Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T09:30:23.020Z Has data issue: false hasContentIssue false
  • English
  • Français

One-way communication complexity of symmetric Boolean functions

Published online by Cambridge University Press:  15 October 2005

Jan Arpe ,
Andreas Jakoby  and
Maciej Liśkiewicz
Jan Arpe
Affiliation:
Institut für Theoretische Informatik, Universität zu Lübeck, Razeburger Allee 160, 23538 Lübeck, Germany; [email protected];[email protected]; [email protected] Supported by DFG research grant Re 672/3.
Andreas Jakoby
Affiliation:
Institut für Theoretische Informatik, Universität zu Lübeck, Razeburger Allee 160, 23538 Lübeck, Germany; [email protected];[email protected]; [email protected] Part of this work was done while visiting International University Bremen, Germany.
Maciej Liśkiewicz
Affiliation:
Institut für Theoretische Informatik, Universität zu Lübeck, Razeburger Allee 160, 23538 Lübeck, Germany; [email protected];[email protected]; [email protected] On leave from Instytut Informatyki, Uniwersytet Wrocławski, Wrocław, Poland.
Get access

Abstract

We study deterministic one-way communication complexity of functions with Hankel communication matrices. 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.

Keywords

Communication complexityBoolean functionsHankel matrices.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 4 , October 2005 , pp. 687 - 706
Copyright
© EDP Sciences, 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ablayev, F., Lower bounds for one-way probabilistic communication complexity and their application to space complexity. Theoret. Comp. Sci. 157 (1996) 139–159. CrossRef
Bläser, M., Jakoby, A., Liśkiewicz, M. and Manthey, B., Privacy in Non-Private Environments, in Proc. of the 10th Ann. Int. Conf. on the Theory and Application of Cryptology and Information Security ASIACRYPT, Springer-Verlag. Lect. Notes. Comput. Sci. 3329 (2004) 137–151. CrossRef
Condon, A., Hellerstein, L., Pottle, S. and Wigderson, A., On the power of finite automata with both nondeterministic and probabilistic states. SIAM J. Comput. 27 (1998) 739–762. CrossRef
Ďuriš, P., Hromkovič, J., Rolim, J.D.P. and Schnitger, G., On the power of Las Vegas for one-way communication complexity, finite automata, and polynomial-time computations, in Proc. of the 14th Int. Symp. on Theoretical Aspects of Computer Science (STACS), Springer-Verlag. Lect. Notes. Comput. Sci. 1200 (1997) 117–128. CrossRef
J.E. Hopcroft and J.D. Ullman, Formal Languages and Their Relation to Automata. Addison-Wesley, Reading, Massachusetts (1969).
J. Hromkovič, Communication Complexity and Parallel Computing. Springer-Verlag (1997).
I.S. Iohvidov, Hankel and Toeplitz Matrices and Forms. Birkhäuser, Boston (1982).
H. Klauck, On quantum and probabilistic communication: Las Vegas and one-way protocols, in Proc. of the 32nd Ann. ACM Symp. on Theory of Computing (STOC) (2000) 644–651.
I. Kremer, N. Nisan and D. Ron, On randomized one-round communication complexity, Computational Complexity 8 (1999) 21–49.
E. Kushilevitz and N. Nisan, Communication Complexity. Camb. Univ. Press (1997).
K. Mehlhorn and E.M. Schmidt, Las Vegas is better than determinism in VLSI and distributed computing, in Proc. of the 14th Ann. ACM Symp. on Theory of Computing (STOC) (1982) 330–337.
I. Newman and M. Szegedy, Public vs. private coin flips in one round communication games, in Proc. of the 28th Ann. ACM Symp. on Theory of Computing (STOC) (1996) 561–570.
Papadimitriou, C. and Sipser, M., Communication complexity. J. Comput. System Sci. 28 (1984) 260–269. CrossRef
Wegener, I., Optimal decision trees and one-time-only branching programs for symmetric Boolean functions. Inform. Control 62 (1984) 129–143. CrossRef
I. Wegener, The complexity of Boolean functions. Wiley-Teubner (1987).
I. Wegener, personal communication (April 2003).
A.C. Yao, Some complexity questions related to distributive computing, in Proc. of the 11th Ann. ACM Symp. on Theory of Computing (STOC) (1979) 209–213.