3 problems

Let $G$ be a black box group and let $N\lhd G$. The Andrews--Curtis graph $\Delta_k(G,N)$ supports a nearest-neighbour random walk, and the AC-replacement algorithm $ACR_k(G,N)$ ru…

Andrews–Curtis black-box conjecture. A random walk on the Andrews–Curtis graph $\Delta_k(G,N)$ provides a good' black box for $N$.

Let $X$ be a black box group encrypting one of the untwisted Chevalley groups ${\rm G}(2^n)$, and let $u\in X$ be a given involution. Constructive recognition conjecture. There is…