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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.
46 lines
1.2 KiB
TeX
46 lines
1.2 KiB
TeX
\section{Performance Metrics}
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Measuring system performance across multiple dimensions provides insights into effectiveness.
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\subsection{Challenge Success Rate}
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In a well-functioning system:
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\begin{equation}
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\text{ChallengeRate} = \frac{\text{Successful Challenges}}{\text{Total Assertions}} \approx 0
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\end{equation}
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Non-zero rates indicate either bugs or attacks.
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\subsection{Average Finality Time}
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Including challenge periods:
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\begin{equation}
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\bar{T}_{\text{finality}} = \tau + P(\text{challenge}) \times T_{\text{resolution}}
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\end{equation}
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For Lux with adaptive periods, this ranges from hours to days depending on stake and history.
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\subsection{Gas Cost Analysis}
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Total gas costs for dispute resolution:
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\begin{equation}
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\text{Gas}_{\text{total}} = \sum_{i=1}^{\log n} \text{Gas}_{\text{bisection}}(i) + \text{Gas}_{\text{one-step}}
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\end{equation}
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Typically 5-10 million gas for full dispute resolution.
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\subsection{Throughput Improvement}
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Rollup throughput compared to L1:
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\begin{equation}
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\text{Speedup} = \frac{\text{TPS}_{\text{rollup}}}{\text{TPS}_{\text{L1}}} = \frac{\text{Sequencer Rate}}{\text{Data Posting Rate}}
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\end{equation}
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Lux rollups achieve 10-100x improvements depending on configuration.
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