[8] E. Kushilevitz and E. Weinreb, The communication complexity of set-disjointness with small sets and 0-1 intersection, in FOCS, 2009, pp. Communication Complexity Communication complexity concerns the following scenario. There are two players with unlimited computational power, each of whom holds ann bit input, say x and y. The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. We then prove two related theorems. [7] E. Kushilevitz and N. Nisan, Communication Complexity, Cambridge University Press, 1997. For every function f : X Y !f0;1g, D(f) = O(N0(f)N1(f)): Proof. Cambridge University Press, 1997. Compression and Direct Sums in Communication Complexity Anup rao University of Washington [Barak, Braverman, Chen, R.] [Braverman, R.] Thursday, September 2, 2010 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. 465{474. Eyal Kushilevitz and Noam Nisan. (1986). 63{72. This note is a contribution to the field of communication complexity. There are two proofs of this theorem presented in Kushilevitz-Nisan… Theorem 9. [ bib | .html ] Troy Lee and Adi Shraibman. At the end of the first section I examine tree-balancing. © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-02983-4 - Communication Complexity Eyal Kushilevitz and Noam Nisan (e.g. [9] , On the complexity of communication complexity, in STOC, 2009, pp. Communication Complexity. We rst give an example exhibiting the largest gap known. 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. 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. A course offered at Rutgers University (Spring 2010). 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). Lower bounds in communication complexity. 16:198:671 Communication Complexity, 2010. [ bib | DOI ] Troy Lee. [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 2 Since exact e¢ciency in the discretized problem still requires the communication of (discrete) Lindahl prices, we are The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. communication burden is the number of transmitted bits. function is at most the product of the nondeterministic and conondeterministic communication complexities of the function. In the second section I summarize the well-known lower bound methods and prove the exact complexity of certain functions. We refer the reader to Kushilevitz & Nisan (1997) for an excellent introduction.