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Perceptrons, PP, and the polynomial hierarchy
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1006/inco.1994.1057openalex-snapshot
Depth Reduction for Circuits of Unbounded Fan-in
inferredcites →https://doi.org/10.1007/978-1-4757-1640-5openalex-snapshot
Problems and Theorems in Analysis
inferredcites →https://doi.org/10.1007/bf01111276openalex-snapshot
Schwankung von Polynomen zwischen Gitterpunkten
inferredcites →https://doi.org/10.1007/bf01744431openalex-snapshot
Parity, circuits, and the polynomial-time hierarchy
inferredcites →https://doi.org/10.1007/bf02582920openalex-snapshot
SeparatingPH fromPP by relativization
inferredcites →https://doi.org/10.1007/bfb0020802openalex-snapshot
Randomized polynomials, threshold circuits, and the polynomial hierarchy
inferredcites →https://doi.org/10.1007/bfb0029603openalex-snapshot
On the power of uniform families of constant depth threshold circuits
inferredcites →https://doi.org/10.1016/0020-0190(91)90140-dopenalex-snapshot
Probabilistic polynomial time is closed under parity reductions
inferredcites →https://doi.org/10.1016/0304-3975(93)90214-eopenalex-snapshot
Probabilistic polynomials, AC0 functions and the polynomial-time hierarchy
inferredcites →https://doi.org/10.1016/0890-5401(91)90075-dopenalex-snapshot
On truth-table reducibility to SAT
inferredcites →https://doi.org/10.1109/fscs.1990.89583openalex-snapshot
ON ACC and threshold circuits
inferredcites →https://doi.org/10.1109/sfcs.1989.63538openalex-snapshot
A note on the power of threshold circuits
inferredcites →https://doi.org/10.1137/0220053openalex-snapshot
PP is as Hard as the Polynomial-Time Hierarchy
inferredcites →https://doi.org/10.1137/0221023openalex-snapshot
Counting Classes are at Least as Hard as the Polynomial-Time Hierarchy
inferredcites →https://doi.org/10.1137/0703024openalex-snapshot
A Comparison of Uniform Approximations on an Interval and a Finite Subset Thereof
inferredcites →https://doi.org/10.1145/103418.103426openalex-snapshot
PP is closed under intersection
inferredcites →https://doi.org/10.1145/103418.103461openalex-snapshot
The expressive power of voting polynomials
inferredcites →https://doi.org/10.7916/d83x8frjopenalex-snapshot
On the Power of Probabilistic Polynomial Time: PNP[log] ⊆ PP
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1006/jcss.1997.1552openalex-snapshot
A Lower Bound for Perceptrons and an Oracle Separation of the PPPHHierarchy
inferred← citeshttps://doi.org/10.1006/jcss.1999.1651openalex-snapshot
Complexity Limitations on Quantum Computation
inferred← citeshttps://doi.org/10.1007/1-4020-8141-3_10openalex-snapshot
Degree Bounds on Polynomials and Relativization Theory
inferred← citeshttps://doi.org/10.1007/3-540-45841-7_30openalex-snapshot
On the Computational Power of Boolean Decision Lists
inferred← citeshttps://doi.org/10.1007/3-540-58715-2_130openalex-snapshot
My favorite ten complexity theorems of the past decade
inferred← citeshttps://doi.org/10.1007/978-1-4612-1872-2_11openalex-snapshot
Polynomials and Combinatorial Definitions of Languages
inferred← citeshttps://doi.org/10.1007/978-3-030-79416-3_25openalex-snapshot
On Separation Between the Degree of a Boolean Function and the Block Sensitivity
inferred← citeshttps://doi.org/10.1007/978-3-540-27798-9_22openalex-snapshot
Learning DNFs and Circuits Using Teaching Assistants
inferred← citeshttps://doi.org/10.1007/978-3-540-27819-1_16openalex-snapshot
Toward Attribute Efficient Learning of Decision Lists and Parities
inferred← citeshttps://doi.org/10.1007/978-3-540-74510-5_33openalex-snapshot
Perceptrons of Large Weight
inferred← citeshttps://doi.org/10.1007/978-3-540-79709-8_27openalex-snapshot
A Uniform Lower Bound on Weights of Perceptrons
inferred← citeshttps://doi.org/10.1007/978-3-540-92182-0_80openalex-snapshot
Unbounded-Error Quantum Query Complexity
inferred← citeshttps://doi.org/10.1007/978-3-642-15155-2_8openalex-snapshot
Weights of Exact Threshold Functions
