Document Open Access Logo

Trade-Offs in Distributed Interactive Proofs

Authors Pierluigi Crescenzi, Pierre Fraigniaud, Ami Paz

PDF
Thumbnail PDF

File

LIPIcs.DISC.2019.13.pdf
  • Filesize: 0.61 MB
  • 17 pages

Document Identifiers

Author Details

Pierluigi Crescenzi
  • IRIF - CNRS and Université de Paris, France
Pierre Fraigniaud
  • IRIF - CNRS and Université de Paris, France
Ami Paz
  • IRIF - CNRS and Université de Paris, France
  • Faculty of Computer Science, University of Vienna, Austria

Funding

  • Fraigniaud, Pierre: Additional support from the INRIA project GANG, and from the ANR project DESCARTES.
  • Paz, Ami: Supported by the Fondation des Sciences Mathématiques de Paris.

Acknowledgements

The authors are thankful to Gianlorenzo D'Angelo for fruitful discussions on the topic of this paper, and to Amir Yehudayoff for discussion on his work [Anup Rao and Amir Yehudayoff, 2015].

Cite AsGet BibTex

Pierluigi Crescenzi, Pierre Fraigniaud, and Ami Paz. Trade-Offs in Distributed Interactive Proofs. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 13:1-13:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.DISC.2019.13

Abstract

The study of interactive proofs in the context of distributed network computing is a novel topic, recently introduced by Kol, Oshman, and Saxena [PODC 2018]. In the spirit of sequential interactive proofs theory, we study the power of distributed interactive proofs. This is achieved via a series of results establishing trade-offs between various parameters impacting the power of interactive proofs, including the number of interactions, the certificate size, the communication complexity, and the form of randomness used. Our results also connect distributed interactive proofs with the established field of distributed verification. In general, our results contribute to providing structure to the landscape of distributed interactive proofs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Theory of computation → Interactive proof systems
  • Theory of computation → Distributed algorithms
Keywords
  • Distributed interactive proofs
  • Distributed verification

