Additional optimization of the guaranteed number of activations in $\mathsf{XS}$-circuits computation algorithm

We propose an additional optimization to the Guaranteed Number of Activations (GNA) computation algorithm. The main idea of this optimization is to replace linear dependence checks based on the matrix rank computations with suffix checks of paths corresponding to partitions in the search tree. Proposed algorithm has been implemented and is two times faster than the previous solution. Using an optimized version of the GNA computation algorithm, we carried out several computational experiments. As a result, we refuted several hypothesis and proposed a scalable $\mathsf{XS}$-circuit construction with an optimal GNA value.