inferred← citeshttps://doi.org/10.1007/978-3-642-21111-9_32openalex-snapshot
Representing Boolean Functions Using Polynomials: More Can Offer Less
inferred← citeshttps://doi.org/10.1007/978-3-642-30870-3_60openalex-snapshot
Lower Bound on Weights of Large Degree Threshold Functions
inferred← citeshttps://doi.org/10.1007/978-3-642-39206-1_26openalex-snapshot
Dual Lower Bounds for Approximate Degree and Markov-Bernstein Inequalities
inferred← citeshttps://doi.org/10.1007/978-3-642-40313-2_46openalex-snapshot
Polynomial Threshold Functions and Boolean Threshold Circuits
inferred← citeshttps://doi.org/10.1007/978-3-662-47672-7_22openalex-snapshot
Hardness Amplification and the Approximate Degree of Constant-Depth Circuits
inferred← citeshttps://doi.org/10.1007/s00037-005-0203-0openalex-snapshot
On the computational power of Boolean decision lists
inferred← citeshttps://doi.org/10.1007/s00037-008-0244-2openalex-snapshot
Polynomials that Sign Represent Parity and Descartes’ Rule of Signs
inferred← citeshttps://doi.org/10.1007/s00037-012-0045-5openalex-snapshot
Improved Approximation of Linear Threshold Functions
inferred← citeshttps://doi.org/10.1007/s00037-018-0175-5openalex-snapshot
Query-to-Communication Lifting for PNP
inferred← citeshttps://doi.org/10.1007/s00493-010-2173-3openalex-snapshot
New degree bounds for polynomial threshold functions
inferred← citeshttps://doi.org/10.1007/s00493-013-2759-7openalex-snapshot
Optimal bounds for sign-representing the intersection of two halfspaces by polynomials
inferred← citeshttps://doi.org/10.1016/j.ic.2011.01.006openalex-snapshot
Complexity classes of equivalence problems revisited
inferred← citeshttps://doi.org/10.1016/j.ic.2014.09.008openalex-snapshot
Polynomial threshold functions and Boolean threshold circuits
inferred← citeshttps://doi.org/10.1016/j.ic.2014.12.003openalex-snapshot
Dual lower bounds for approximate degree and Markov–Bernstein inequalities
inferred← citeshttps://doi.org/10.1016/j.ipl.2006.04.007openalex-snapshot
On computing the smallest four-coloring of planar graphs and non-self-reducible sets in P
inferred← citeshttps://doi.org/10.1016/j.jcss.2006.01.002openalex-snapshot
LWPP and WPP are not uniformly gap-definable
inferred← citeshttps://doi.org/10.1016/j.jcss.2006.05.001openalex-snapshot
Error-bounded probabilistic computations between MA and AM
inferred← citeshttps://doi.org/10.1016/j.jcss.2007.06.021openalex-snapshot
Extremal properties of polynomial threshold functions
inferred← citeshttps://doi.org/10.1016/j.tcs.2005.07.032openalex-snapshot
A note on the circuit complexity of PP
inferred← citeshttps://doi.org/10.1016/j.tcs.2011.04.043openalex-snapshot
Unbounded-error quantum query complexity
inferred← citeshttps://doi.org/10.1016/s0022-0000(05)80024-8openalex-snapshot
Gap-definable counting classes
inferred← citeshttps://doi.org/10.1016/s0304-3975(98)00061-9openalex-snapshot
Relating polynomial time to constant depth
inferred← citeshttps://doi.org/10.1051/ita:1999100openalex-snapshot
Immunity and Simplicity for Exact Counting and Other Counting Classes
inferred← citeshttps://doi.org/10.1070/rm2009v064n05abeh004646openalex-snapshot
Reducing by 1 the degree of a polynomial with fixed sign function can increase exponentially its weight and length
inferred← citeshttps://doi.org/10.1098/rspa.2005.1546openalex-snapshot
Quantum computing, postselection, and probabilistic polynomial-time
inferred← citeshttps://doi.org/10.1103/physrevresearch.3.013213openalex-snapshot
Hardness of efficiently generating ground states in postselected quantum computation
inferred← citeshttps://doi.org/10.1109/ccc.1997.612312openalex-snapshot
A lower bound for perceptrons and an oracle separation of the PP/sup PH/ hierarchy
inferred← citeshttps://doi.org/10.1109/ccc.2003.1214406openalex-snapshot
Extremal properties of polynomial threshold functions
inferred← citeshttps://doi.org/10.1109/ccc.2004.1313846openalex-snapshot
Polynomials that sign represent parity and descartes rule of signs
inferred← citeshttps://doi.org/10.1109/ccc.2004.25openalex-snapshot
