The known emulation of interactive proof systems by public-coins interactive proof systems proceeds by selecting, at each round, a message such that each message is selected with probability that is at most polynomially larger than its probability in the original protocol.
Specifically, the possible messages are essentially clustered according to ... more >>>

In this note, we study the recursive teaching dimension(RTD) of concept classes of low VC-dimension. Recall that the VC-dimension of $C \subseteq \{0,1\}^n$, denoted by $VCD(C)$, is the maximum size of a shattered subset of $[n]$, where $Y\subseteq [n]$ is shattered if for every binary string $\vec{b}$ of length $|Y|$, ... more >>>

Monotone span programs are a linear-algebraic model of computation which were introduced by Karchmer and Wigderson in 1993. They are known to be equivalent to linear secret sharing schemes, and have various applications in complexity theory and cryptography. Lower bounds for monotone span programs have been difficult to obtain because ... more >>>