From e21eb74179b22b9878ee98f894cb798c9e296d76 Mon Sep 17 00:00:00 2001 From: Danny Willems Date: Wed, 29 Nov 2023 23:35:22 +0100 Subject: [PATCH 1/2] Explictly add selector and coin exponent --- book/src/kimchi/lookup.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/book/src/kimchi/lookup.md b/book/src/kimchi/lookup.md index a261672716..51ee9badc1 100644 --- a/book/src/kimchi/lookup.md +++ b/book/src/kimchi/lookup.md @@ -89,7 +89,7 @@ For example, the following **query** tells us that we want to check if $r_0 \opl The grand product argument for the lookup consraint will look like this at this point: $$ -\mathsf{acc}_i = \mathsf{acc}_{i-1} \cdot \frac{(1+\beta) \cdot {\color{green}(\gamma + w_0(g^i) + j \cdot w_2(g^i) + j^2 \cdot 2 \cdot w_1(g^i))} \cdot (\gamma(1 + \beta) + t_{i-1} + \beta t_i)}{(\gamma(1+\beta) + s_{i-1} + \beta s_{i})(\gamma(1+\beta) + s_{n+i-1} + \beta s_{n+i})} +\mathsf{acc}_i = \mathsf{acc}_{i-1} \cdot \frac{(1+\beta) \cdot {\color{green}(\gamma + j^0 \cdot 1 \cdot w_0(g^i) + j \cdot 1 \cdot w_2(g^i) + j^2 \cdot 2 \cdot w_1(g^i))} \cdot (\gamma(1 + \beta) + t_{i-1} + \beta t_i)}{(\gamma(1+\beta) + s_{i-1} + \beta s_{i})(\gamma(1+\beta) + s_{n+i-1} + \beta s_{n+i})} $$ Not all rows need to perform queries into a lookup table. We will use a query selector in the next section to make the constraints work with this in mind. From f87c26a23c2b600d14a13b654acf092155775a2a Mon Sep 17 00:00:00 2001 From: Danny Willems Date: Wed, 29 Nov 2023 23:38:33 +0100 Subject: [PATCH 2/2] Explicit the coin and the multiplicator --- book/src/kimchi/lookup.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/book/src/kimchi/lookup.md b/book/src/kimchi/lookup.md index 51ee9badc1..c777c4c701 100644 --- a/book/src/kimchi/lookup.md +++ b/book/src/kimchi/lookup.md @@ -116,7 +116,7 @@ where $\color{green}{\mathsf{query}}$ is constructed so that a dummy query ($0 \ $$ \begin{align} -\mathsf{query} := &\ \mathsf{selector} \cdot (\gamma + w_0(g^i) + j \cdot w_2(g^i) + j^2 \cdot 2 \cdot w_1(g^i)) + \\ +\mathsf{query} := &\ \mathsf{selector} \cdot (\gamma + j^0 \cdot 1 \cdot w_0(g^i) + j \cdot 1 \cdot w_2(g^i) + j^2 \cdot 2 \cdot w_1(g^i)) + \\ &\ (1- \mathsf{selector}) \cdot (\gamma + 0 + j \cdot 0 + j^2 \cdot 0) \end{align} $$