Joshua Buresh-Oppenheim, Rahul Santhanam

We consider a general approach to the hoary problem of (im)proving circuit lower bounds. We define notions of hardness condensing and hardness extraction, in analogy to the corresponding notions from the computational theory of randomness. A hardness condenser is a procedure that takes in a Boolean function as input, as ... more >>>

Andreas Lenz, Cyrus Rashtchian, Paul Siegel, Eitan Yaakobi

A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most prior work on covering codes has focused on the ... more >>>

Vladimir Podolskii, Dmitrii Sluch

Boolean function $F(x,y)$ for $x,y \in \{0,1\}^n$ is an XOR function if $F(x,y) = f(x\oplus y)$ for some function $f$ on $n$ input bits, where $\oplus$ is a bit-wise XOR. XOR functions are relevant in communication complexity, partially for allowing Fourier analytic technique. For total XOR functions it is known ... more >>>