Deconstructing Subset Construction -- Reducing While Determinizing

TL;DR

The paper introduces a new method for NFA determinization that uses intermediate minimization and state equivalence tracking to reduce exploration space, improving worst-case performance.

Contribution

It presents a general framework with equivalence registries and optimizations that can be integrated into existing subset construction or Brzozowski's methods.

Findings

Improved worst-case scenarios in NFA determinization.

Effective on synthetic and real-world examples.

Open-source implementation available.

Abstract

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.