Decidability of membership problems for flat rational subsets of $\mathrm{GL}(2,\mathbb{Q})$ and singular matrices

Volker Diekert, Igor Potapov, Pavel Semukhin

We consider membership problems for rational subsets of the semigroup of $2\times 2$ matrices over $\mathbb{Q}$. For a semigroup $M$, the rational subsets $\mathrm{Rat}(M)$ are def…