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FOCS
2003
IEEE
15 years 9 months ago
Polynomial Degree vs. Quantum Query Complexity
The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bo...
Andris Ambainis
FOCS
1998
IEEE
15 years 8 months ago
The Quantum Communication Complexity of Sampling
Sampling is an important primitive in probabilistic and quantum algorithms. In the spirit of communication complexity, given a function f : X
Andris Ambainis, Leonard J. Schulman, Amnon Ta-Shm...
FOCS
1991
IEEE
15 years 7 months ago
Communication Complexity Towards Lower Bounds on Circuit Depth
Karchmer, Raz, and Wigderson, 1991, discuss the circuit depth complexity of n bit Boolean functions constructed by composing up to d = logn=loglogn levels of k = logn bit boolean
Jeff Edmonds, Steven Rudich, Russell Impagliazzo, ...
GD
2009
Springer
15 years 7 months ago
Complexity of Some Geometric and Topological Problems
We show that recognizing intersection graphs of convex sets has the same complexity as deciding truth in the existential theory of the reals. Comparing this to similar results on t...
Marcus Schaefer
DAGSTUHL
2006
15 years 5 months ago
Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical "black box" function drawn from some set of such bl...
Howard Barnum