The plural in the title hints that there are several complexities involved here.
The most traditional one is the computational complexity of the verifier; but, in the context of Interactive Proofs of Proximity (IPPs), the query complexity of the verifier and the communication complexity of the system should ... more >>>

We study interactive proofs when the prover and the verifier access the same underlying data through independent noisy views. The noise is \emph{persistent} for each party: each location is corrupted once, and repeated queries to the same location return the same corrupted value. We introduce two models in this setting: ... more >>>

How can we trust the correctness of a learned model on a particular input of interest? Model accuracy is typically measured $on\ average$ over a distribution of inputs, giving no guarantee for any fixed input. This paper proposes a theoretically-founded solution to this problem: to train $Self$-$Proving\ models$ that prove ... more >>>

What are the minimal cryptographic assumptions that suffice for constructing efficient argument systems, and for which tasks? Recently, Amit and Rothblum [STOC 2023] showed that one-way functions suffice for constructing constant-round arguments for bounded-depth computations. In this work we ask: what other tasks have efficient argument systems based only on ... more >>>

We study the following question: what cryptographic assumptions are needed for obtaining constant-round computationally-sound argument systems? We focus on argument systems with almost-linear verification time for subclasses of $\mathbf{P}$, such as depth-bounded computations.
Kilian's celebrated work [STOC 1992] provides such 4-message arguments for $\mathbf{P}$ (actually, for $\mathbf{NP}$) using collision-resistant hash ... more >>>