, Volume 81, Issue 11–12, pp 4200–4237 | Cite as

Information Complexity of the AND Function in the Two-Party and Multi-party Settings

  • Yuval Filmus
  • Hamed Hatami
  • Yaqiao LiEmail author
  • Suzin You
Part of the following topical collections:
  1. Special Issue: Computing and Combinatorics


In a recent breakthrough paper Braverman et al. (in: STOC’13, pp 151–160, 2013) developed a local characterization for the zero-error information complexity in the two-party model, and used it to compute the exact internal and external information complexity of the 2-bit AND function. In this article, we extend their results on AND function to the multi-party number-in-hand model by proving that the generalization of their protocol has optimal internal and external information cost for certain natural distributions. Our proof has new components, and in particular, it fixes a minor gap in the proof of Braverman et al.


Information complexity AND function Multi-party number-in-hand model Concavity condition 



Yuval Filmus is supported by Israel Science Foundation (Grant No. 2022103), Hamed Hatami is supported by an NSERC grant.


  1. 1.
    Bar-Yossef, Z., Jayram, T.S., Kumar, R., Sivakumar, D.: An information statistics approach to data stream and communication complexity. J. Comput. Syst. Sci. 68(4), 702–732 (2004)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Braverman, M., Garg, A., Pankratov, D., Weinstein, O.: From information to exact communication (extended abstract). In: STOC’13, pp. 151–160. ACM (2013)Google Scholar
  3. 3.
    Braverman, M., Garg, A., Pankratov, D., Weinstein, O.: Information lower bounds via self-reducibility. Theory Comput. Syst. 59(2), 377–396 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Braverman, M., Rao, A.: Information equals amortized communication. IEEE Trans. Inf. Theory 60(10), 6058–6069 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chakrabarti, A., Khot, S., Sun, X.: Near-optimal lower bounds on the multi-party communication complexity of set disjointness. In: Proceedings of 18th IEEE Annual Conference on Computational Complexity, 2003., pp. 107–117. IEEE (2003)Google Scholar
  6. 6.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, Hoboken (2012)zbMATHGoogle Scholar
  7. 7.
    Dagan, Y., Filmus, Y., Hatami, H., Li, Y.: Trading information complexity for error. Theor. Comput. 14(6), 1–73 (2018)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Gronemeier, A.: Nof-multiparty information complexity bounds for pointer jumping. In: International Symposium on Mathematical Foundations of Computer Science, pp. 459–470. Springer (2006)Google Scholar
  9. 9.
    Gronemeier, A.: Asymptotically optimal lower bounds on the nih-multi-party information. arXiv preprint arXiv:0902.1609 (2009)
  10. 10.
    Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)zbMATHGoogle Scholar
  11. 11.
    Ma, N., Ishwar, P.: Some results on distributed source coding for interactive function computation. IEEE Trans. Inf. Theory 57(9), 6180–6195 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Ma, N., Ishwar, P.: The infinite-message limit of two-terminal interactive source coding. IEEE Trans. Inf. Theory 59(7), 4071–4094 (2013)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Pankratov, D.: Communication complexity and information complexity. Ph.D. thesis, The University of Chicago (2015)Google Scholar
  14. 14.
    Razborov, A.A.: On the distributional complexity of disjointness. Theor. Comput. Sci. 106(2), 385–390 (1992)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Yao, A.C.C.: Some complexity questions related to distributive computing(preliminary report). STOC’79, pp. 209–213. ACM (1979)Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Technion — Israel Institute of TechnologyHaifaIsrael
  2. 2.McGill UniversityMontréalCanada

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