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> Theory Seminar - Feb 15
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Theory Seminar - Feb 15
Event date: Friday, February 15, 2013, at 11:10 AM
Location: GB 248
Speaker: Thomas Watson
University of California, Berkeley
Title: The Computational Complexity of Randomness
Abstract:
This talk will give an overview of our doctoral research, which addresses several topics regarding the role of randomness in computational complexity. The bulk of the talk will focus on "Time Hierarchies for Sampling Distributions", in which we show that "a little more time gives a lot more power to sampling algorithms." More precisely, we prove that for every constant k>=2, every polynomial time bound t, and every polynomially small eps, there exists a family of distributions on k elements that can be sampled exactly in polynomial time but cannot be sampled within statistical distance 1-1/k-eps in time t. This implies the following general time hierarchy for sampling distributions on arbitrary-size domains such as {0,1}^n: For every polynomial time bound t and every constant eps>0, there exists a family of distributions that can be sampled exactly in polynomial time but cannot be sampled within statistical distance 1-eps in time t. Our proof involves a new connection to list-decodable codes for communication over a certain type of noisy channel.