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Restructured from flat .tex/.pdf files into per-paper subdirectories. Added Antje Worring as co-author on all papers. Synced PDFs to pdfs/ for download site.
34 lines
1.3 KiB
TeX
34 lines
1.3 KiB
TeX
\section{System Model}
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\label{sec:model}
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\begin{definition}[DAG Structure]
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The transaction DAG $G = (V, E)$ consists of vertices $V$ (transactions) and directed
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edges $E$ where $(u, v) \in E$ means $v$ is a parent of $u$. Each vertex $v$ has:
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\begin{itemize}[nosep]
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\item A set of parents $\text{parents}(v) \subseteq V$ with $|\text{parents}(v)| \geq 1$.
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\item An ancestry cone $\text{cone}(v) = \{u \in V : u \text{ is reachable from } v\}$.
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\item A conflict set $\mathcal{C}(v)$ of vertices consuming the same UTXO.
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\end{itemize}
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\end{definition}
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\begin{definition}[Frontier]
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The frontier $F(r)$ at round $r$ is the set of maximal unfinalized vertices:
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\[
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F(r) = \{v \in V : v \text{ is not finalized and } \nexists u \text{ unfinalized with } v \in \text{cone}(u)\}
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\]
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Intuitively, frontier vertices are the ``tips'' of the unfinalized DAG.
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\end{definition}
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\begin{definition}[Supernova Burst]
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A supernova burst at round $r$ triggered by frontier vertex $v$ is the set:
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\[
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\text{burst}(v, r) = \{u \in \text{cone}(v) : u \text{ is not yet finalized}\}
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\]
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All vertices in the burst are finalized simultaneously.
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\end{definition}
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%% -----------------------------------------------------------------------
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%% 3. THE NOVA PROTOCOL
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%% -----------------------------------------------------------------------
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