Research output per year
Research output per year
Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, Toniann Pitassi
Research output: Contribution to journal › Article › peer-review
Lifting theorems are theorems that relate the query complexity of a function f : {0, 1}n → {0, 1} to the communication complexity of the composed function f ○ gn for some "gadget"g : {0, 1}b × {0, 1}b → {0,1}. Such theorems allow transferring lower bounds from query complexity to the communication complexity, and have seen numerous applications in 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 significantly increase the range of gadgets for which such lifting theorems hold. 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 of the theorem. Second, our result can be seen as a strong generalization of a direct-sum theorem for functions with low discrepancy.
Original language | English |
---|---|
Pages (from-to) | 171-210 |
Number of pages | 40 |
Journal | SIAM Journal on Computing |
Volume | 50 |
Issue number | 1 |
DOIs | |
State | Published - 2021 |
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review