Abstract
We study deterministic one-way communication complexity of functions with Hankel communication matrices. In this paper some structural properties of such matrices are established and applied to the one-way two-party communication complexity of symmetric Boolean functions. It is shown that the number of required communication bits does not depend on the communication direction, provided that neither direction needs maximum complexity. Moreover, in order to obtain an optimal protocol, it is in any case sufficient to consider only the communication direction from the party with the shorter input to the other party. These facts do not hold for arbitrary Boolean functions in general. Next, gaps between one-way and two-way communication complexity for symmetric Boolean functions are discussed. Finally, we give some generalizations to the case of multiple parties.
This is a preview of subscription content, log in via an institution to check access.
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
Ablayev, F.: Lower bounds for one-way probabilistic communication complexity and their application to space complexity. Theoretical Comp. Sc. 157, 139–159 (1996)
Condon, A., Hellerstein, L., Pottle, S., Wigderson, A.: On the power of finite automata with both nondeterministic and probabilistic states. SIAM J. Comput. 27, 739–762 (1998)
Ďuriš, P., Hromkovič, J., Rolim, J.D.P., Schnitger, G.: On the power of Las Vegas for one-way communication complexity, finite automata, and polynomialtime computations. In: Proc. 14th STACS, pp. 117–128. Springer, Heidelberg (1997)
Hopcroft, J.E., Ullman, J.D.: Formal Languages and Their Relation to Automata. Addison-Wesley, Reading (1969)
Hromkovič, J.: Communication Complexity and Parallel Computing. Springer, Heidelberg (1997)
Iohvidov, I.S.: Hankel and Toeplitz Matrices and Forms. Birkhäuser, Boston (1982)
Klauck, H.: On quantum and probabilistic communication: Las Vegas and one-way protocols. In: Proc. 32nd STOC, pp. 644–651 (2000)
Kremer, I., Nisan, N., Ron, D.: On randomized one-round communication complexity. Computational Complexity 8, 21–49 (1999)
Kushilevitz, E., Nisan, N.: Communication Complexity. Camb. Univ. Press, New York (1997)
Mehlhorn, K., Schmidt, E.M.: Las Vegas is better than determinism in VLSI and distributed computing. In: Proc. 14th STOC, pp. 330–337 (1982)
Newman, I., Szegedy, M.: Public vs. private coin flips in one round communication games. In: Newman, I., Szegedy, M. (eds.) Proc. 28th STOC, pp. 561–570 (1996)
Papadimitriou, C., Sipser, M.: Communication complexity. J. Comput. System Sci. 28, 260–269 (1984)
Wegener, I.: The complexity of Boolean functions. Wiley-Teubner, Chichester (1987)
Wegener, I.: personal communication (April 2003)
Yao, A.C.: Some complexity questions related to distributive computing. In: Proc. 11th STOC, pp. 209–213 (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arpe, J., Jakoby, A., Liśkiewicz, M. (2003). One-Way Communication Complexity of Symmetric Boolean Functions. In: Lingas, A., Nilsson, B.J. (eds) Fundamentals of Computation Theory. FCT 2003. Lecture Notes in Computer Science, vol 2751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45077-1_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-45077-1_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40543-6
Online ISBN: 978-3-540-45077-1
eBook Packages: Springer Book Archive