Query-to-Communication Lifting Using Low-Discrepancy Gadgets

Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, Toniann Pitassi

Research output: Contribution to journalArticlepeer-review

Abstract

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 languageEnglish
Pages (from-to)171-210
Number of pages40
JournalSIAM Journal on Computing
Volume50
Issue number1
DOIs
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics.

Keywords

  • Communication complexity
  • Lifting
  • Query complexity

ASJC Scopus subject areas

  • General Mathematics
  • General Computer Science

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