papers/zoo-gpu-evm/sections/03-gpu-execution-model.tex

\section{GPU Execution Model}

\label{sec:gpu-model}

\subsection{Amdahl's Law for Blockchain Execution}

Let $f$ denote the sequential fraction (state conflicts + overhead) and $p$ the number of parallel execution units (GPU SMs).
By Amdahl's law:

\begin{equation}
S(p) = \frac{1}{f + \frac{1-f}{p}}
\label{eq:amdahl}
\end{equation}

\begin{definition}[Sequential Fraction]
\begin{equation}
f = \frac{|C|}{|T|} + \frac{\text{overhead}_{\text{analysis}} + \text{overhead}_{\text{merge}}}{W_{\text{total}}}
\end{equation}
\end{definition}

On Zoo L2, empirical measurements yield $f \in [0.03, 0.08]$, mean $\bar{f} = 0.047$.
For H100 with $p = 132$ SMs: $S(132) \approx 18.6\times$.
Theoretical bound: $S_{\max} = 1/f \approx 21.3\times$.

\subsection{Workload Decomposition}

\begin{table}[h]
\centering
\begin{tabular}{lcc}
\toprule
\textbf{Workload} & \textbf{Block Gas Fraction} & \textbf{Conflict Rate} \\
\midrule
Simple transfers (EOA $\to$ EOA) & 12\% & 0.1\% \\
AI Mining submissions & 35\% & 0.8\% \\
DEX swaps and liquidity ops & 28\% & 11.2\% \\
FHE ciphertext operations & 15\% & 0.3\% \\
Governance and staking & 7\% & 2.1\% \\
Other contract calls & 3\% & 5.4\% \\
\bottomrule
\end{tabular}
\caption{Workload decomposition and conflict rates on Zoo L2 (30-day average)}
\label{tab:workload}
\end{table}

DEX operations exhibit the highest conflict rate (11.2\%) due to shared liquidity pool state.
AI Mining and FHE are nearly conflict-free as they write to isolated storage slots.

\subsection{Memory Bandwidth Bounds}

GPU EVM execution is bounded by memory bandwidth, not compute.
On H100's 3.35~TB/s HBM3:

\begin{equation}
\text{Throughput}_{\max} = \frac{B_{\text{mem}}}{b_{\text{avg}}} = \frac{3.35 \times 10^{12}}{1.46 \times 10^{3}} \approx 2.29 \times 10^{9} \text{ ops/sec}
\end{equation}

where $b_{\text{avg}} = 1.46$~KB is average memory traffic per gas operation.
This ceiling matches empirical measurements, confirming \cevm{} saturates GPU memory bandwidth.

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