Separating the polynomial-time hierarchy by oracles
Proc. 26th annual symposium on Foundations of computer science
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
With probability one, a random oracle separates PSPACE from the polynomial-time hierarchy
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Finite monoids and the fine structure of NC1
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Finite monoids and the fine structure of NC1
Journal of the ACM (JACM)
On the method of approximations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Circuits and local computation
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Exact time bounds for computing boolean functions on PRAMs without simultaneous writes
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Functions with bounded symmetric communication complexity and circuits with mod m gates
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
The expressive power of voting polynomials
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
On the degree of Boolean functions as real polynomials
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On the degree of polynomials that approximate symmetric Boolean functions (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The history and status of the P versus NP question
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Size-depth trade-offs for threshold circuits
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
On the computational power of depth 2 circuits with threshold and modulo gates
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A weight-size trade-off for circuits with MOD m gates
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Exponential lower bounds for depth 3 Boolean circuits
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
An exponential lower bound for depth 3 arithmetic circuits
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Computational bounds for fundamental problems on general-purpose parallel models
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
Linear gaps between degrees for the polynomial calculus modulo distinct primes
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Lower bounds for matrix product, in bounded depth circuits with arbitrary gates
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Affine projections of symmetric polynomials
Journal of Computer and System Sciences - Complexity 2001
Bounded-Depth Frege Systems with Counting Axioms Polynomially Simulate Nullstellensatz Refutations
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the Minimal Hardware Complexity of Pseudorandom Function Generators
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Quantum Circuits with Unbounded Fan-out
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
An Exact Characterization of Symmetric Functions in qAC0[2]
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
On the Derandomization of Constant Depth Circuits
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
The computing power of programs over finite monoids
Journal of Automata, Languages and Combinatorics - Selected papers of the workshop on logic and algebra for concurrency
Upper and Lower Bounds for Some Depth-3 Circuit Classes
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
On TC/sup 0/, AC/sup 0/, and Arithmetic Circuits
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Pseudorandom functions in TC0 and cryptographic limitations to proving lower bounds
Computational Complexity
Some connections between bounded query classes and non-uniform complexity
Information and Computation
Complexity of some arithmetic problems for binary polynomials
Computational Complexity
The correlation between parity and quadratic polynomials mod 3
Journal of Computer and System Sciences - Special issue on computational complexity 2002
On the computational power of probabilistic and quantum branching program
Information and Computation
Combinatorics, Probability and Computing
SIGACT news complexity theory column 53
ACM SIGACT News
Zero-knowledge from secure multiparty computation
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Circuit lower bounds for Merlin-Arthur classes
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
ACM SIGACT News
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Communication in the presence of replication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Elusive functions and lower bounds for arithmetic circuits
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Threshold circuits of bounded depth
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
The matching problem for bipartite graphs with polynomially bounded permanents is in NC
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Time-Space Tradeoffs for Counting NP Solutions Modulo Integers
Computational Complexity
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
The Complexity of Local List Decoding
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Polynomials that Sign Represent Parity and Descartes' Rule of Signs
Computational Complexity
Algebrization: A New Barrier in Complexity Theory
ACM Transactions on Computation Theory (TOCT)
Guest Column: correlation bounds for polynomials over {0 1}
ACM SIGACT News
Random graphs and the parity quantifier
Proceedings of the forty-first annual ACM symposium on Theory of computing
Ehrenfeucht-Fraïssé Games on Random Structures
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
Depth Reduction for Circuits with a Single Layer of Modular Counting Gates
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Random Low Degree Polynomials are Hard to Approximate
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
On the Power of Small-Depth Computation
Foundations and Trends® in Theoretical Computer Science
Amplifying lower bounds by means of self-reducibility
Journal of the ACM (JACM)
