One-way communication complexity of symmetric boolean functions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 4, pp. 687-706.

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.

DOI : https://doi.org/10.1051/ita:2005037
Classification : 68Q99,  06E30,  94A05,  68R15
Mots clés : communication complexity, boolean functions, Hankel matrices
@article{ITA_2005__39_4_687_0,
     author = {Arpe, Jan and Jakoby, Andreas and Li\'skiewicz, Maciej},
     title = {One-way communication complexity of symmetric boolean functions},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {687--706},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {4},
     year = {2005},
     doi = {10.1051/ita:2005037},
     mrnumber = {2172147},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2005037/}
}
TY  - JOUR
AU  - Arpe, Jan
AU  - Jakoby, Andreas
AU  - Liśkiewicz, Maciej
TI  - One-way communication complexity of symmetric boolean functions
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2005
DA  - 2005///
SP  - 687
EP  - 706
VL  - 39
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita:2005037/
UR  - https://www.ams.org/mathscinet-getitem?mr=2172147
UR  - https://doi.org/10.1051/ita:2005037
DO  - 10.1051/ita:2005037
LA  - en
ID  - ITA_2005__39_4_687_0
ER  - 
Arpe, Jan; Jakoby, Andreas; Liśkiewicz, Maciej. One-way communication complexity of symmetric boolean functions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 4, pp. 687-706. doi : 10.1051/ita:2005037. http://www.numdam.org/articles/10.1051/ita:2005037/

[1] F. Ablayev, Lower bounds for one-way probabilistic communication complexity and their application to space complexity. Theoret. Comp. Sci. 157 (1996) 139-159. | Zbl 0871.68009

[2] M. Bläser, A. Jakoby, M. Liśkiewicz and B. Manthey, 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. | Zbl 1094.94507

[3] A. Condon, L. Hellerstein, S. Pottle and A. Wigderson, On the power of finite automata with both nondeterministic and probabilistic states. SIAM J. Comput. 27 (1998) 739-762. | Zbl 0911.68049

[4] P. Ďuriš, J. Hromkovič, J.D.P. Rolim and G. Schnitger, 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. | Zbl 0939.68071

[5] J.E. Hopcroft and J.D. Ullman, Formal Languages and Their Relation to Automata. Addison-Wesley, Reading, Massachusetts (1969). | MR 237243 | Zbl 0196.01701

[6] J. Hromkovič, Communication Complexity and Parallel Computing. Springer-Verlag (1997). | MR 1442518 | Zbl 0873.68098

[7] I.S. Iohvidov, Hankel and Toeplitz Matrices and Forms. Birkhäuser, Boston (1982). | MR 677503 | Zbl 0493.15018

[8] 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.

[9] I. Kremer, N. Nisan and D. Ron, On randomized one-round communication complexity, Computational Complexity 8 (1999) 21-49. | Zbl 0942.68059

[10] E. Kushilevitz and N. Nisan, Communication Complexity. Camb. Univ. Press (1997). | MR 1426129 | Zbl 0869.68048

[11] 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.

[12] 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. | Zbl 0936.68050

[13] C. Papadimitriou and M. Sipser, Communication complexity. J. Comput. System Sci. 28 (1984) 260-269. | Zbl 0584.68064

[14] I. Wegener, Optimal decision trees and one-time-only branching programs for symmetric Boolean functions. Inform. Control 62 (1984) 129-143. | Zbl 0592.94025

[15] I. Wegener, The complexity of Boolean functions. Wiley-Teubner (1987). | MR 905473 | Zbl 0623.94018

[16] I. Wegener, personal communication (April 2003).

[17] 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.

Cité par Sources :