Probabilistic communication complexity
Journal of Computer and System Sciences
Relations between communication complexity classes
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
Perceptrons, PP, and the polynomial hierarchy
Computational Complexity - Special issue on circuit complexity
SIAM Journal on Computing
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STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A note on quantum black-box complexity of almost all Boolean functions
Information Processing Letters
Information Processing Letters
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
A linear lower bound on the unbounded error probabilistic communication complexity
Journal of Computer and System Sciences - Complexity 2001
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Nondeterministic Quantum Query and Communication Complexities
SIAM Journal on Computing
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FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On Computation and Communication with Small Bias
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Lower Bounds for Quantum Communication Complexity
SIAM Journal on Computing
Extremal properties of polynomial threshold functions
Journal of Computer and System Sciences
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SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
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ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Unbounded-error classical and quantum communication complexity
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Quantum weakly nondeterministic communication complexity
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Unbounded-error one-way classical and quantum communication complexity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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This work studies the quantum query complexity of Boolean functions in an unbounded-error scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication complexity model, the unbounded-error quantum query complexity is exactly half of its classical counterpart for any (partial or total) Boolean function. Moreover, connecting the query and communication complexity results, we show that the ''black-box'' approach to convert quantum query algorithms into communication protocols by Buhrman-Cleve-Wigderson [STOC'98] is optimal even in the unbounded-error setting. We also study a related setting, called the weakly unbounded-error setting, where the cost of a query algorithm is given by q+log(1/2(p-1/2)), where q is the number of queries made and p1/2 is the success probability of the algorithm. In contrast to the case of communication complexity, we show a tight multiplicative @Q(logn) separation between quantum and classical query complexity in this setting for a partial Boolean function. The asymptotic equivalence between them is also shown for some well-studied total Boolean functions.