Information Complexity of the AND Function in the Two-Party and Multi-party Settings
- 56 Downloads
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.
KeywordsInformation 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.
- 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
- 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
- 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.Gronemeier, A.: Asymptotically optimal lower bounds on the nih-multi-party information. arXiv preprint arXiv:0902.1609 (2009)
- 13.Pankratov, D.: Communication complexity and information complexity. Ph.D. thesis, The University of Chicago (2015)Google Scholar
- 15.Yao, A.C.C.: Some complexity questions related to distributive computing(preliminary report). STOC’79, pp. 209–213. ACM (1979)Google Scholar