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fix notation
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Shvier committed Jun 4, 2024
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2 changes: 1 addition & 1 deletion content/docs/background/poly-iop.md
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Expand Up @@ -16,7 +16,7 @@ At the end of the protocol, $\mathcal{V}$ outputs **acc** if and only if the two

Moreover, a Poly-IOP has to satisfy the following properties.

**Definition 3 (Completeness).** If each pair of $(\mathcal{C}_{P_i},P_i)$ and $(\mathcal{C}_{Q_j},Q_j)$ is valid and $\{Q_j\}$ satisfy $\mathcal{R}(\{P_i\})$, $\text{Pr}[out_{\mathcal{V}}=\textbf{acc}]\ge{1}$.
**Definition 3 (Completeness).** If each pair of $(\mathcal{C}_{P_i},P_i)$ and $(\mathcal{C}_{Q_j},Q_j)$ is valid and $\{Q_j\}$ satisfy $\mathcal{R}(\{P_i\})$, $\text{Pr}[out_{\mathcal{V}}=\textbf{acc}]=1$.

**Definition 4 (Soundness).** If $(\mathcal{C}_{P_i},P_i)$ or $(\mathcal{C}_{Q_j},Q_j)$ are not a valid pair, or $\{Q_j\}$ does not satisfy $\mathcal{R}(\{P_i\})$, $\text{Pr}[out_{\mathcal{V}}=\textbf{rej}]\ge{1-\text{negl}(k)}$.

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