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Simplifying Armoni’s PRG

Authors Ben Chen , Amnon Ta-Shma

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Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Pseudorandomness and derandomization
Keywords
  • PRG
  • ROBP
  • read-once
  • random
  • psuedorandom
  • armoni
  • derandomization

Metrics

Abstract

We propose a simple variant of the INW pseudo-random generator, where blocks have varying lengths, and prove it gives the same parameters as the more complicated construction of Armoni’s PRG. This shows there is no need for the specialized PRGs of Nisan and Zuckerman and Armoni, and they can be obtained as simple variants of INW.
For the construction to work we need space-efficient extractors with tiny entropy loss. We use the extractors from [Chattopadhyay and Liao, 2020] instead of [Guruswami et al., 2009] taking advantage of the very high min-entropy regime we work with. We remark that using these extractors has the additional benefit of making the dependence on the branching program alphabet Σ correct.

Cite As Get BibTex

Ben Chen and Amnon Ta-Shma. Simplifying Armoni’s PRG. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 36:1-36:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2025.36

Author Details

Ben Chen
  • Department of Computer Science, Tel Aviv University, Israel
Amnon Ta-Shma
  • Department of Computer Science, Tel Aviv University, Israel

Funding

  • Chen, Ben: Israel Science Foundation (grant number 443/22).
  • Ta-Shma, Amnon: Israel Science Foundation (grant number 443/22).

References

  1. Roy Armoni. On the derandomization of space-bounded computations. In International Workshop on Randomization and Approximation Techniques in Computer Science, pages 47-59. Springer, 1998. URL: https://doi.org/10.1007/3-540-49543-6_5.
  2. Eshan Chattopadhyay and Jyun-Jie Liao. Optimal error pseudodistributions for read-once branching programs. arXiv preprint arXiv:2002.07208, 2020. URL: https://arxiv.org/abs/2002.07208.
  3. Kuan Cheng and Ruiyang Wu. Weighted pseudorandom generators for read-once branching programs via weighted pseudorandom reductions. arXiv preprint arXiv:2502.08272, 2025. URL: https://doi.org/10.48550/arXiv.2502.08272.
  4. Gil Cohen, Dean Doron, Ori Sberlo, and Amnon Ta-Shma. Approximating iterated multiplication of stochastic matrices in small space. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, pages 35-45, 2023. URL: https://doi.org/10.1145/3564246.3585181.
  5. Zeev Dvir, Swastik Kopparty, Shubhangi Saraf, and Madhu Sudan. Extensions to the method of multiplicities, with applications to kakeya sets and mergers. SIAM Journal on Computing, 42(6):2305-2328, 2013. URL: https://doi.org/10.1137/100783704.
  6. Venkatesan Guruswami, Christopher Umans, and Salil Vadhan. Unbalanced expanders and randomness extractors from parvaresh-vardy codes. Journal of the ACM (JACM), 56(4):1-34, 2009. URL: https://doi.org/10.1145/1538902.1538904.
  7. Russell Impagliazzo, Noam Nisan, and Avi Wigderson. Pseudorandomness for network algorithms. In Proceedings of the twenty-sixth annual ACM symposium on Theory of computing, pages 356-364, 1994. URL: https://doi.org/10.1145/195058.195190.
  8. Daniel M Kane, Jelani Nelson, and David P Woodruff. Revisiting norm estimation in data streams. arXiv preprint arXiv:0811.3648, 2008. URL: https://arxiv.org/abs/0811.3648.
  9. Noam Nisan. Pseudorandom generators for space-bounded computations. In Proceedings of the twenty-second annual ACM symposium on Theory of computing, pages 204-212, 1990. URL: https://doi.org/10.1145/100216.100242.
  10. Noam Nisan and David Zuckerman. Randomness is linear in space. Journal of Computer and System Sciences, 52(1):43-52, 1996. URL: https://doi.org/10.1006/JCSS.1996.0004.
  11. Amnon Ta-Shma and Christopher Umans. Better condensers and new extractors from parvaresh-vardy codes. In 2012 IEEE 27th Conference on Computational Complexity, pages 309-315. IEEE, 2012. URL: https://doi.org/10.1109/CCC.2012.25.
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