= Group encoding of a modular machine
A <modular machine> can be encoded by <HNN extensions> of $K=\mathbb Z^2*\langle t\rangle$. The kernel of $K\to\mathbb Z^2$ has a <free basis of a group> $t(r,s)=x^{-r}y^{-s}tx^ry^s$. Associated-subgroup maps send these basis elements according to the two arithmetic transition types. In the resulting group, membership of $t(r,s)$ in the subgroup generated by $t$ and the instruction stable letters is equivalent to $(r,s)\in H_0(\mathcal M)$. One more <HNN extension> centralizes that finitely generated subgroup, converting membership to equality and hence to the <word problem for a group>.
Back to article page
