Lower bounds on the size of bounded depth circuits over a complete basis with logical addition

From MaRDI portal
Publication:1095871

DOI10.1007/BF01137685zbMath0632.94030OpenAlexW2009994177WikidataQ29042011 ScholiaQ29042011MaRDI QIDQ1095871

Alexander A. Razborov

Publication date: 1987

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01137685




Related Items (more than 100 items found - showing only first 100)

Hardness Characterisations and Size-width Lower Bounds for QBF ResolutionImmunity and Simplicity for Exact Counting and Other Counting ClassesSolution Sets for Equations over Free Groups are EDT0L LanguagesA Hierarchy Theorem for Interactive Proofs of ProximityOn small depth threshold circuitsApproximate Degree in Classical and Quantum ComputingFaster All-Pairs Shortest Paths via Circuit ComplexityNonuniform ACC Circuit Lower BoundsRandomized feasible interpolation and monotone circuits with a local oracleSkew Circuits of Small WidthStrong Average-Case Circuit Lower Bounds from Nontrivial DerandomizationCharacterizing Propositional Proofs as Noncommutative FormulasCollapsing modular counting in bounded arithmetic and constant depth propositional proofsThe Shifted Partial Derivative Complexity of Elementary Symmetric PolynomialsSeparating counting communication complexity classesConstructive Relationships Between Algebraic Thickness and NormalityOn the Size of Depth-Three Boolean Circuits for Computing Multilinear FunctionsWorst-Case to Average-Case Reductions for Subclasses of PConstant-Round Interactive Proof Systems for AC0[2 and NC1] ⋮ On the complexity of algebraic numbers, and the bit-complexity of straight-line programs1Unnamed ItemOn the probabilistic degree of OR over the realsIs it possible to improve Yao's XOR lemma using reductions that exploit the efficiency of their oracle?A note on uniform circuit lower bounds for the counting hierarchy (extended abstract)Paradigms for Unconditional Pseudorandom GeneratorsUnnamed ItemUnnamed ItemThe work of Mark BravermanCommunication and information complexityMonomial Boolean functions with large high-order nonlinearitiesOn the correlation of symmetric functionsUnnamed ItemUnnamed ItemThe Computational Power of Depth Five Arithmetic CircuitsOn polynomial approximations to ACAgnostic Learning from Tolerant Natural ProofsDepth Reduction for CompositesLearning Read-Constant Polynomials of Constant Degree Modulo CompositesNEXP Does Not Have Non-uniform Quasipolynomial-Size ACC Circuits of o(loglogn) DepthDegree lower bounds of tower-type for approximating formulas with parity quantifiersCircuit complexity of regular languagesNatural proofsAn exact characterization of symmetric functions in \(qAC^{0}[2\)] ⋮ A lower bound for primalityFine-grained secure attribute-based encryptionUnnamed ItemUnnamed ItemUnnamed ItemUnnamed ItemUnnamed ItemUnnamed ItemOn the degree of univariate polynomials over the integersNew bounds for energy complexity of Boolean functionsUnnamed ItemOn the modulo degree complexity of Boolean functionsOn the Probabilistic Degrees of Symmetric Boolean FunctionsFine-grained cryptography revisitedUnnamed ItemPropositional proof complexityCorrelation Bounds for Poly-size $\mbox{\rm AC}^0$ Circuits with n 1 − o(1) Symmetric GatesOn systems of equations over free partially commutative groupsOn the correlation of symmetric functionsEhrenfeucht-Fraïssé Games on Random StructuresPseudorandom Generators from the Second Fourier Level and Applications to AC0 with Parity GatesExpander-Based Cryptography Meets Natural ProofsDepth Reduction for Circuits with a Single Layer of Modular Counting GatesParity helps to compute majorityOn the Symmetries of and Equivalence Test for Design Polynomials.Bounded-Depth Frege Complexity of Tseitin Formulas for All GraphsAverage-Case Lower Bounds and Satisfiability Algorithms for Small Threshold CircuitsUnnamed ItemThe Power of Programs over Monoids in DAUnnamed ItemUnnamed ItemFrom Circuit Complexity to Faster All-Pairs Shortest PathsPseudorandom Functions: Three Decades LaterReed-Muller CodesAsymptotic invariants, complexity of groups and related problemsAffine projections of symmetric polynomials.Exact lower time bounds for computing Boolean functions on CREW PRAMsThe expressive power of voting polynomialsExpander-based cryptography meets natural proofsCorrelation lower bounds from correlation upper boundsThe correlation between parity and quadratic polynomials mod \(3\)Threshold circuits of bounded depthA lower bound for depth-3 circuits with MOD \(m\) gatesFine-grained secure computationExploring crypto dark matter: new simple PRF candidates and their applicationsFine-grained secure attribute-based encryptionLow-complexity weak pseudorandom functions in \(\mathtt{AC}0[\mathtt{MOD}2\)] ⋮ On the degree of Boolean functions as real polynomialsOn ACCRepresenting Boolean functions as polynomials modulo composite numbersCircuits constructed with MOD\(_ q\) gates cannot compute ``and in sublinear sizeA note on a theorem of Barrington, Straubing and ThérienCircuit lower bounds from learning-theoretic approachesA note on some languages in uniform \(ACC^ 0\)On uniformity within \(NC^ 1\)Energy complexity of satisfying assignments in monotone circuits: on the complexity of computing the best caseImplicit function theorem over free groups.



Cites Work


This page was built for publication: Lower bounds on the size of bounded depth circuits over a complete basis with logical addition