Abstract
We study the communication complexity of symmetric XOR functions, namely functions f: {0,1}n ×{0,1}n →{0,1} that can be formulated as f(x,y) = D(|x ⊕ y|) for some predicate D: {0,1,...,n} →{0,1}, where |x ⊕ y| is the Hamming weight of the bitwise XOR of x and y. We give a public-coin randomized protocol in the Simultaneous Message Passing (SMP) model, with the communication cost matching the known lower bound for the quantum and two-way model up to a logarithm factor. As a corollary, this closes a quadratic gap between the previous quantum lower bound and the randomized upper bound in the one-way model. This answers an open question raised in Shi and Zhang [SZ09], and disqualifies the problem from being a candidate to separate randomized and quantum one-way communication complexities.
This work was supported by Hong Kong General Research Fund No. 419309 and No. 418710.
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References
Gavinsky, D., Kempe, J., de Wolf, R.: Quantum communication cannot simulate a public coin, arXiv:quant-ph/0411051 (2004)
Huang, W., Shi, Y., Zhang, S., Zhu, Y.: The communication complexity of the hamming distance problem. Information Processing Letters 99(4), 149–153 (2006)
Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)
Lee, T., Shraibman, A.: Lower bounds on communication complexity. Foundations and Trends in Theoretical Computer Science 3(4), 263–398 (2009)
Lee, T., Zhang, S.: Composition theorems in communication complexity. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 475–489. Springer, Heidelberg (2010)
Newman, I.: Private vs. common random bits in communication complexity. Information Processing Letters 39(2), 67–71 (1991)
Shi, Y., Zhang, Z.: Communication complexities of XOR functions. Quantum Information and Computation 9(3&4), 255–263 (2009)
Yao, A.: Some complexity questions related to distributive computing. In: Proceedings of the Eleventh Annual ACM Symposium on Theory of Computing (STOC), pp. 209–213 (1979)
Yao, A.: On the power of quantum fingerprinting. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, pp. 77–81 (2003)
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Leung, M.L., Li, Y., Zhang, S. (2011). Tight Bounds on Communication Complexity of Symmetric XOR Functions in One-Way and SMP Models. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_39
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DOI: https://doi.org/10.1007/978-3-642-20877-5_39
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