\mathbb{B}_{20}$) or (contract creation transaction) $\varnothing$ ($\mathbb{B}_0$) &
\reff{4.2(4.3)} \\\hline

$T_{\mathrm{v}}$ &
value, number of Wei to be transferred ($\mathbb{N}_{256}$) &
\reff{4.2(4.3), 6.2} \\\hline

$T_{\mathrm{w}}$ &
one of transaction signature values ($\mathbb{N}_{5}$) &
\reff{4.2(4.3)} \\\hline

$\mathbf{t}$ &
touched accounts ($A_{\mathbf{t}}$) &
\reff{8(), 9.3()} \\\hline

$\texttt{\small TRIE}()$ &
!!! &
\reff{4.1, (4.4.1), 4.3.2(4.4.2), 7, 8, 11.4} \\\hline

$\mathbf{U}$ &
set of uncle block headers &
\reff{4.3.0(4.4.0)} \\\hline

$V()$ &
block header validity function &
\reff{4.3.4(4.4.4), 11.1} \\\hline

$v()$ &
account validity function &
\reff{4.1} \\\hline

$v$ &
(contract creation) endowment or (message call) value &
\reff{7, 8} \\\hline

$\tilde{v}$ &
value to be transferred for the {\small DELEGATECALL} instruction &
\reff{8} \\\hline

$v'$ &
account's pre-existing value &
\reff{\textbf{7}} \\\hline

$v_0$ &
up-front cost &
\reff{6.2} \\\hline

$W$ &
!!! &
\reff{9.4.2()} \\\hline

$w$ &
!!! &
\reff{7(), 8(), 9.4.0(), 9.4.1, 9.4.2, 9.5} \\\hline

$X()$ &
!!! &
\reff{9.4.0} \\\hline

$X_{\mathrm{0,1,2,4}}()$ &
!!! &
\reff{(9.4.0)} \\\hline

$x$ &
difficulty adjustment factor &
\reff{\textbf{4.3.4}(4.4.4), 11.4} \\\hline

$Z()$ &
function which check an exceptional halting state of the machine (cf. $H()$) &
\reff{9.4.0, 9.4.1, 9.4.2} \\\hline

$z$ &
status code !!! &
\reff{6.2(), 7(), 8()} \\\hline

\end{longtabu}

%\end{multicols}

\end{document}