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Scott Aaronson and Avi Wigderson. Algebrization: A New Barrier in Complexity Theory. TOCT, 1(1):2:1-2:54, 2009. URL: https://doi.org/10.1145/1490270.1490272.
  2. Amir Abboud, Aviad Rubinstein, and R. Ryan Williams. Distributed PCP Theorems for Hardness of Approximation in P. In 58th IEEE Annual Symposium on Foundations of Computer Science, FOCS, pages 25-36, 2017. URL: https://doi.org/10.1109/FOCS.2017.12.
  3. Daniel Apon, Jonathan Katz, and Alex J. Malozemoff. One-round multi-party communication complexity of distinguishing sums. Theor. Comput. Sci., 501:101-108, 2013. URL: https://doi.org/10.1016/j.tcs.2013.07.026.
  4. Maria Axenovich, Jochen Harant, Jakub Przybylo, Roman Soták, Margit Voigt, and Jenny Weidelich. A note on adjacent vertex distinguishing colorings of graphs. Discrete Applied Mathematics, 205:1-7, 2016. URL: https://doi.org/10.1016/j.dam.2015.12.005.
  5. Alkida Balliu, Gianlorenzo D'Angelo, Pierre Fraigniaud, and Dennis Olivetti. What can be verified locally? J. Comput. Syst. Sci., 97:106-120, 2018. URL: https://doi.org/10.1016/j.jcss.2018.05.004.
  6. Keren Censor-Hillel, Ami Paz, and Mor Perry. Approximate Proof-Labeling Schemes. In Structural Information and Communication Complexity - 24th International Colloquium, SIROCCO, pages 71-89, 2017. URL: https://doi.org/10.1007/978-3-319-72050-0_5.
  7. Yi-Jun Chang, Seth Pettie, and Hengjie Zhang. Distributed Triangle Detection via Expander Decomposition. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pages 821-840, 2019. URL: https://doi.org/10.1137/1.9781611975482.51.
  8. Sebastian Czerwinski, Jaroslaw Grytczuk, and Wiktor Zelazny. Lucky labelings of graphs. Inf. Process. Lett., 109(18):1078-1081, 2009. URL: https://doi.org/10.1016/j.ipl.2009.05.011.
  9. Andrew Drucker, Fabian Kuhn, and Rotem Oshman. On the power of the congested clique model. In ACM Symposium on Principles of Distributed Computing, PODC, pages 367-376, 2014. URL: https://doi.org/10.1145/2611462.2611493.
  10. Laurent Feuilloley and Pierre Fraigniaud. Survey of Distributed Decision. Bulletin of the EATCS, 119, 2016. URL: http://eatcs.org/beatcs/index.php/beatcs/article/view/411.
  11. Laurent Feuilloley, Pierre Fraigniaud, and Juho Hirvonen. A Hierarchy of Local Decision. In 43rd International Colloquium on Automata, Languages, and Programming, ICALP, pages 118:1-118:15, 2016. URL: https://doi.org/10.4230/LIPIcs.ICALP.2016.118.
  12. Laurent Feuilloley, Pierre Fraigniaud, Juho Hirvonen, Ami Paz, and Mor Perry. Redundancy in Distributed Proofs. In 32nd International Symposium on Distributed Computing, DISC, pages 24:1-24:18, 2018. URL: https://doi.org/10.4230/LIPIcs.DISC.2018.24.
  13. Pierre Fraigniaud, Mika Göös, Amos Korman, Merav Parter, and David Peleg. Randomized distributed decision. Distributed Computing, 27(6):419-434, 2014. URL: https://doi.org/10.1007/s00446-014-0211-x.
  14. Pierre Fraigniaud, Amos Korman, and David Peleg. Towards a complexity theory for local distributed computing. J. ACM, 60(5):35:1-35:26, 2013. URL: https://doi.org/10.1145/2499228.
  15. Pierre Fraigniaud, Boaz Patt-Shamir, and Mor Perry. Randomized proof-labeling schemes. Distributed Computing, 32(3):217-234, 2019. Google Scholar
  16. John Gill. Computational Complexity of Probabilistic Turing Machines. SIAM J. Comput., 6(4):675-695, 1977. URL: https://doi.org/10.1137/0206049.
  17. Mika Göös, Toniann Pitassi, and Thomas Watson. Zero-Information Protocols and Unambiguity in Arthur-Merlin Communication. Algorithmica, 76(3):684-719, 2016. URL: https://doi.org/10.1007/s00453-015-0104-9.
  18. Mika Göös and Jukka Suomela. Locally Checkable Proofs in Distributed Computing. Theory of Computing, 12(1):1-33, 2016. URL: https://doi.org/10.4086/toc.2016.v012a019.
  19. Karthik C. S., Bundit Laekhanukit, and Pasin Manurangsi. On the parameterized complexity of approximating dominating set. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC, pages 1283-1296, 2018. URL: https://doi.org/10.1145/3188745.3188896.
  20. Gillat Kol, Rotem Oshman, and Raghuvansh R. Saxena. Interactive Distributed Proofs. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC, pages 255-264, 2018. URL: https://dl.acm.org/citation.cfm?id=3212771.
  21. Amos Korman and Shay Kutten. Distributed verification of minimum spanning trees. Distributed Computing, 20(4):253-266, 2007. URL: https://doi.org/10.1007/s00446-007-0025-1.
  22. Amos Korman, Shay Kutten, and David Peleg. Proof labeling schemes. Distributed Computing, 22(4):215-233, 2010. URL: https://doi.org/10.1007/s00446-010-0095-3.
  23. Eyal Kushilevitz and Noam Nisan. Communication complexity. Cambridge University Press, 1997. Google Scholar
  24. Moni Naor, Merav Parter, and Eylon Yogev. The Power of Distributed Verifiers in Interactive Proofs. CoRR, abs/1812.10917, 2018. URL: http://arxiv.org/abs/1812.10917.
  25. Moni Naor and Larry J. Stockmeyer. What Can be Computed Locally? SIAM J. Comput., 24(6):1259-1277, 1995. URL: https://doi.org/10.1137/S0097539793254571.
  26. Noam Nisan. The communication complexity of threshold gates. In Combinatorics, Paul Erdos is Eighty, volume 1, pages 301-315, 1993. Google Scholar
  27. Anup Rao and Amir Yehudayoff. Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness. In 30th Conference on Computational Complexity, CCC, pages 88-101, 2015. URL: https://doi.org/10.4230/LIPIcs.CCC.2015.88.
  28. Larry J. Stockmeyer. The Polynomial-Time Hierarchy. Theor. Comput. Sci., 3(1):1-22, 1976. URL: https://doi.org/10.1016/0304-3975(76)90061-X.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023 Schloss Dagstuhl - LZI GmbH Imprint Privacy Contact