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Pseudorandom bits for constant depth circuits
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/3-540-16486-3_108openalex-snapshot
Expanders, randomness, or time versus space
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Probabilistic encryption
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Arthur-Merlin games: A randomized proof system, and a hierarchy of complexity classes
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∑11-Formulae on finite structures
inferredcites →https://doi.org/10.1016/0304-3975(76)90061-xopenalex-snapshot
The polynomial-time hierarchy
inferredcites →https://doi.org/10.1016/s0019-9958(85)80043-7openalex-snapshot
Pseudorandom number generation and space complexity
inferredcites →https://doi.org/10.1109/sfcs.1978.37openalex-snapshot
Two theorems on random polynomial time
inferredcites →https://doi.org/10.1109/sfcs.1981.35openalex-snapshot
Parity, circuits, and the polynomial-time hierarchy
inferredcites →https://doi.org/10.1109/sfcs.1982.45openalex-snapshot
Theory and application of trapdoor functions
inferredcites →https://doi.org/10.1109/sfcs.1982.72openalex-snapshot
How to generate cryptographically strong sequences of pseudo random bits
inferredcites →https://doi.org/10.1109/sfcs.1985.19openalex-snapshot
Deterministic simulation of probabilistic constant depth circuits
inferredcites →https://doi.org/10.1109/sfcs.1985.49openalex-snapshot
Separating the polynomial-time hierarchy by oracles
inferredcites →https://doi.org/10.1137/0210008openalex-snapshot
Relative to a Random Oracle A , ${\bf P}^A \ne {\bf NP}^A \ne \text{co-}{\bf NP}^A $ with Probability 1
inferredcites →https://doi.org/10.1137/0213053openalex-snapshot
How to Generate Cryptographically Strong Sequences of Pseudorandom Bits
inferredcites →https://doi.org/10.1145/12130.12137openalex-snapshot
Private coins versus public coins in interactive proof systems
inferredcites →https://doi.org/10.1145/22145.22192openalex-snapshot
Trading group theory for randomness
inferredcites →https://doi.org/10.1145/800057.808715openalex-snapshot
A theorem on probabilistic constant depth Computations
inferredcites →https://doi.org/10.1145/800061.808762openalex-snapshot
A complexity theoretic approach to randomness
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Randomness vs Time: Derandomization under a Uniform Assumption
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On the Complexity of Parallel Hardness Amplification for One-Way Functions
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Randomness-Efficient Sampling Within NC 1
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On the Derandomization of Constant Depth Circuits
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On Proving Circuit Lower Bounds against the Polynomial-Time Hierarchy: Positive and Negative Results
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Hard Sets and Pseudo-random Generators for Constant Depth Circuits
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Randomness-Optimal Characterization of Two NP Proof Systems
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Deterministic Hypergraph Coloring and Its Applications
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Randomness-efficient non-interactive zero knowledge
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Using hard problems to derandomize algorithms: An incomplete survey
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Derandomization in Combinatorial Optimization
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On the Size of Depth-Three Boolean Circuits for Computing Multilinear Functions
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On Algorithmic Statistics for Space-Bounded Algorithms
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A Note on Approximate Counting for k-DNF
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Random Access to Advice Strings and Collapsing Results
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Impossibility Results on Weakly Black-Box Hardness Amplification
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Randomisation and Derandomisation in Descriptive Complexity Theory
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Uniform Derandomization from Pathetic Lower Bounds
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Improved Pseudorandom Generators for Depth 2 Circuits
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Improving the Space-Bounded Version of Muchnik’s Conditional Complexity Theorem via “Naive” Derandomization
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Correlation Bounds for Poly-size $\mbox{\rm AC}^0$ Circuits with n 1 − o(1) Symmetric Gates
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Boolean Function Complexity: Advances and Frontiers
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Pseudorandomness for Linear Length Branching Programs and Stack Machines
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Modern Cryptography, Probabilistic Proofs and Pseudorandomness
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Pseudorandom generators and the frequency of simplicity
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Do probabilistic algorithms outperform deterministic ones?
