We give new lower bounds for the fragments of the Ideal Proof System (IPS) introduced by Grochow and Pitassi (JACM 2018). The Ideal Proof System is a central topic in algebraic proof complexity developed in the context of Nullstellensatz refutation (Beame, Impagliazzo, Krajicek, Pitassi, Pudlak, FOCS 1994) and simulates Extended ... more >>>

Interactive proofs of proximity (IPPs) are a relaxation of interactive proofs, analogous to property testing, in which soundness is required to hold only for inputs that are far from the property being verified. In such proof systems, the verifier has oracle access to the input, and it engages in two ... more >>>

We show that for a randomly sampled unsatisfiable $O(\log n)$-CNF over $n$ variables the randomized two-party communication cost of finding a clause falsified by the given variable assignment is linear in $n$.

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