6 problems

Let $(P)$ denote the problem considered by the genetic algorithm, let $n$ be its rank, and let $s$ be its instance length. A mean instance means the average-run setting used in the…

Let $n=10$, and let $k$ be the mean length of all words occurring during the entire run of the genetic algorithm whose words are to be reduced. Rank-10 reduction-complexity conject…

Let $V_n$ be the Vershik group of rank $n$, and let $u\in V_n$ be a word with minimal generator length $l(u)$. Its Knuth–Bendix normal form is denoted by $\overline{u}$. Normal-for…

Let $\Delta$ and $\Gamma$ be simplicial graphs, and let $\mathbb{G}(\Delta)$ and $\mathbb{G}(\Gamma)$ be the corresponding partially commutative groups. The Tame Embedding Problem…

Let $\Gamma$ be a weakly chordal graph, meaning that it contains no induced cycle $C_n$ or complement $\overline{C}_n$ for $n\geq 5$. Let $\mathbb{G}(\Gamma)$ denote the partially…

Let $\Gamma_1$ and $\Gamma_2$ be finite graphs. For a graph $\Gamma$, let $\Gamma^e$ denote its extension graph, whose vertices are conjugates of vertices of $\Gamma$, with adjacen…