Motivated by the quest for a broader understanding of communication complexity of simple functions, we introduce the class of ''permutation-invariant'' functions. A partial function $f:\{0,1\}^n \times \{0,1\}^n\to \{0,1,?\}$ is permutation-invariant if for every bijection $\pi:\{1,\ldots,n\} \to \{1,\ldots,n\}$ and every $\mathbf{x}, \mathbf{y} \in \{0,1\}^n$, it is the case that $f(\mathbf{x}, \mathbf{y}) ... more >>>

In a recent work (Ghazi et al., SODA 2016), the authors with Komargodski and Kothari initiated the study of communication with contextual uncertainty, a setup aiming to understand how efficient communication is possible when the communicating parties imperfectly share a huge context. In this setting, Alice is given a function ... more >>>