Monotone bipartite graph properties are evasive
SIAM Journal on Computing
Lower bounds on the complexity of graph properties
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
SIAM Journal on 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 growth of polynomials bounded at equally spaced points
SIAM Journal on Mathematical Analysis
The probabilistic communication complexity of set intersection
SIAM Journal on Discrete Mathematics
On the distributional complexity of disjointness
Theoretical Computer Science
On read-once threshold formulae and their randomized decision tree complexity
Theoretical Computer Science - Special issue on structure in complexity theory
Information Processing Letters
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Nondeterministic communication with a limited number of advice bits
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Communication complexity
A framework for fast quantum mechanical algorithms
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Complexity theory retrospective II
Exponential separation of quantum and classical communication complexity
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Space Time Tradeoffs for Graph Properties
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Complexity Limitations on Quantum Computation
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
The Quantum Communication Complexity of Sampling
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
On the Quantum Complexity of Majority
On the Quantum Complexity of Majority
A topological approach to evasiveness
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Generic oracles and oracle classes
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Rapid sampling though quantum computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second 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
Quantum communication and complexity
Theoretical Computer Science - Natural computing
Introduction to Recent Quantum Algorithms
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
On Quantum Versions of the Yao Principle
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Lower bounds for local search by quantum arguments
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Quantum algorithms for the triangle problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Zero-knowledge against quantum attacks
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Quantum Queries on Permutations with a Promise
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
The quantum query complexity of certification
Quantum Information & Computation
Quantum search of partially ordered sets
Quantum Information & Computation
A note on quantum algorithms and the minimal degree of ε-error polynomials for symmetric functions
Quantum Information & Computation
A panoply of quantum algorithms
Quantum Information & Computation
Private data release via learning thresholds
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Bounds for error reduction with few quantum queries
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Superiority of exact quantum automata for promise problems
Information Processing Letters
Making polynomials robust to noise
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Communication lower bounds using directional derivatives
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the tradeoffs between the number of queries of quantum search algorithms, their error probability, the size of the search space, and the number of solutions in this space. Using this, we deduce new lower and upper bounds for quantum versions of amplification problems. Next, we establish nearly optimal quantum-classical separations for the query complexity of monotone functions in the zero-error model (where our quantum zero-error model is defined so as to be robust when the quantum gates are noisy).Also, we present a communication complexity problem related to a total function for which there is a quantum-classical communication complexity gap in the zero-error model. Finally, we prove separations for monotone graph properties in the zero-error and other error models which imply that the evasiveness conjecture for such properties does not hold for quantum computers.