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Bounded Simultaneous Messages

Authors Andrej Bogdanov, Krishnamoorthy Dinesh, Yuval Filmus, Yuval Ishai, Avi Kaplan, Sruthi Sekar

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ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
  • Theory of computation → Probabilistic computation
Keywords
  • Simultaneous Messages
  • Instance Hiding
  • Algebraic degree
  • Preprocessing
  • Lower Bounds

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Abstract

We consider the following question of bounded simultaneous messages (BSM) protocols: Can computationally unbounded Alice and Bob evaluate a function f(x,y) of their inputs by sending polynomial-size messages to a computationally bounded Carol? The special case where f is the mod-2 inner-product function and Carol is bounded to AC⁰ has been studied in previous works. The general question can be broadly motivated by applications in which distributed computation is more costly than local computation. 
In this work, we initiate a more systematic study of the BSM model, with different functions f and computational bounds on Carol. In particular, we give evidence against the existence of BSM protocols with polynomial-size Carol for naturally distributed variants of NP-complete languages.

Cite As Get BibTex

Andrej Bogdanov, Krishnamoorthy Dinesh, Yuval Filmus, Yuval Ishai, Avi Kaplan, and Sruthi Sekar. Bounded Simultaneous Messages. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.FSTTCS.2023.23

Author Details

Andrej Bogdanov
  • School of EECS, University of Ottawa, Canada
Krishnamoorthy Dinesh
  • Dept. of Computer Science and Engineering, Indian Institute of Technology, Palakkad, India
Yuval Filmus
  • The Henry and Marylin Taub Faculty of Computer Science, Technion, Haifa, Israel
Yuval Ishai
  • The Henry and Marylin Taub Faculty of Computer Science, Technion, Haifa, Israel
Avi Kaplan
  • The Henry and Marylin Taub Faculty of Computer Science, Technion, Haifa, Israel
Sruthi Sekar
  • University of California, Berkeley, CA, USA

Funding

  • Bogdanov, Andrej: Supported by an NSERC Discovery Grant.
  • Filmus, Yuval: Supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC.
  • Ishai, Yuval: Supported by ERC Project NTSC (742754), ISF grant 2774/20, and BSF grant 2018393.
  • Kaplan, Avi: Supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 802020-ERC-HARMONIC, and ERC Project NTSC (742754).
  • Sekar, Sruthi: Supported by DARPA under Agreement No. HR00112020026, AFOSR Award FA9550-19-1-0200, NSF CNS Award 1936826, and research grants by the Sloan Foundation, and Visa Inc.

Acknowledgements

The authors would like to thanks the anonymous reviewers for their comments.

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