Deconstructing Subset Construction -- Reducing While Determinizing
John Nicol, Markus Frohme
TL;DR
The paper tackles the canonicalization of NFAs by addressing the exponential state blowup during determinization. It introduces OTF, an on-the-fly framework that interleaves minimization with subset construction and leverages equivalence registries to exploit language-equivalence among metastates. Two registries, the Convexity Closure Lattice (CCL) and CCL with Similarity (CCLS), illustrate how lattice structure and precomputed similarity can prune the exploration space and merge equivalent states, improving performance on structure-rich real-world NFAs. The approach is validated against classic methods and Brzozowski’s algorithm, showing notable improvements for complex problems while maintaining competitiveness for simpler cases, and it is implemented as an open-source tool for experimentation.
Abstract
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.