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Query-To-Communication Lifting for BPP Using Inner Product

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

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ACM Subject Classification
  • Theory of computation → Communication complexity
  • Theory of computation → Oracles and decision trees
Keywords
  • lifting theorems
  • inner product
  • BPP Lifting
  • Deterministic Lifting

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Abstract

We prove a new query-to-communication lifting for randomized protocols, with inner product as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting. Prior to this work, such a theorem was known only for deterministic protocols, due to Chattopadhyay et al. [Arkadev Chattopadhyay et al., 2017] and Wu et al. [Xiaodi Wu et al., 2017]. The only query-to-communication lifting result for randomized protocols, due to Göös, Pitassi and Watson [Mika Göös et al., 2017], used the much larger indexing gadget.
Our proof also provides a unified treatment of randomized and deterministic lifting. Most existing proofs of deterministic lifting theorems use a measure of information known as thickness. In contrast, Göös, Pitassi and Watson [Mika Göös et al., 2017] used blockwise min-entropy as a measure of information. Our proof uses the blockwise min-entropy framework to prove lifting theorems in both settings in a unified way.

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Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, and Toniann Pitassi. Query-To-Communication Lifting for BPP Using Inner Product. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICALP.2019.35

Author Details

Arkadev Chattopadhyay
  • School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India
Yuval Filmus
  • Department of Computer Science, Technion Israel Institute of Technology, Haifa, Israel
Sajin Koroth
  • Department of Computer Science, University of Haifa, Haifa, Israel
Or Meir
  • Department of Computer Science, University of Haifa, Haifa, Israel
Toniann Pitassi
  • Department of Computer Science, University of Toronto, Canada

Funding

  • Filmus, Yuval: Taub Fellow - supported by the Taub Foundations. The research was funded by ISF grant 1337/16.
  • Koroth, Sajin: Supported by the Israel Science Foundation (grant No. 1445/16)
  • Meir, Or: Partially supported by ISF grant by the Israel Science Foundation (grant No. 1445/16).

Acknowledgements

We thank Daniel Kane for some very enlightening conversations and suggestions. This work was done (in part) while the authors were visiting the Simons Institute for the Theory of Computing.

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