In the paper where he first defined Communication Complexity, Yao asks: \emph{Is computing $CC(f)$ (the 2-way communication complexity of a given function $f$) NP-complete?} The problem of deciding whether $CC(f) \le k$, when given the communication matrix for $f$ and a number $k$, is easily seen to be in NP. ... more >>>

We consider random walks on "balanced multislices"
of any "grid" that respects the "symmetries" of the grid, and show that a broad class of such walks are good spectral expanders. (A grid is a set of points of the form $\mathcal{S}^n$ for finite $\mathcal{S}$, and a balanced multi-slice is the ... more >>>

Inductive inference, introduced by Solomonoff (Information and Control, 1964), is a foundational concept in knowledge acquisition, formulated as the task of extrapolating a sequence of symbols. In his seminal work, Solomonoff established a fundamental theorem for recursion-theoretic universal inductive inference, applicable to sequences generated by all Turing machines, based on ... more >>>