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The complexity of constructing pseudorandom generators from hard functions
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Randomness-Efficient Sampling within NC1
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Derandomizing Arthur-Merlin Games and Approximate Counting Implies Exponential-Size Lower Bounds
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Pseudorandom Generators, Typically-Correct Derandomization, and Circuit Lower Bounds
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Pseudorandom Generators for Combinatorial Checkerboards
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Bounded-Depth Circuits Cannot Sample Good Codes
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Pseudorandom generators for CC0[p] and the Fourier spectrum of low-degree polynomials over finite fields
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DNF sparsification and a faster deterministic counting algorithm
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Explicit List-Decodable Codes with Optimal Rate for Computationally Bounded Channels
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Expander-Based Cryptography Meets Natural Proofs
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A Technique for Hardness Amplification Against $$\textsf{AC}^0$$
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Improving the Space-Bounded Version of Muchnik’s Conditional Complexity Theorem via “Naive” Derandomization
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Small-Bias is Not Enough to Hit Read-Once CNF
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On Algorithmic Statistics for Space-bounded Algorithms
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Random Access to Advice Strings and Collapsing Results
inferred← citeshttps://doi.org/10.1007/s10601-018-9301-xopenalex-snapshot
Not all FPRASs are equal: demystifying FPRASs for DNF-counting
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Construction of one-Lee weight and two-Lee weight codes over F p + vF p
inferred← citeshttps://doi.org/10.1016/0022-0000(92)90047-mopenalex-snapshot
Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
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AC0∘MOD2 lower bounds for the Boolean Inner Product
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Extremal set theory and LWE based access structure hiding verifiable secret sharing with malicious-majority and free verification
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An optimal approximation algorithm for Bayesian inference
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Large sets in AC0 have many strings with low Kolmogorov complexity
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An Almost m-wise Independent Random Permutation of the Cube
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A Primer on Pseudorandom Generators
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Uniform derandomization from pathetic lower bounds
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De-randomizing BPP: the state of the art
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Hardness vs. randomness within alternating time
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On Constructing Parallel Pseudorandom Generators from One-Way Functions
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Pseudorandom Bits for Constant Depth Circuits with Few Arbitrary Symmetric Gates
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Norms, XOR Lemmas, and Lower Bounds for GF(2) Polynomials and Multiparty Protocols
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Derandomizing Arthur-Merlin Games and Approximate Counting Implies Exponential-Size Lower Bounds
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Hitting Set Generators for Sparse Polynomials over Any Finite Fields
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DNF Sparsification and a Faster Deterministic Counting Algorithm
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A Derandomized Switching Lemma and an Improved Derandomization of AC0
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Deterministic Approximate Counting for Juntas of Degree-2 Polynomial Threshold Functions
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Algorithms for Circuits and Circuits for Algorithms
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Hardness Amplification for Errorless Heuristics
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Polylogarithmic Independence Can Fool DNF Formulas
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Discrepancy and the Power of Bottom Fan-in in Depth-three Circuits
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Hardness Amplification for Errorless Heuristics
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Smooth Histograms for Sliding Windows
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Bounded Independence Fools Halfspaces
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Pseudorandom Generators for CC0[p] and the Fourier Spectrum of Low-Degree Polynomials over Finite Fields
inferred← citeshttps://doi.org/10.1109/focs.2010.8openalex-snapshot
Bounded Independence Fools Degree-2 Threshold Functions
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Pseudorandomness for Read-Once Formulas
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Better Pseudorandom Generators from Milder Pseudorandom Restrictions
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An Average-Case Depth Hierarchy Theorem for Boolean Circuits
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Deterministic Search for CNF Satisfying Assignments in Almost Polynomial Time
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Indistinguishability by Adaptive Procedures with Advice, and Lower Bounds on Hardness Amplification Proofs
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High-precision Estimation of Random Walks in Small Space
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Hardness vs Randomness, Revised: Uniform, Non-Black-Box, and Instance-Wise
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Constructive Separations and Their Consequences
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Distinguishing, Predicting, and Certifying: On the Long Reach of Partial Notions of Pseudorandomness
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Deterministic approximate counting of depth-2 circuits
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Computational pseudo-randomness
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Pseudorandom generators, measure theory, and natural proofs
