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On the correlation of symmetric functions
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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_92openalex-snapshot
With probability one, a random oracle separates PSPACE from the polynomial-time hierarchy
inferredcites →https://doi.org/10.1007/978-1-4757-1779-2openalex-snapshot
A Classical Introduction to Modern Number Theory
inferredcites →https://doi.org/10.1007/978-1-4757-2103-4openalex-snapshot
A Classical Introduction to Modern Number Theory
inferredcites →https://doi.org/10.1007/bf01263424openalex-snapshot
Representing Boolean functions as polynomials modulo composite numbers
inferredcites →https://doi.org/10.1007/bf01744431openalex-snapshot
Parity, circuits, and the polynomial-time hierarchy
inferredcites →https://doi.org/10.1007/bfb0080437openalex-snapshot
Equations over Finite Fields An Elementary Approach
inferredcites →https://doi.org/10.1016/0020-0190(87)90036-6openalex-snapshot
Random oracles separate PSPACE from the polynomial-time hierarchy
inferredcites →https://doi.org/10.1016/0020-0190(91)90035-gopenalex-snapshot
An oracle separating ΘP from PPPH
inferredcites →https://doi.org/10.1016/0022-0000(89)90033-0openalex-snapshot
With probability one, a random oracle separates PSPACE from the polynomial-time hierarchy
inferredcites →https://doi.org/10.1016/0168-0072(83)90038-6openalex-snapshot
∑11-Formulae on finite structures
inferredcites →https://doi.org/10.1109/sfcs.1985.49openalex-snapshot
Separating the polynomial-time hierarchy by oracles
inferredcites →https://doi.org/10.1145/129712.129756openalex-snapshot
Representing Boolean functions as polynomials modulo composite numbers
inferredcites →https://doi.org/10.1145/28395.28404openalex-snapshot
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1007/11821069_34openalex-snapshot
On the Correlation Between Parity and Modular Polynomials
inferred← citeshttps://doi.org/10.1007/3-540-59042-0_63openalex-snapshot
Lower bounds for depth-three circuits with equals and mod-gates
inferred← citeshttps://doi.org/10.1007/pl00001599openalex-snapshot
A complex-number Fourier technique for lower bounds on the Mod-m degree
inferred← citeshttps://doi.org/10.1007/s00026-014-0230-0openalex-snapshot
Asymptotic Behavior of Perturbations of Symmetric Functions
inferred← citeshttps://doi.org/10.1007/s00037-017-0153-3openalex-snapshot
Block-symmetric polynomials correlate with parity better than symmetric
inferred← citeshttps://doi.org/10.1007/s00200-018-0351-5openalex-snapshot
Generalized Walsh transforms of symmetric and rotation symmetric Boolean functions are linear recurrent
inferred← citeshttps://doi.org/10.1007/s00224-011-9332-9openalex-snapshot
On the Correlation Between Parity and Modular Polynomials
inferred← citeshttps://doi.org/10.1007/s002240000126openalex-snapshot
Exponential Sums and Circuits with a Single Threshold Gate and Mod-Gates
inferred← citeshttps://doi.org/10.1007/s10801-018-0840-4openalex-snapshot
Closed formulas for exponential sums of symmetric polynomials over Galois fields
inferred← citeshttps://doi.org/10.1007/s11128-020-02652-2openalex-snapshot
Quantum and classical query complexities for generalized Deutsch–Jozsa problems
inferred← citeshttps://doi.org/10.1016/b978-0-12-811129-1.00006-7openalex-snapshot
Special Types of Boolean Functions
inferred← citeshttps://doi.org/10.1016/j.crma.2005.03.008openalex-snapshot
Estimation of certain exponential sums arising in complexity theory
inferred← citeshttps://doi.org/10.1016/j.dam.2016.06.018openalex-snapshot
Hamming weights of symmetric Boolean functions
inferred← citeshttps://doi.org/10.1016/j.dam.2016.10.005openalex-snapshot
Modular periodicity of exponential sums of symmetric Boolean functions
inferred← citeshttps://doi.org/10.1016/j.dam.2022.03.016openalex-snapshot
Walsh–Hadamard transforms of generalized p-ary functions and C-finite sequences
inferred← citeshttps://doi.org/10.1016/j.dam.2023.10.003openalex-snapshot
Short k -rotation symmetric Boolean functions
inferred← citeshttps://doi.org/10.1016/j.disc.2018.03.019openalex-snapshot
