A zero-knowledge proof enables a prover to convince a verifier that $x \in S$, without revealing anything beyond this fact. By running a zero-knowledge proof $k$ times, it is possible to prove (still in zero-knowledge) that $k$ separate instances $x_1,\dots,x_k$ are all in $S$. However, this increases the communication by ... more >>>

Motivated by the inapproximability of reconfiguration problems, we present a new PCP-type characterization of PSPACE, which we call a probabilistically checkable reconfiguration proof (PCRP): Any PSPACE computation can be encoded into an exponentially long sequence of polynomially long proofs such that every adjacent pair of the proofs differs in at ... more >>>

Proving super-polynomial lower bounds on the size of proofs of unsatisfiability of Boolean formulas using resolution over parities, is an outstanding problem that has received a lot of attention after its introduction by Raz and Tzamaret (2008). Very recently, Efremenko, Garlik and Itsykson (2023) proved the first exponential lower bounds ... more >>>