Properties of complexity measures for prams and wrams
Theoretical Computer Science
SIAM Journal on Computing
Journal of Computer and System Sciences
On the Monte Carlo Boolean decision tree complexity of read-once formulae
Random Structures & Algorithms
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
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
A note on quantum black-box complexity of almost all Boolean functions
Information Processing Letters
Arthur-Merlin games in Boolean decision trees
Journal of Computer and System Sciences
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Nondeterministic Quantum Query and Communication Complexities
SIAM Journal on Computing
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
On the Power of Quantum Proofs
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
The quantum query complexity of certification
Quantum Information & Computation
Quantum weakly nondeterministic communication complexity
Theoretical Computer Science
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Given a Boolean function f, we study two natural generalizations of the certificate complexity C(f): the randomized certificate complexity RC(f) and the quantum certificate complexity QC(f). Using Ambainis' adversary method, we exactly characterize QC(f) as the square root of RC(f). We then use this result to prove the new relation R"0(f)=O(Q"2(f)^2Q"0(f)logn) for total f, where R"0, Q"2, and Q"0 are zero-error randomized, bounded-error quantum, and zero-error quantum query complexities respectively. Finally we give asymptotic gaps between the measures, including a total f for which C(f) is superquadratic in QC(f), and a symmetric partial f for which QC(f)=O(1) yet Q"2(f)=@W(n/logn).