Pseudodistributions That Beat All Pseudorandom Generators

by Edward Pyne and Salil Vadhan

Theory of Computing, Volume 22(3), pp. 1-63, 2026

Bibliography with links to cited articles

[1]   Rohit Agrawal: Samplers and extractors for unbounded functions. In Proc. 23rd Internat. Conf. on Randomization and Computation (RANDOM’19), pp. 59:1–21. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2019. [doi:10.4230/LIPIcs.APPROX-RANDOM.2019.59]

[2]   AmirMahdi Ahmadinejad, Jonathan A. Kelner, Jack Murtagh, John Peebles, Aaron Sidford, and Salil P. Vadhan: High-precision estimation of random walks in small space. In Proc. 61st FOCS, pp. 1295–1306. IEEE Comp. Soc., 2020. [doi:10.1109/FOCS46700.2020.00123]

[3]   Alexander E. Andreev, Andrea E. F. Clementi, and José D. P. Rolim: A new general derandomization method. J. ACM, 45(1):179–213, 1998. [doi:10.1145/273865.273933]

[4]   Alexander E. Andreev, Andrea E. F. Clementi, José D. P. Rolim, and Luca Trevisan: Weak random sources, hitting sets, and BPP simulations. SIAM J. Comput., 28(6):2103–2116, 1999. [doi:10.1137/s0097539797325636]

[5]   Roy Armoni: On the derandomization of space-bounded computations. In Proc. 2nd Internat. Workshop on Randomization and Computation (RANDOM’98), pp. 47–59. Springer, 1998. [doi:10.1007/3-540-49543-6_5]

[6]   Jaroslaw Blasiok: Optimal streaming and tracking distinct elements with high probability. ACM Trans. Algorithms, 16(1):3:1–28, 2019. Preliminary version in SODA’18. [doi:10.1145/3309193]

[7]   Manuel Blum and Silvio Micali: How to generate cryptographically strong sequences of pseudorandom bits. SIAM J. Comput., 13(4):850–864, 1984. [doi:10.1137/0213053]

[8]   Andrej Bogdanov, Zeev Dvir, Elad Verbin, and Amir Yehudayoff: Pseudorandomness for width-2 branching programs. Theory of Computing, 9(7):283–293, 2013. [doi:10.4086/toc.2013.v009a007, ECCC:TR09-070]

[9]   Andrej Bogdanov, William M. Hoza, Gautam Prakriya, and Edward Pyne: Hitting sets for regular branching programs. In Proc. 37th Comput. Complexity Conf. (CCC’22), pp. 3:1–22. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2022. [doi:10.4230/LIPIcs.CCC.2022.3]

[10]   Mark Braverman, Gil Cohen, and Sumegha Garg: Hitting sets with near-optimal error for read-once branching programs. In Proc. 50th STOC, pp. 353–362. ACM Press, 2018. [doi:10.1145/3188745.3188780]

[11]   Mark Braverman, Anup Rao, Ran Raz, and Amir Yehudayoff: Pseudorandom generators for regular branching programs. SIAM J. Comput., 43(3):973–986, 2014. Preliminary version in FOCS’10. [doi:10.1137/120875673]

[12]   Harry Buhrman and Lance Fortnow: One-sided versus two-sided error in probabilistic computation. In Proc. 16th Symp. Theoret. Aspects of Comp. Sci. (STACS’99), pp. 100–109. Springer, 1999. [doi:10.1007/3-540-49116-3_9]

[13]   Eshan Chattopadhyay and Jyun-Jie Liao: Optimal error pseudodistributions for read-once branching programs. In Proc. 35th Comput. Complexity Conf. (CCC’20, virtual conference), pp. 25:1–27. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2020. [doi:10.4230/LIPIcs.CCC.2020.25]

[14]   Eshan Chattopadhyay and Jyun-Jie Liao: Recursive Error Reduction for Regular Branching Programs. In Proc. 15th Innovations in Theoret. Comp. Sci. Conf. (ITCS’24), pp. 29:1–20. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2024. [doi:10.4230/LIPIcs.ITCS.2024.29]

