function is at most the product of the nondeterministic and conondeterministic communication complexities of the function. There are two proofs of this theorem presented in Kushilevitz-Nisan… At the end of the first section I examine tree-balancing. The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. [8] E. Kushilevitz and E. Weinreb, The communication complexity of set-disjointness with small sets and 0-1 intersection, in FOCS, 2009, pp. Neither knows the other’s input, and they wish to collaboratively compute f(x,y) where functionf: {0,1}n×{0,1}n →{0,1} is known to both. We rst give an example exhibiting the largest gap known. communication burden is the number of transmitted bits. 2 Since exact e¢ciency in the discretized problem still requires the communication of (discrete) Lindahl prices, we are This note is a contribution to the field of communication complexity. Communication Complexity. The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. Cambridge University Press, 1997. [7] E. Kushilevitz and N. Nisan, Communication Complexity, Cambridge University Press, 1997. [9] , On the complexity of communication complexity, in STOC, 2009, pp. 465{474. Compression and Direct Sums in Communication Complexity Anup rao University of Washington [Barak, Braverman, Chen, R.] [Braverman, R.] Thursday, September 2, 2010 There are two players with unlimited computational power, each of whom holds ann bit input, say x and y. Theorem 9. In the second section I summarize the well-known lower bound methods and prove the exact complexity of certain functions. Eyal Kushilevitz and Noam Nisan. A course offered at Rutgers University (Spring 2010). For every function f : X Y !f0;1g, D(f) = O(N0(f)N1(f)): Proof. [ bib | .html ] Troy Lee and Adi Shraibman. We refer the reader to Kushilevitz & Nisan (1997) for an excellent introduction. 63{72. © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-02983-4 - Communication Complexity Eyal Kushilevitz and Noam Nisan We then prove two related theorems. [12, 13, 6, 15]) on communication complexity.2 The theme of communication complexity lower bounds also provides a convenient excuse to take a guided tour of numerous models, problems, and algorithms that are central to modern research in the theory of algorithms 16:198:671 Communication Complexity, 2010. (e.g. Such discrete problems have been examined in the computer science …eld of communication complexity, pioneered by Yao (1979) and surveyed in Kushilevitz and Nisan (1997). [ bib | DOI ] Troy Lee. We are concerned with ideas circling around the PHcc-vs.-PSPACEcc problem, a long-standing open problem in structural communi-cation complexity, first posed in Babai et al. Lower bounds in communication complexity. On Rank vs. Communication Complexity Noam Nisan y Avi Wigderson z Abstract This paper concerns the open problem of Lov asz and Saks re-garding the relationship between the communication complexity of a boolean function and the rank of the associated matrix. (1986). Communication Complexity Communication complexity concerns the following scenario.