From 07af9ea3e7575f0e0bd9b9aee079d7c633b908a2 Mon Sep 17 00:00:00 2001 From: Daira Hopwood Date: Wed, 17 Feb 2021 17:09:10 +0000 Subject: [PATCH] Book: generalize input columns to expressions in lookup argument. Signed-off-by: Daira Hopwood --- book/src/concepts/arithmetization.md | 4 ++-- book/src/design/proving-system/lookup.md | 3 +++ 2 files changed, 5 insertions(+), 2 deletions(-) diff --git a/book/src/concepts/arithmetization.md b/book/src/concepts/arithmetization.md index 940925b..385a0eb 100644 --- a/book/src/concepts/arithmetization.md +++ b/book/src/concepts/arithmetization.md @@ -30,8 +30,8 @@ A UPA circuit depends on a ***configuration***: another row relative to this one (with wrap-around, i.e. taken modulo $n$). The maximum degree of each polynomial is given by the polynomial degree bound. -* A sequence of ***lookup arguments*** defined over tuples of ***input columns*** and - ***table columns***. +* A sequence of ***lookup arguments*** defined over tuples of ***input expressions*** + (which are multivariate polynomials as above) and ***table columns***. A UPA circuit also defines: diff --git a/book/src/design/proving-system/lookup.md b/book/src/design/proving-system/lookup.md index 8107671..1f54b41 100644 --- a/book/src/design/proving-system/lookup.md +++ b/book/src/design/proving-system/lookup.md @@ -89,6 +89,9 @@ ways: - The commitments to the columns of $S$ can be precomputed, then combined cheaply once the challenge is known by taking advantage of the homomorphic property of Pedersen commitments. + - The columns of $A$ can be given as arbitrary polynomial expressions using relative + references. These will be substituted into the product column constraint, subject to + the maximum degree bound. This potentially saves one or more advice columns. - Then, a lookup argument for an arbitrary-width relation can be implemented in terms of a subset argument, i.e. to constrain $\mathcal{R}(x, y, ...)$ in each row, consider $\mathcal{R}$ as a set of tuples $S$ (using the method of the previous point), and check