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An Evaluation of Massively Parallel Algorithms for DFA Minimization

Jan Martens, Anton Wijs

TL;DR

This work empirically verify that parallel partition refinement algorithms from the literature perform better in practice, even though their time complexity is worse, and introduces a novel algorithm based on partition refinement with an extra parallel partial transitive closure step that performs better in practice.

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.

An Evaluation of Massively Parallel Algorithms for DFA Minimization

TL;DR

This work empirically verify that parallel partition refinement algorithms from the literature perform better in practice, even though their time complexity is worse, and introduces a novel algorithm based on partition refinement with an extra parallel partial transitive closure step that performs better in practice.

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.

Paper Structure

This paper contains 16 sections, 2 equations, 2 figures, 3 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The algorithms
  4. Transitive closure
  5. Naive partition refinement
  6. Sorting arrays
  7. Partition refinement using partial transitive closure
  8. Experiments
  9. Benchmarks
  10. Fibonacci DFAs:
  11. Bit-splitters:
  12. VLTSs:
  13. Results
  14. Transitive approach:
  15. Partition refinement algorithms:
  16. ...and 1 more sections

Figures (2)

  • Figure 1: The DFA $A=(\{q_0, \dots , q_9\}, \{a\}, \delta, \{q_9\}, q_0)$ with the extra partial transitive closure from $q_0$ added in dashed arrows.
  • Figure 2: The DFA $\mathtt{Fib}_5$ on the left, and the DFA $\mathcal{B}_3$ on the right.

Theorems & Definitions (1)

  • Definition 1