Average case complete problems
SIAM Journal on Computing
Average-case analysis of algorithms and data structures
Handbook of theoretical computer science (vol. A)
SIAM Journal on Computing
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The Average-Case Complexity of Determining the Majority
SIAM Journal on Computing
Quantum cryptanalysis of hash and claw-free functions
ACM SIGACT News
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
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
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Quantum Queries on Permutations with a Promise
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
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We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial [3]. We show that for average-case complexity under the uniform distribution, quantum algorithms can be exponentially faster than classical algorithms. Under non-uniform distributions the gap can even be super-exponential. We also prove some general bounds for average-case complexity and show that the average-case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical complexity.