[15]   Lijie Chen, William M. Hoza, Xin Lyu, Avishay Tal, and Hongxun Wu: Weighted pseudorandom generators via inverse analysis of random walks and shortcutting. In Proc. 64th FOCS, pp. 1224–1239. IEEE Comp. Soc., 2023. [doi:10.1109/FOCS57990.2023.00072]

[16]   Kuan Cheng and William M. Hoza: Hitting sets give two-sided derandomization of small space. Theory of Computing, 18(21):1–32, 2022. Preliminary version in CCC’20. [doi:10.4086/toc.2022.v018a021]

[17]   Gil Cohen, Dean Doron, Oren Renard, Ori Sberlo, and Amnon Ta-Shma: Error reduction for weighted PRGs against Read Once Branching Programs. In Proc. 36th Comput. Complexity Conf. (CCC’21), pp. 22:1–17. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2021. [doi:10.4230/LIPIcs.CCC.2021.22]

[18]   Michael B. Cohen, Jonathan Kelner, Rasmus Kyng, John Peebles, Richard Peng, Anup B. Rao, and Aaron Sidford: Solving directed Laplacian systems in nearly-linear time through sparse LU factorizations. In Proc. 59th FOCS, pp. 898–909. IEEE Comp. Soc., 2018. [doi:10.1109/FOCS.2018.00089]

[19]   Michael B. Cohen, Jonathan Kelner, John Peebles, Richard Peng, Anup B. Rao, Aaron Sidford, and Adrian Vladu: Almost-linear-time algorithms for Markov chains and new spectral primitives for directed graphs. In Proc. 49th STOC, pp. 410–419. ACM Press, 2017. [doi:10.1145/3055399.3055463]

[20]   Anindya De: Pseudorandomness for permutation and regular branching programs. In Proc. 26th IEEE Conf. on Comput. Complexity (CCC’11), pp. 221–231. IEEE Comp. Soc., 2011. [doi:10.1109/CCC.2011.23]

[21]   Oded Goldreich: A primer on pseudorandom generators. Volume 55 of University Lecture Series. Amer. Math. Soc., 2010. Link at AMS. Accessible at The Weizmann Institute.

[22]   Oded Goldreich: A sample of samplers: A computational perspective on sampling. In Oded Goldreich, editor, Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation, volume 6650 of LNCS, pp. 302–332. Springer, 2011. [doi:10.1007/978-3-642-22670-0_24, ECCC:TR97-020]

[23]   Oded Goldreich, Salil Vadhan, and Avi Wigderson: Simplified derandomization of BPP using a hitting set generator. In Oded Goldreich, editor, Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation, volume 6650 of LNCS, pp. 59–67. Springer, 2011. [doi:10.1007/978-3-642-22670-0_8]

[24]   Parikshit Gopalan, Raghu Meka, Omer Reingold, Luca Trevisan, and Salil Vadhan: Better pseudorandom generators from milder pseudorandom restrictions. In Proc. 53rd FOCS, pp. 120–129. IEEE Comp. Soc., 2012. [doi:10.1109/focs.2012.77]

[25]   William M. Hoza: Better pseudodistributions and derandomization for space-bounded computation. In Proc. 25th Internat. Conf. on Randomization and Computation (RANDOM’21), pp. 28:1–23. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2021. [doi:10.4230/LIPIcs.APPROX/RANDOM.2021.28]

[26]   William M. Hoza, Edward Pyne, and Salil P. Vadhan: Pseudorandom generators for unbounded-width permutation branching programs. In Proc. 12th Innovations in Theoret. Comp. Sci. Conf. (ITCS’21), pp. 7:1–20. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2021. [doi:10.4230/LIPIcs.ITCS.2021.7]

[27]   Russell Impagliazzo, Noam Nisan, and Avi Wigderson: Pseudorandomness for network algorithms. In Proc. 26th STOC, pp. 356–364. ACM Press, 1994. [doi:10.1145/195058.195190]

[28]   Piotr Indyk: Stable distributions, pseudorandom generators, embeddings, and data stream computation. J. ACM, 53(3):307–323, 2006. [doi:10.1145/1147954.1147955]

[29]   Daniel M. Kane, Jelani Nelson, and David P. Woodruff: Revisiting norm estimation in data streams, 2008. [arXiv:0811.3648]

