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Improved Parallel Derandomization via Finite Automata with Applications

Authors Jeff Giliberti , David G. Harris

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ACM Subject Classification
  • Theory of computation → Parallel algorithms
  • Theory of computation → Pseudorandomness and derandomization
Keywords
  • Parallel Algorithms
  • Derandomization
  • MAX-CUT
  • Gale-Berlekamp Switching Game

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Abstract

A central approach to algorithmic derandomization is the construction of small-support probability distributions that "fool” randomized algorithms, often enabling efficient parallel (NC) implementations. An abstraction of this idea is fooling polynomial-space statistical tests computed via finite automata [Sivakumar STOC'02]; this encompasses a wide range of properties including k-wise independence and sums of random variables.
We present new parallel algorithms to fool finite-state automata, with significantly reduced processor complexity. Briefly, our approach is to iteratively sparsify distributions using a work-efficient lattice rounding routine and maintain accuracy by tracking an aggregate weighted error that is determined by the Lipschitz value of the statistical tests being fooled. 
We illustrate with improved applications to the Gale-Berlekamp Switching Game and to approximate MAX-CUT via SDP rounding. These involve further several optimizations, such as the truncation of the state space of the automata and FFT-based convolutions to compute transition probabilities efficiently.

Cite As Get BibTex

Jeff Giliberti and David G. Harris. Improved Parallel Derandomization via Finite Automata with Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.70

Author Details

Jeff Giliberti
  • University of Maryland, College Park, MD, USA
David G. Harris
  • University of Maryland, College Park, MD, USA

Funding

  • Giliberti, Jeff: JG gratefully acknowledges financial support by the Fulbright U.S. Graduate Student Program, sponsored by the U.S. Department of State and the Italian-American Fulbright Commission. This content does not necessarily represent the views of the Program.

Acknowledgements

Thanks to Mohsen Ghaffari and Christoph Grunau for explaining the works [Ghaffari and Grunau, 2024] and [Ghaffari et al., 2023].

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