Polynomials that sign represent parity and Descartes rule of signs
inferred← citeshttps://doi.org/10.1109/ccc.2006.32openalex-snapshot
Oracles Are Subtle But Not Malicious
inferred← citeshttps://doi.org/10.1109/ccc.2007.18openalex-snapshot
On Computation and Communication with Small Bias
inferred← citeshttps://doi.org/10.1109/ccc.2009.8openalex-snapshot
Improved Approximation of Linear Threshold Functions
inferred← citeshttps://doi.org/10.1109/focs.2009.68openalex-snapshot
Bounded Independence Fools Halfspaces
inferred← citeshttps://doi.org/10.1109/focs.2010.8openalex-snapshot
Bounded Independence Fools Degree-2 Threshold Functions
inferred← citeshttps://doi.org/10.1109/focs.2017.10openalex-snapshot
A Nearly Optimal Lower Bound on the Approximate Degree of AC^0
inferred← citeshttps://doi.org/10.1109/focs.2018.00014openalex-snapshot
A Short List of Equalities Induces Large Sign Rank
inferred← citeshttps://doi.org/10.1109/ictta.2004.1307935openalex-snapshot
Complexity of the exact domatic number problem and of the exact conveyor flow shop problem
inferred← citeshttps://doi.org/10.1109/isit57864.2024.10619486openalex-snapshot
Nearest Neighbor Representations of Neural Circuits
inferred← citeshttps://doi.org/10.1109/sct.1993.336538openalex-snapshot
The polynomial method in circuit complexity
inferred← citeshttps://doi.org/10.1134/s0001434610050263openalex-snapshot
A small decrease in the degree of a polynomial with a given sign function can exponentially increase its weight and length
inferred← citeshttps://doi.org/10.1134/s0032946009010062openalex-snapshot
Perceptrons of large weight
inferred← citeshttps://doi.org/10.1134/s0081543811060149openalex-snapshot
Degree-uniform lower bound on the weights of polynomials with given sign function
inferred← citeshttps://doi.org/10.1137/100783030openalex-snapshot
Bounded Independence Fools Halfspaces
inferred← citeshttps://doi.org/10.1137/100785260openalex-snapshot
The Intersection of Two Halfspaces Has High Threshold Degree
inferred← citeshttps://doi.org/10.1137/15m1015704openalex-snapshot
Breaking the Minsky--Papert Barrier for Constant-Depth Circuits
inferred← citeshttps://doi.org/10.1137/17m1161737openalex-snapshot
A Nearly Optimal Lower Bound on the Approximate Degree of AC$^0$
inferred← citeshttps://doi.org/10.1137/19m1271348openalex-snapshot
A Short List of Equalities Induces Large Sign-Rank
inferred← citeshttps://doi.org/10.1145/3188745.3188784openalex-snapshot
The polynomial method strikes back: tight quantum query bounds via dual polynomials
inferred← citeshttps://doi.org/10.1145/780542.780592openalex-snapshot
New degree bounds for polynomial threshold functions
inferred← citeshttps://doi.org/10.1587/transfun.2022dml0003openalex-snapshot
Lower Bounds on the PTF Weight of ODD-MAXBIT Function
inferred← citeshttps://doi.org/10.2168/lmcs-9(2:13)2013openalex-snapshot
Lower Bound on Weights of Large Degree Threshold Functions
inferred← citeshttps://doi.org/10.26421/qic8.10-4openalex-snapshot
A note on quantum algorithms and the minimal degree of epsilon-error polynomials for symmetric functions
inferred← citeshttps://doi.org/10.4213/mzm8734openalex-snapshot
Небольшое уменьшение степени многочлена с заданной знаковой функцией может экспоненциально увеличить его вес и длину
inferred← citeshttps://doi.org/10.4213/rm9303openalex-snapshot
Уменьшение на единицу степени многочлена с заданной знаковой функцией может экспоненциально увеличить его вес и длину
inferred← citeshttps://doi.org/10.48550/arxiv.1503.07261openalex-snapshot
Dual Polynomials for Collision and Element Distinctness
inferred← citeshttps://doi.org/10.48550/arxiv.1606.04016openalex-snapshot
Adaptivity vs Postselection
inferred← citeshttps://doi.org/10.48550/arxiv.quant-ph/0412143openalex-snapshot
Limits on Efficient Computation in the Physical World
inferred← citeshttps://doi.org/10.48550/arxiv.quant-ph/0412187openalex-snapshot
Quantum Computing, Postselection, and Probabilistic Polynomial-Time
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