13 problems

Property H conjecture. Every Artin–Tits presentation satisfies Property $H$. The conjecture asks whether transformations of type $\infty$ are unnecessary for reducing every word re…

Relative permutational Boone--Higman conjecture. Let $\Gamma$ be a finitely generated group with solvable word problem. Then there exists a group $G$ with a type…

Relative Boone--Higman conjecture. Let $\Gamma$ be a finitely generated group with solvable word problem. Then $\Gamma$ sharply embeds in a finitely presented relatively simple gro…

Boone--Higman conjecture. Every finitely generated group with solvable word problem embeds in a finitely presented simple group.

Let a group $\Gamma$ act faithfully on a set $S$. The action is of type (A) if $\Gamma$ is finitely presented, every stabilizer $\operatorname{Stab}_{\Gamma}(s)$ is finitely genera…

Non-positive surface curvature implies solvable word problem. If $\sigma_+(X)\leq 0$ then the word problem is solvable in $\pi_1(X)$.

Let $M=\operatorname{Mon}\langle A\mid w_i=1\ (1\leq i\leq p)\rangle$ be a finitely presented special monoid. A monoid has deterministic context-free word problem when its word pro…

Let $M$ be a finitely presented special monoid, generated by $A$, with virtually free group of units. For inputs $u,v\in A^*$, write $n=|u|+|v|$. Quadratic-time word problem conjec…

Let $G_{k+1}^k$ be one of the groups under consideration, and let $H_k$ be its subgroup generated by $b_1,\dots,b_k$. For distinct indices $i,j,m,l\in\{1,\dots,k\}$, consider the r…

EDT0L and ET0L word-problem conjecture. A group has EDT0L word problem if and only if it is finite, and a group has ET0L word problem if and only if it is virtually free.

Let $M$ be an Artin–Tits monoid. A padding of a multifraction is obtained by inserting an even number of trivial components at its beginning; semi-convergence up to $f$-padding mea…

Let $M$ be an Artin–Tits monoid, and let $\mathcal{R}$-reduction be the reduction system on multifractions associated with $M$. Conjecture A. $\mathcal{R}$-reduction is semi-conver…

Let $M$ be an Artin–Tits monoid and let $\mathcal{R}_{M}$ be its reduction system on multifractions. Two multifractions are right reducts of the same multifraction if they are obta…