An Evaluation of Massively Parallel Algorithms for DFA Minimization

TL;DR

This paper evaluates four massively parallel algorithms for DFA minimization on GPUs, revealing practical performance insights and introducing a novel algorithm that outperforms existing methods on certain benchmarks.

Contribution

It compares existing parallel DFA minimization algorithms and introduces a new algorithm with improved practical performance on GPU architectures.

Findings

Theoretically optimal algorithms are not always practically efficient on GPUs.

Parallel partition refinement algorithms perform better in practice despite worse theoretical complexity.

The new algorithm with parallel partial transitive closure shows improved runtime on specific benchmarks.

Abstract

We study parallel algorithms for the minimization of Deterministic Finite Automata (DFAs). In particular, we implement four different massively parallel algorithms on Graphics Processing Units (GPUs). Our results confirm the expectations that the algorithm with the theoretically best time complexity is not practically suitable to run on GPUs due to the large amount of resources needed. We empirically verify that parallel partition refinement algorithms from the literature perform better in practice, even though their time complexity is worse. Lastly, we introduce a novel algorithm based on partition refinement with an extra parallel partial transitive closure step and show that on specific benchmarks it has better run-time complexity and performs better in practice.