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Improved Error Reduction for Weighted PRGs

Authors Ben Chen , Gil Cohen , Dean Doron , Yuval Khaskelberg , Amnon Ta-Shma

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ACM Subject Classification
  • Theory of computation → Pseudorandomness and derandomization
Keywords
  • Space-bounded computation
  • pseudorandom generators

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Abstract

We devise an error-reduction procedure that transforms a PRG for length-n, width-w read-once branching programs with error 1/poly(n) and seed length s₀, over any alphabet, into a weighted PRG with seed length s₀ + O(log 1/ε + log log ((log w)/log n)) ⋅ log w). Using this reduction, we improve upon the state-of-the-art weighted PRG constructions of Hoza (RANDOM 2021) and Cheng and Wu (SODA 2026), achieving optimal dependence on the program’s arity while matching the best known bounds in all other parameters. 
Our motivation for obtaining optimal dependence on the arity stems from a result of Cheng and Hoza (CCC 2020, ToC 2022), who showed that a PRG with optimal arity and error dependence yields a PRG with seed length O(log^{3/2} n) (for, say, constant width), thereby breaking the long-standing log-squared barrier.

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Ben Chen, Gil Cohen, Dean Doron, Yuval Khaskelberg, and Amnon Ta-Shma. Improved Error Reduction for Weighted PRGs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 39:1-39:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.39

Author Details

Ben Chen
  • School of Computer Science and AI, Tel-Aviv University, Israel
Gil Cohen
  • School of Computer Science and AI, Tel-Aviv University, Israel
Dean Doron
  • Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Beer Sheva, Israel
Yuval Khaskelberg
  • School of Computer Science and AI, Tel-Aviv University, Israel
Amnon Ta-Shma
  • School of Computer Science and AI, Tel-Aviv University, Israel

Funding

  • Chen, Ben: Funded by the Israel Science Foundation grant 443/22 and the Blavatnik fund.
  • Cohen, Gil: Funded by ERC starting grant 949499 and by the Israel Science Foundation grant 2989/24.
  • Doron, Dean: Funded in part by the Israel Science Foundation grant 857/25.
  • Khaskelberg, Yuval: Funded by ERC starting grant 949499.
  • Ta-Shma, Amnon: Funded by the Israel Science Foundation grant 443/22.

Acknowledgements

We thank William Hoza for bringing to our attention Lemma 4.9 in [Cheng and Hoza, 2022], which already proves one of the theorems stated in an earlier version of this paper. We also thank Kuan Cheng and Ruiyang Wu for a useful discussion about their work [Cheng and Wu, 2026].

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