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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
727 B
TeX
34 lines
727 B
TeX
\section{Mathematical Foundations}
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\label{sec:math}
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\subsection{Expected Rounds to Finality}
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The expected number of rounds to achieve consensus:
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\begin{equation}
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\mathbb{E}[\text{rounds}] = \beta + O\left(\log\frac{1}{\delta}\right)
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\end{equation}
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where $\delta$ is the confidence parameter.
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\subsection{Byzantine Tolerance Bound}
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For Byzantine fraction $f$ and committee size $k$:
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\begin{equation}
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\text{Safe if } f < k \cdot (\theta - 0.5)
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\end{equation}
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\subsection{Threshold Evolution}
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The threshold evolution follows:
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\begin{align}
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\theta(0) &= 0.5 \quad \text{(neutral)} \\
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\theta(\infty) &\to \theta_{\max} \approx 0.8 \quad \text{(high confidence)}
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\end{align}
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Rate controlled by cooling parameter $\tau$.
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