Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Exact lower time bounds for computing Boolean functions on CREW PRAMs
Journal of Computer and System Sciences
The quantum query complexity of approximating the median and related statistics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
On Quantum Versions of the Yao Principle
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Bounds for Small-Error and Zero-Error Quantum Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Agnostically Learning Halfspaces
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the power of Ambainis lower bounds
Theoretical Computer Science
The quantum query complexity of the abelian hidden subgroup problem
Theoretical Computer Science
Extremal properties of polynomial threshold functions
Journal of Computer and System Sciences
The pattern matrix method for lower bounds on quantum communication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Improved Separations between Nondeterministic and Randomized Multiparty Communication
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
Improved Separations between Nondeterministic and Randomized Multiparty Communication
ACM Transactions on Computation Theory (TOCT)
A lower bound for agnostically learning disjunctions
COLT'07 Proceedings of the 20th annual conference on Learning theory
ALGOSENSORS'10 Proceedings of the 6th international conference on Algorithms for sensor systems, wireless adhoc networks, and autonomous mobile entities
SIAM Journal on Computing
Quantum interpolation of polynomilas
Quantum Information & Computation
Quantum communication complexity of block-composed functions
Quantum Information & Computation
A note on quantum algorithms and the minimal degree of ε-error polynomials for symmetric functions
Quantum Information & Computation
Quantum property testing for bounded-degree graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Bounded Independence Fools Halfspaces
SIAM Journal on Computing
A quantum lower bound for the query complexity of simon's problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Impossibility of succinct quantum proofs for collision-freeness
Quantum Information & Computation
SIAM Journal on Computing
Dual lower bounds for approximate degree and markov-bernstein inequalities
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Faster private release of marginals on small databases
Proceedings of the 5th conference on Innovations in theoretical computer science
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In this paper, we provide matching (up to a constant factor) upper and lower bounds on the degree of polynomials that represent symmetric boolean functions with an error 1/3. Let &Ggr;(f)=min{|2k–n+1|:fk ≠ fk+ 1 and 0 ≤ k ≤ n – 1} where fi is the value of f on inputs with exactly i 1's. We prove that the minimum degree over all the approximating polynomials of f is &THgr;((n(n-&Ggr;(f))).5). We apply the techniques and tools from approximation theory to derive this result.