The $\epsilon$-approximate degree $\widetilde{\text{deg}}_\epsilon(f)$ of a Boolean function $f$ is the least degree of a real-valued polynomial that approximates $f$ pointwise to error $\epsilon$. The approximate degree of $f$ is at least $k$ iff there exists a pair of probability distributions, also known as a dual polynomial, that are perfectly ... more >>>

Consider a PPT two-party protocol ?=(A,B) in which the parties get no private inputs and obtain outputs O^A,O^B?{0,1}, and let V^A and V^B denote the parties’ individual views. Protocol ? has ?-agreement if Pr[O^A=O^B]=1/2+?. The leakage of ? is the amount of information a party obtains about the event {O^A=O^B}; ... more >>>

We continue the study of list recovery properties of high-rate tensor codes, initiated by Hemenway, Ron-Zewi, and Wootters (FOCS'17). In that work it was shown that the tensor product of an efficient (poly-time) high-rate globally list recoverable code is {\em approximately} locally list recoverable, as well as globally list recoverable ... more >>>