On the computational power of probabilistic and quantum branching program
Information and Computation
Polylogarithmic independence fools AC0 circuits
Journal of the ACM (JACM)
Some properties of MODmcircuits computing simple functions
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
The descriptive complexity approach to LOGCFL
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On covering and rank problems for boolean matrices and their applications
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
BQP and the polynomial hierarchy
Proceedings of the forty-second ACM symposium on Theory of computing
Incremental query evaluation in a ring of databases
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Cracks in the defenses: scouting out approaches on circuit lower bounds
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Twelve problems in proof complexity
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
A uniform lower bound on weights of perceptrons
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Poly-logarithmic independence fools bounded-depth boolean circuits
Communications of the ACM
Hardness of Reconstructing Multivariate Polynomials over Finite Fields
SIAM Journal on Computing
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
On the complexity of powering in finite fields
Proceedings of the forty-third annual ACM symposium on Theory of computing
Characterizing definability of second-order generalized quantifiers
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
Nexp does not have non-uniform quasipolynomial-size ACC circuits of o(log log n) depth
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Counting, fanout and the complexity of quantum ACC
Quantum Information & Computation
Quantum lower bound for recursive Fourier sampling
Quantum Information & Computation
Quantum lower bounds for fanout
Quantum Information & Computation
A note on quantum algorithms and the minimal degree of ε-error polynomials for symmetric functions
Quantum Information & Computation
Learning read-constant polynomials of constant degree modulo composites
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Correlation bounds for poly-size AC0 circuits with n1-o(1) symmetric gates
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Hard functions for low-degree polynomials over prime fields
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Symmetric functions capture general functions
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Guest column: a casual tour around a circuit complexity bound
ACM SIGACT News
On the degree of univariate polynomials over the integers
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
On beating the hybrid argument
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Definability of languages by generalized first-order formulas over (N,+)
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Lower bounds for circuits with few modular and symmetric gates
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
An algebraic point of view on the crane beach property
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Exponential lower bound for bounded depth circuits with few threshold gates
Information Processing Letters
Computational complexity since 1980
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
On the correlation between parity and modular polynomials
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Random access to advice strings and collapsing results
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Secure computation of constant-depth circuits with applications to database search problems
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Bounds on the power of constant-depth quantum circuits
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Feasible proofs of matrix properties with csanky's algorithm
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Protecting circuits from leakage: the computationally-bounded and noisy cases
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Degree lower bounds of tower-type for approximating formulas with parity quantifiers
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Representing the boolean OR function by quadratic polynomials modulo 6
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
On the complexity of hard-core set constructions
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Permanent does not have succinct polynomial size arithmetic circuits of constant depth
Information and Computation
Hard Functions for Low-Degree Polynomials over Prime Fields
ACM Transactions on Computation Theory (TOCT)
Arthur-Merlin streaming complexity
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Random graphs and the parity quantifier
Journal of the ACM (JACM)
Graph Isomorphism is Not AC0-Reducible to Group Isomorphism
ACM Transactions on Computation Theory (TOCT)
Candidate weak pseudorandom functions in AC0 ○ MOD2
Proceedings of the 5th conference on Innovations in theoretical computer science
Nonuniform ACC Circuit Lower Bounds
Journal of the ACM (JACM)
Degree lower bounds of tower-type for approximating formulas with parity quantifiers
ACM Transactions on Computational Logic (TOCL)
Isolating an Odd Number of Elements and Applications in Complexity Theory
Theory of Computing Systems
Lower Bounds for Randomized Exclusive Write PRAMs
Theory of Computing Systems
| Hi-index | 0.02 |
We use algebraic methods to get lower bounds for complexity of different functions based on constant depth unbounded fan-in circuits with the given set of basic operations. In particular, we prove that depth k circuits with gates NOT, OR and MODp where p is a prime require Exp(&Ogr;(n1/2k)) gates to calculate MODr functions for any r ≠ pm. This statement contains as special cases Yao's PARITY result [ Ya 85 ] and Razborov's new MAJORITY result [Ra 86] (MODm gate is an oracle which outputs zero, if the number of ones is divisible by m).