Abstract
The paper [Harry Buhrman, Michal Koucký, Nikolay Vereshchagin. Randomized Individual Communication Complexity. IEEE Conference on Computational Complexity 2008: 321-331] considered communication complexity of the following problem. Alice has a binary string x and Bob a binary string y, both of length n, and they want to compute or approximate Kolmogorov complexity C(x|y) of x conditional to y. It is easy to show that deterministic communication complexity of approximating C(x|y) with additive error α is at least n − 2α − O(1). The above referenced paper asks what is randomized communication complexity of this problem and shows that for r-round randomized protocols its communication complexity is at least Ω((n/α)1/r). In this paper, for some positive ε, we show the lower bound 0.99n for (worst case) communication length of any randomized protocol that with probability at least 0.01 approximates C(x|y) with additive error εn for all input pairs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alon, N., Spencer, J.: The probabilistic method, 2nd edn. John Wiley & Sons (2000)
Ambainis, A., Buhrman, H., Gasarch, W.I., Kalyanasundaram, B., Torenvliet, L.: The communication complexity of enumeration, elimination and selection. Journal of Computer and System Sciences 63, 148–185 (2001)
Buhrman, H., Klauck, H., Vereshchagin, N.K., Vitányi, P.M.B.: Individual communication complexity. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 19–30. Springer, Heidelberg (2004)
Buhrman, H., Koucký, M., Vereshchagin, N.: Randomized Individual Communication Complexity. In: IEEE Conference on Computational Complexity, pp. 321–331 (2008)
Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press (1997)
Li, M., Vitányi, P.: An Introduction to Kolmogorov Complexity and its Applications. Springer (1997)
Yao, A.C.-C.: Probabilistic computations: Toward a unified measure of complexity. In: 18th Annual IEEE Symposium on Foundation of Computer Science, pp. 222–227 (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Vereshchagin, N. (2014). Randomized Communication Complexity of Approximating Kolmogorov Complexity. In: Hirsch, E.A., Kuznetsov, S.O., Pin, JÉ., Vereshchagin, N.K. (eds) Computer Science - Theory and Applications. CSR 2014. Lecture Notes in Computer Science, vol 8476. Springer, Cham. https://doi.org/10.1007/978-3-319-06686-8_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-06686-8_28
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06685-1
Online ISBN: 978-3-319-06686-8
eBook Packages: Computer ScienceComputer Science (R0)