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A complexity theoretic approach to randomness

Author:

Michael SipserAuthors Info & Claims

STOC '83: Proceedings of the fifteenth annual ACM symposium on Theory of computing

Pages 330 - 335

https://doi.org/10.1145/800061.808762

Published: 01 December 1983 Publication History

Abstract

We study a time bounded variant of Kolmogorov complexity. This notion, together with universal hashing, can be used to show that problems solvable probabilistically in polynomial time are all within the second level of the polynomial time hierarchy. We also discuss applications to the theory of probabilistic constructions.

References

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M. Sipser, "Three approaches to a definition of finite state randomness," unpublished manuscript.

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Cited By

Meel KChakraborty SAkshay SWooldridge MDy JNatarajan S(2024)Auditable algorithms for approximate model countingProceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence and Thirty-Sixth Conference on Innovative Applications of Artificial Intelligence and Fourteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v38i9.28936(10654-10661)Online publication date: 20-Feb-2024
https://dl.acm.org/doi/10.1609/aaai.v38i9.28936
Semenov AShen AVereshchagin N(2024)Kolmogorov's Last Discovery? (Kolmogorov and Algorithmic Statistics)Theory of Probability & Its Applications10.1137/S0040585X97T99164768:4(582-606)Online publication date: 7-Feb-2024
https://doi.org/10.1137/S0040585X97T991647
Li JPyne ETell R(2024)Distinguishing, Predicting, and Certifying: On the Long Reach of Partial Notions of Pseudorandomness2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00095(1-13)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00095
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Index Terms

A complexity theoretic approach to randomness
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Models of computation
    1. Probabilistic computation

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Published In

cover image ACM Conferences

STOC '83: Proceedings of the fifteenth annual ACM symposium on Theory of computing

December 1983

487 pages

ISBN:0897910990

DOI:10.1145/800061

Copyright © 1983 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 December 1983

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Cited By

Meel KChakraborty SAkshay SWooldridge MDy JNatarajan S(2024)Auditable algorithms for approximate model countingProceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence and Thirty-Sixth Conference on Innovative Applications of Artificial Intelligence and Fourteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v38i9.28936(10654-10661)Online publication date: 20-Feb-2024
https://dl.acm.org/doi/10.1609/aaai.v38i9.28936
Semenov AShen AVereshchagin N(2024)Kolmogorov's Last Discovery? (Kolmogorov and Algorithmic Statistics)Theory of Probability & Its Applications10.1137/S0040585X97T99164768:4(582-606)Online publication date: 7-Feb-2024
https://doi.org/10.1137/S0040585X97T991647
Li JPyne ETell R(2024)Distinguishing, Predicting, and Certifying: On the Long Reach of Partial Notions of Pseudorandomness2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00095(1-13)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00095
Hromkovič J(2024)Kolmogorov Complexity and Nondeterminism Versus Determinism for Polynomial Time ComputationsTheoretical Computer Science10.1016/j.tcs.2024.114747(114747)Online publication date: Jul-2024
https://doi.org/10.1016/j.tcs.2024.114747
Liu YPass R(2024)On One-Way Functions, the Worst-Case Hardness of Time-Bounded Kolmogorov Complexity, and Computational DepthTheory of Cryptography10.1007/978-3-031-78011-0_8(222-252)Online publication date: 2-Dec-2024
https://doi.org/10.1007/978-3-031-78011-0_8
Brandt N(2024)Lower Bounds for Levin–Kolmogorov ComplexityTheory of Cryptography10.1007/978-3-031-78011-0_7(191-221)Online publication date: 2-Dec-2024
https://doi.org/10.1007/978-3-031-78011-0_7
Chaidos PKiayias AReyzin LZinovyev A(2024)Approximate Lower Bound ArgumentsAdvances in Cryptology – EUROCRYPT 202410.1007/978-3-031-58737-5_3(55-84)Online publication date: 28-Apr-2024
https://doi.org/10.1007/978-3-031-58737-5_3
Liu YPass R(2024)A Direct PRF Construction from Kolmogorov ComplexityAdvances in Cryptology – EUROCRYPT 202410.1007/978-3-031-58737-5_14(375-406)Online publication date: 28-Apr-2024
https://doi.org/10.1007/978-3-031-58737-5_14
Hirahara SLu ZRen H(2023)Bounded RelativizationProceedings of the conference on Proceedings of the 38th Computational Complexity Conference10.4230/LIPIcs.CCC.2023.6(1-45)Online publication date: 17-Jul-2023
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2023.6
Верещагин НVereshchagin NСемeнов АSemenov AШень АShen' A(2023)Последнее открытие Колмогорова? (Колмогоров и алгоритмическая статистика)Kolmogorov’s last discovery? (Kolmogorov and algorithmic statistics)Теория вероятностей и ее примененияTeoriya Veroyatnostei i ee Primeneniya10.4213/tvp565068:4(719-750)Online publication date: 23-Oct-2023
https://doi.org/10.4213/tvp5650
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