Non UBC
DSpace
Sajin Koroth
2020-01-07T09:22:10Z
2019-07-10T11:18
Lifting theorems are theorems that relate the query complexity of a function f : {0, 1}^n â {0, 1} to the communication complexity of the composed function f â ¦ g^n, for some â gadgetâ g : {0, 1}^b Ã {0, 1}^b â {0, 1}. Such theorems allow transferring lower bounds from query complexity to the communication complexity, and have seen numerous applications in the recent years. In addition, such theorems can be viewed as a strong generalization of a direct-sum theorem for the gadget g.
We prove a new lifting theorem that works for all gadgets g that have logarithmic length and exponentially-small discrepancy, for both deterministic and randomized communication complexity. Thus, we increase the range of gadgets for which such lifting theorems hold considerably.
Our result has two main motivations: First, allowing a larger variety of gadgets may support more applications. In particular, our work is the first to prove a randomized lifting theorem for logarithmic-size gadgets, thus improving some applications the theorem. Second, our result can be seen a strong generalization of a direct-sum theorem for functions with low discrepancy.
Joint work with Arkadev Chattopadhyay, Yuval Filmus, Or Meir, Toniann Pitassi
https://circle.library.ubc.ca/rest/handle/2429/73160?expand=metadata
53.0 minutes
video/mp4
Author affiliation: Simon Fraser University
Banff (Alta.)
10.14288/1.0387521
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Postdoctoral
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Computer Science, Theoretical Computer Science
Query-to-Communication lifting using low-discrepancy gadgets
Moving Image
http://hdl.handle.net/2429/73160