Recursions associated to trapezoid, symmetric and rotation symmetric functions over Galois fields
inferred← citeshttps://doi.org/10.1016/j.disc.2025.114852openalex-snapshot
On monomial dihedral symmetric Boolean functions
inferred← citeshttps://doi.org/10.1016/j.ffa.2020.101632openalex-snapshot
Value distribution of elementary symmetric polynomials and its perturbations over finite fields
inferred← citeshttps://doi.org/10.1016/j.ipl.2016.03.012openalex-snapshot
Correlation lower bounds from correlation upper bounds
inferred← citeshttps://doi.org/10.1016/j.jcss.2004.01.003openalex-snapshot
The correlation between parity and quadratic polynomials mod3
inferred← citeshttps://doi.org/10.1016/j.jnt.2005.04.005openalex-snapshot
Incomplete quadratic exponential sums in several variables
inferred← citeshttps://doi.org/10.1016/j.jnt.2009.08.016openalex-snapshot
Uniqueness of optimal mod 3 polynomials for parity
inferred← citeshttps://doi.org/10.1016/j.laa.2018.03.013openalex-snapshot
Hadamard matrices and the spectrum of quadratic symmetric polynomials over finite fields
inferred← citeshttps://doi.org/10.1016/j.tcs.2022.09.034openalex-snapshot
Certificate complexity of elementary symmetric Boolean functions
inferred← citeshttps://doi.org/10.1109/ccc.2001.933885openalex-snapshot
Lower bounds for approximations by low degree polynomials over Z/sub m/
inferred← citeshttps://doi.org/10.1109/ccc.2002.1004341openalex-snapshot
The correlation between parity and quadratic polynomials mod 3
inferred← citeshttps://doi.org/10.1109/focs.2007.24openalex-snapshot
Computing Equilibria in Anonymous Games
inferred← citeshttps://doi.org/10.1109/focs.2007.30openalex-snapshot
Discrepancy and the Power of Bottom Fan-in in Depth-three Circuits
inferred← citeshttps://doi.org/10.1109/tit.2015.2455052openalex-snapshot
Recent Results on Balanced Symmetric Boolean Functions
inferred← citeshttps://doi.org/10.1109/tit.2017.2750674openalex-snapshot
Diophantine Equations With Binomial Coefficients and Perturbations of Symmetric Boolean Functions
inferred← citeshttps://doi.org/10.1216/rmj.2022.52.1355openalex-snapshot
Recursions for modified Walsh transforms of some families of Boolean functions
inferred← citeshttps://doi.org/10.1515/jmc-2020-0042openalex-snapshot
Sensitivities and block sensitivities of elementary symmetric Boolean functions
inferred← citeshttps://doi.org/10.1561/0400000033openalex-snapshot
On the Power of Small-Depth Computation
inferred← citeshttps://doi.org/10.1561/9781601983015openalex-snapshot
On the Power of Small-Depth Computation
inferred← citeshttps://doi.org/10.2140/involve.2018.11.127openalex-snapshot
Generalized exponential sums and the power of computers
inferred← citeshttps://doi.org/10.3233/fi-2021-2076openalex-snapshot
Testing Boolean Functions Properties
inferred← citeshttps://doi.org/10.37236/2004openalex-snapshot
Linear Recurrences and Asymptotic Behavior of Exponential Sums of Symmetric Boolean Functions
inferred← citeshttps://doi.org/10.37236/495openalex-snapshot
Which Chessboards have a Closed Knight's Tour within the Rectangular Prism?
inferred← citeshttps://doi.org/10.3934/amc.2026038openalex-snapshot
Closed formula for exponential sums of cubic $ k $ -cycles over Galois fields
inferred← citeshttps://doi.org/10.3934/amc.2026062openalex-snapshot
Permutation equivalence of $ k $ -rotation symmetric monomial Boolean functions
inferred← citeshttps://doi.org/10.4230/dagsemproc.07411.7openalex-snapshot
Uniqueness of Optimal Mod 3 Circuits for Parity
inferred← citeshttps://doi.org/10.48550/arxiv.1603.00534openalex-snapshot
Modular periodicity of exponential sums of symmetric Boolean functions and some of its consequences
inferred← citeshttps://doi.org/10.48550/arxiv.1702.08038openalex-snapshot
Recursions associated to trapezoid, symmetric and rotation symmetric functions over Galois fields
inferred← citeshttps://doi.org/10.48550/arxiv.1802.09121openalex-snapshot
Limits on representing Boolean functions by linear combinations of simple functions: thresholds, ReLUs, and low-degree polynomials
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