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Discrepancy sets and pseudorandom generators for combinatorial rectangles
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Constant depth circuits and the Lutz hypothesis
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Randomness vs. time: de-randomization under a uniform assumption
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Pseudorandom generators in propositional proof complexity
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Bounded Round Interactive Proofs in Finite Groups
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Pseudorandom Bits for Constant‐Depth Circuits with Few Arbitrary Symmetric Gates
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Polylogarithmic Independence Can Fool DNF Formulas
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Hardness Amplification Proofs Require Majority
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Bounded Independence Fools Halfspaces
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Protecting Circuits from Computationally Bounded and Noisy Leakage
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A Fixed-Depth Size-Hierarchy Theorem for $\mathrm{AC}^0[\oplus]$ via the Coin Problem
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Hardness vs. Randomness, Revised: Uniform, Non-Black-Box, and Instance-wise
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Pseudorandom Generators in Propositional Proof Complexity
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On Proving Circuit Lower Bounds against the Polynomial-Time Hierarchy
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Using Nondeterminism to Amplify Hardness
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Deterministic Hypergraph Coloring and Its Applications
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DERANDOMIZATION: A BRIEF OVERVIEW
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Using nondeterminism to amplify hardness
inferred← citeshttps://doi.org/10.1145/1814370.1814389openalex-snapshot
Typically-correct derandomization
inferred← citeshttps://doi.org/10.1145/1924421.1924446openalex-snapshot
Poly-logarithmic independence fools bounded-depth boolean circuits
inferred← citeshttps://doi.org/10.1145/195058.195190openalex-snapshot
Pseudorandomness for network algorithms
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On beating the hybrid argument
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Average-case lower bounds for formula size
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Interactive proofs of proximity
inferred← citeshttps://doi.org/10.1145/258533.258590openalex-snapshot
P = BPP if E requires exponential circuits
inferred← citeshttps://doi.org/10.1145/2591796.2591808openalex-snapshot
On derandomizing algorithms that err extremely rarely
inferred← citeshttps://doi.org/10.1145/2591796.2591846openalex-snapshot
Pseudorandom generators with optimal seed length for non-boolean poly-size circuits
inferred← citeshttps://doi.org/10.1145/3018057openalex-snapshot
Pseudorandom Generators with Optimal Seed Length for Non-Boolean Poly-Size Circuits
inferred← citeshttps://doi.org/10.1145/3095799openalex-snapshot
An Average-Case Depth Hierarchy Theorem for Boolean Circuits
inferred← citeshttps://doi.org/10.1145/3313276.3316339openalex-snapshot
A fixed-depth size-hierarchy theorem for AC 0 [⊕] via the coin problem
inferred← citeshttps://doi.org/10.1145/3406325.3451054openalex-snapshot
An improved derandomization of the switching lemma
inferred← citeshttps://doi.org/10.1145/3604943.3604950openalex-snapshot
Guest Column: New ways of studying the BPP = P conjecture
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When Connectivity Is Hard, Random Walks Are Easy with Non-determinism
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Using the Planted Clique Conjecture for Cryptography: Public-Key Encryption from Planted Clique and Noisy 𝑘-LIN over Expanders
inferred← citeshttps://doi.org/10.1145/502090.502099openalex-snapshot
Extractors and pseudorandom generators
inferred← citeshttps://doi.org/10.1162/neco_a_00841openalex-snapshot
McCulloch-Pitts Brains and Pseudorandom Functions
inferred← citeshttps://doi.org/10.1201/9781420011296.ch18openalex-snapshot
Parallel Algorithms via the Probabilistic Method
inferred← citeshttps://doi.org/10.1515/9780823295708-025openalex-snapshot
CHAPTER NOTES AND REFERENCES
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Chapter 8 Notes and References
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Pairwise Independence and Derandomization
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On the Power of Small-Depth Computation
inferred← citeshttps://doi.org/10.1561/0400000108openalex-snapshot
Quantified Derandomization: How to Find Water in the Ocean
inferred← citeshttps://doi.org/10.1561/0400000109openalex-snapshot
Paradigms for Unconditional Pseudorandom Generators
inferred← citeshttps://doi.org/10.1561/9781601983015openalex-snapshot
On the Power of Small-Depth Computation
inferred← citeshttps://doi.org/10.1561/9781933019765openalex-snapshot
Pairwise Independence and Derandomization
inferred← citeshttps://doi.org/10.2168/lmcs-7(3:14)2011openalex-snapshot
Randomisation and Derandomisation in Descriptive Complexity Theory
inferred← citeshttps://doi.org/10.4230/lipics.approx-random.2018.56openalex-snapshot
Improved Pseudorandom Generators from Pseudorandom Multi-Switching Lemmas
inferred← citeshttps://doi.org/10.4230/lipics.approx/random.2023.44openalex-snapshot
Bounded Independence Plus Noise Fools Products
inferred← citeshttps://doi.org/10.46298/theoretics.24.3openalex-snapshot
Constructive Separations and Their Consequences
inferred← citeshttps://doi.org/10.48550/arxiv.0902.3757openalex-snapshot
Bounded Independence Fools Halfspaces
inferred← citeshttps://doi.org/10.48550/arxiv.0911.3389openalex-snapshot
Bounded Independence Fools Degree-2 Threshold Functions
inferred← citeshttps://doi.org/10.48550/arxiv.1205.3534openalex-snapshot
DNF Sparsification and a Faster Deterministic Counting Algorithm
inferred← citeshttps://doi.org/10.48550/arxiv.1311.6531openalex-snapshot
Brains and pseudorandom generators
inferred← citeshttps://doi.org/10.48550/arxiv.1603.01573openalex-snapshot
McCulloch-Pitts brains and pseudorandom functions
inferred← citeshttps://doi.org/10.5040/9780755625963.0007openalex-snapshot
Chapter Notes and References
inferred← citeshttps://doi.org/10.5555/2833227.2833257openalex-snapshot
On randomness extraction in AC0
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