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This document is an informal summary on the FRI low degree test and DEEP algebraic linking, following the well-known line of work of Ben-Sasson, et al.
Based on its most recent soundness analysis, we discuss parameter settings for practical security levels, how FRI is turned into a polynomial commitment scheme, and the soundness of DEEP sampling in the list decoding regime.
In particular, we illustrate the DEEP method applied to proving satisfiability of algebraic intermediate representations and prove a soundness error bound which slightly improves the one in the ethSTARK documentation (IACR eprint 2019/582).