[30]   Eyal Kaplan, Moni Naor, and Omer Reingold: Derandomized constructions of k-wise (almost) independent permutations. Algorithmica, 55(1):113–133, 2009. Preliminary version in RANDOM’05. [doi:10.1007/s00453-008-9267-y]

[31]    Michal Koucký, Prajakta Nimbhorkar, and Pavel Pudlák: Pseudorandom generators for group products: Extended abstract. In Proc. 43rd STOC, pp. 263–272. ACM Press, 2011. [doi:10.1145/1993636.1993672]

[32]   Raghu Meka, Omer Reingold, and Avishay Tal: Pseudorandom generators for width-3 branching programs. In Proc. 51st STOC, pp. 626–637. ACM Press, 2019. [doi:10.1145/3313276.3316319]

[33]   Noam Nisan: Pseudorandom bits for constant depth circuits. Combinatorica, 11(1):63–70, 1991. [doi:10.1007/BF01375474]

[34]   Noam Nisan: Pseudorandom generators for space-bounded computation. Combinatorica, 12(4):449–461, 1992. [doi:10.1007/bf01305237]

[35]   Noam Nisan and Avi Wigderson: Hardness vs. randomness. J. Comput. System Sci., 49(2):149–167, 1994. Preliminary version in FOCS’88. [doi:10.1016/S0022-0000(05)80043-1]

[36]   Noam Nisan and David Zuckerman: Randomness is linear in space. J. Comput. System Sci., 52(1):43–52, 1996. Preliminary version in STOC’93. See updated version at author’s website. [doi:10.1006/jcss.1996.0004]

[37]   Edward Pyne and Salil Vadhan: Pseudodistributions that beat all pseudorandom generators. Electron. Colloq. Comput. Complexity, TR21-019, 2021. [ECCC]

[38]   Edward Pyne and Salil Vadhan: Pseudodistributions that beat all pseudorandom generators (Extended abstract). In Proc. 36th Comput. Complexity Conf. (CCC’21), pp. 33:1–15. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2021. [doi:10.4230/LIPIcs.CCC.2021.33]

[39]   Omer Reingold, Thomas Steinke, and Salil Vadhan: Pseudorandomness for regular branching programs via Fourier analysis. In Proc. 17th Internat. Workshop on Randomization and Computation (RANDOM’13), pp. 655–670. Springer, 2013. [doi:10.1007/978-3-642-40328-6_45]

[40]   Omer Reingold, Luca Trevisan, and Salil Vadhan: Pseudorandom walks on regular digraphs and the RL vs. L problem. In Proc. 38th STOC, pp. 457–466. ACM Press, 2006. [doi:10.1145/1132516.1132583, ECCC:TR05-022]

[41]   Eyal Rozenman and Salil Vadhan: Derandomized squaring of graphs. In Proc. 9th Internat. Workshop on Randomization and Computation (RANDOM’05), pp. 436–447. Springer, 2005. [doi:10.1007/11538462_37]

[42]   Michael Saks and Shiyu Zhou: BPHSPACE(S) DSPACE(S32). J. Comput. System Sci., 58(2):376–403, 1999. Preliminary version in FOCS’95. [doi:10.1006/jcss.1998.1616]

[43]   Jirí Síma and Stanislav Zák: Almost k-wise independent sets establish hitting sets for width-3 1-branching programs. In Proc. Comp. Sci. Symp. in Russia (CSR’11), pp. 120–133. Springer, 2011. [doi:10.1007/978-3-642-20712-9_10]

[44]   Thomas Steinke: Pseudorandomness for permutation branching programs without the group theory. Electron. Colloq. Comput. Complexity, TR12-083, 2012. [ECCC]

[45]   Salil P. Vadhan: Pseudorandomness. Found. Trends Theor. Comp. Sci., 7(1–3):1–336, 2012. [doi:10.1561/0400000010]

[46]   Andrew C. Yao: Theory and applications of trapdoor functions (extended abstract). In Proc. 23rd FOCS, pp. 80–91. IEEE Comp. Soc., 1982. [doi:10.1109/sfcs.1982.45]

[47]   David Zuckerman: Randomness-optimal oblivious sampling. Random Struct. Algor., 11(4):345–367, 1997. [doi:10.1002/(sici)1098-2418(199712)11:4¡345::aid-rsa4¿3.0.co;2-z]