One-way communication complexity of symmetric Boolean functions

Jan Arpe; Andreas Jakoby; Maciej Liśkiewicz

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 39, Issue: 4, page 687-706
  • ISSN: 0988-3754

Abstract

top
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.

How to cite

top

Arpe, Jan, Jakoby, Andreas, and Liśkiewicz, Maciej. "One-way communication complexity of symmetric Boolean functions." RAIRO - Theoretical Informatics and Applications 39.4 (2010): 687-706. <http://eudml.org/doc/92785>.

@article{Arpe2010,
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. },
author = {Arpe, Jan, Jakoby, Andreas, Liśkiewicz, Maciej},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Communication complexity; Boolean functions; Hankel matrices.},
language = {eng},
month = {3},
number = {4},
pages = {687-706},
publisher = {EDP Sciences},
title = {One-way communication complexity of symmetric Boolean functions},
url = {http://eudml.org/doc/92785},
volume = {39},
year = {2010},
}

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
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 4
SP - 687
EP - 706
AB - 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.
LA - eng
KW - Communication complexity; Boolean functions; Hankel matrices.
UR - http://eudml.org/doc/92785
ER -

References

top
  1. F. Ablayev, Lower bounds for one-way probabilistic communication complexity and their application to space complexity. Theoret. Comp. Sci. 157 (1996) 139–159.  Zbl0871.68009
  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.  Zbl1094.94507
  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.  Zbl0911.68049
  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.  
  5. J.E. Hopcroft and J.D. Ullman, Formal Languages and Their Relation to Automata. Addison-Wesley, Reading, Massachusetts (1969).  Zbl0196.01701
  6. J. Hromkovič, Communication Complexity and Parallel Computing. Springer-Verlag (1997).  Zbl0873.68098
  7. I.S. Iohvidov, Hankel and Toeplitz Matrices and Forms. Birkhäuser, Boston (1982).  Zbl0493.15018
  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.  Zbl1296.68058
  9. I. Kremer, N. Nisan and D. Ron, On randomized one-round communication complexity, Computational Complexity8 (1999) 21–49.  Zbl0942.68059
  10. E. Kushilevitz and N. Nisan, Communication Complexity. Camb. Univ. Press (1997).  
  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.  Zbl0936.68050
  13. C. Papadimitriou and M. Sipser, Communication complexity. J. Comput. System Sci.28 (1984) 260–269.  Zbl0584.68064
  14. I. Wegener, Optimal decision trees and one-time-only branching programs for symmetric Boolean functions. Inform. Control62 (1984) 129–143.  Zbl0592.94025
  15. I. Wegener, The complexity of Boolean functions. Wiley-Teubner (1987).  Zbl0623.94018
  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.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.