4 problems

Let $\mathcal{Y}^*=\bigcup_{k\in\mathbb{N}\setminus\{0\}}\mathcal{Y}^k$ be the set of nonempty finite strings over $\mathcal{Y}$, let $\{Y_k:k\in\mathbb{N}\}$ be the Markov chain a…

Let $P_{X_k}^{+}$ and $P_{X_k}^{-}$ denote the distributions of the observations at layer $k$ conditioned on the source bit being $1$ and $0$, respectively. Fix…

Let a cellular automaton or probabilistic cellular automaton evolve configurations in the binary state space on the one-dimensional lattice $\mathbb{Z}$. The GKL cellular automaton…

Strict V-causality hierarchy conjecture. For every $k$, there exists a $V^kBox$ which is $V^k$-causal but not $V^{k+1}$-causal.