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 >>>

Probabilistically checkable proofs (PCPs) allow encoding a computation so that it can be quickly verified by only reading a few symbols. Inspired by tree codes (Schulman, STOC'93), we propose tree PCPs; these are PCPs that evolve as the computation progresses so that a proof for time $t$ is obtained by ... more >>>