Deconstructing Subset Construction -- Reducing While Determinizing
This work addresses efficiency issues in automata theory for researchers and practitioners, though it appears incremental as it builds on classic methods like subset construction.
The paper tackles the NFA canonization problem by introducing intermediate minimization steps to reduce exploration space, resulting in improved worst-case scenarios on real-world examples from automatic sequences.
We present a novel perspective on the NFA canonization problem, which introduces intermediate minimization steps to reduce the exploration space on-the-fly. Essential to our approach are so-called equivalence registries which manage information about equivalent states and allow for incorporating further optimization techniques such as convexity closures or simulation to boost performance. 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 real-world examples from automatic sequences and observe that we are able to improve especially worst-case scenarios. We implement our approach in an open-source library for users to experiment with.