5 problems

Semilinearity conjecture. The set of P-positions of every multidimensional subtraction game with nonnegative vectors of differences is semilinear.

Let $d$ be a positive integer and let ${\cal D}\subset\mathbb{Z}^{d}$ be a finite difference set satisfying … for every $(a_1,\dots,a_d)\in{\cal D}$. The positions are vectors…

Let ${\sc Nim}^1_{n,=k}$ be the impartial game on nonnegative integer vectors in which a move decreases exactly $k$ coordinates by one. A position from which the previous player ca…

Let Langton's ant start from a configuration of finite support. Finite-support escape conjecture. The head eventually leaves the pattern and begins traveling in a rational directio…

Let $k,l\geq 2$ be multiplicatively independent integers. A set $S$ of rational numbers is simultaneously $k$- and $l$-automatic if it is accepted by finite automata in both bases.…