Quantum and classical query complexities of local search are polynomially related
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
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
New upper and lower bounds for randomized and quantum local search
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Polynomial degree vs. quantum query complexity
Journal of Computer and System Sciences - Special issue on FOCS 2003
On the power of Ambainis lower bounds
Theoretical Computer Science
Negative weights make adversaries stronger
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Lower bounds on quantum query complexity for read-once decision trees with parity nodes
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Lower bounds using kolmogorov complexity
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
All quantum adversary methods are equivalent
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Reflections for quantum query algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On the black-box complexity of sperner's lemma
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We prove a very general lower bound technique forquantum and randomized query complexity, that is easyto prove as well as to apply. To achieve this, we introducethe use of Kolmogorov complexity to query complexity.Our technique generalizes the weighted, unweightedmethods of Ambainis, and the spectral method of Barnum,Saks and Szegedy. As an immediate consequence of ourmain theorem, it can be shown that adversary methodscan only prove lower bounds for boolean functions f in0(\min (\sqrt {nC_0 (f)} ,\sqrt {nC_1 (f)})), where C_0, C_1 is the certificate complexity, and n is the size of the input. We also derive a general form of the ad hoc weighted method used byHøyer, Neerbek and Shi to give a quantum lower bound on ordered search and sorting.