Deconstructing Subset Construction -- Reducing While Determinizing

We present a novel perspective on the NFA canonization problem, which introduces intermediate minimization steps to reduce the exploration space on-the-fly. Central to our approach are equivalence registries which track and unify language-equivalent states, and allow for additional optimizations such as convexity closures and simulation. Due to the generality of our approach, these concepts can be embedded in classic subset construction or Brzozowski's approach. We evaluate our approach on a set of synthetic and real-world examples from automatic sequences and observe that we are able to improve especially worst-case scenarios. We provide an open-source library implementing our approach.