We prove a lower bound on the communication complexity of computing the $n$-fold xor of an arbitrary function $f$, in terms of the communication complexity and rank of $f$. We prove that $D(f^{\oplus n}) \geq n \cdot \Big(\frac{\Omega(D(f))}{\log rk(f)} -\log rk(f)\Big )$, where here $D(f), D(f^{\oplus n})$ represent the ... more >>>

Time efficient decoding algorithms for error correcting codes often require linear space. However, locally decodable codes yield more efficient randomized decoders that run in time $n^{1+o(1)}$ and space $n^{o(1)}$. In this work we focus on deterministic decoding.
Gronemeier showed that any non-adaptive deterministic decoder for a good code running ... more >>>

The input to the Tree Evaluation problem is a binary tree of height $h$ in which each internal vertex is associated with a function mapping pairs of $\ell$-bit strings to $\ell$-bit strings, and each leaf is assigned an $\ell$-bit string.
The desired output is the value of the root, ... more >>>