4 problems

Hof–Knill–Simon conjecture. The language of $\mathbf{u}$ contains infinitely many palindromes if and only if $\mathcal{L}(\mathbf{u})$ coincides with the language of a fixed point…

Let $r\geq 2$, let $\rho_1,\ldots,\rho_r$ be pairwise multiplicatively independent algebraic numbers, and, for each $i$ with $1\leq i\leq r$, let $\mathbf a_i$ be a $\rho_i$-morphi…

Let $\xi$ be an irrational real number whose base-$b$ expansion is an automatic or morphic sequence for some integer $b\geq 2$. Bugeaud–Krieger–Shallit conjecture. The irrationalit…

Let $f53f$ be a morphic sequence, and let $p_{\mathbf{w}}(n)$ denote its factor-complexity function. Morphic-sequence complexity spectrum conjecture. The function $p_{\mathbf{w}}$…