Construction of Very Hard Functions for Multiparty Communication Complexity

Ján Maňuch

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 34, Issue: 1, page 61-75
  • ISSN: 0988-3754

Abstract

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We consider the multiparty communication model defined in [4] using the formalism from [8]. First, we correct an inaccuracy in the proof of the fundamental result of [6] providing a lower bound on the nondeterministic communication complexity of a function. Then we construct several very hard functions, i.e., functions such that those as well as their complements have the worst possible nondeterministic communication complexity. The problem to find a particular very hard function was proposed in [7], where it has been shown that almost all functions are very hard. We also prove that combining two very hard functions by the Boolean operation xor gives a very hard function.

How to cite

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Maňuch, Ján. "Construction of Very Hard Functions for Multiparty Communication Complexity." RAIRO - Theoretical Informatics and Applications 34.1 (2010): 61-75. <http://eudml.org/doc/222016>.

@article{Maňuch2010,
abstract = { We consider the multiparty communication model defined in [4] using the formalism from [8]. First, we correct an inaccuracy in the proof of the fundamental result of [6] providing a lower bound on the nondeterministic communication complexity of a function. Then we construct several very hard functions, i.e., functions such that those as well as their complements have the worst possible nondeterministic communication complexity. The problem to find a particular very hard function was proposed in [7], where it has been shown that almost all functions are very hard. We also prove that combining two very hard functions by the Boolean operation xor gives a very hard function. },
author = {Maňuch, Ján},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {multiparty communication model},
language = {eng},
month = {3},
number = {1},
pages = {61-75},
publisher = {EDP Sciences},
title = {Construction of Very Hard Functions for Multiparty Communication Complexity},
url = {http://eudml.org/doc/222016},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Maňuch, Ján
TI - Construction of Very Hard Functions for Multiparty Communication Complexity
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 1
SP - 61
EP - 75
AB - We consider the multiparty communication model defined in [4] using the formalism from [8]. First, we correct an inaccuracy in the proof of the fundamental result of [6] providing a lower bound on the nondeterministic communication complexity of a function. Then we construct several very hard functions, i.e., functions such that those as well as their complements have the worst possible nondeterministic communication complexity. The problem to find a particular very hard function was proposed in [7], where it has been shown that almost all functions are very hard. We also prove that combining two very hard functions by the Boolean operation xor gives a very hard function.
LA - eng
KW - multiparty communication model
UR - http://eudml.org/doc/222016
ER -

References

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  7. P. Duris, Multiparty communication complexity and very hard functions (to appear).  
  8. J. Hromkovic, Communication complexity and parallel computing, An EATCS Series. Springer (1997).  
  9. E. Kushilevitz and N. Nisan, Communication complexity. Cambridge Univ. Press. xiii (1997).  
  10. R.J. Lipton and R. Sedgewick, Lower bounds for VLSI, Proceedings, 13th ACM STOC (1981) 300-307.  
  11. O.B. Lupanov, Ob odnom metode sinteza skhem (Russian). Izv. Vyssh. Uchebn. Zaved., Radiofizika1 (1958) 120-140.  
  12. C. Shannon, The synthesis of two-terminal switching circuits. Bell Syst. Techn. J.28 (1949) 59-98.  
  13. A.C. Yao, The entropic limitations on VLSI computations, Proceedings, 13th ACM STOC (1981) 308-311.  

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