We obtain a lower bound of n on the k-party randomized communication complexity of the Disjointness function in the ‘Number on the Forehead’ model of multiparty communication when k is a constant. For k = o(log logn), the bounds remain super-polylogarithmic i.e. (logn). The previous best lower bound for three players until recently was Ω(logn). Our bound separates the communication complexity c...

In the multiparty communication game (CFL-game) of Chandra, Furst, and Lipton (Proc. 15th ACM STOC, 1983, 94–99) k players collaboratively evaluate a function f(x0, . . . , xk−1) in which player i knows all inputs except xi. The players have unlimited computational power. The objective is to minimize communication. In this paper, we study the Simultaneous Messages (SM) model of multiparty commu...

193

Since the introduction of communication complexity four decades ago, complexity theorists have generally achieved better results and separations in communication complexity than in normal complexity classes. For instance, it is known that no pair of P, BPP, NP, and PP are equal, while not a single pair of all the corresponding normal classes P, BPP, NP, and PP have been proven different. Fewer ...

Many known methods for analysing the communication complexity of unstructured search are based on the hardness of the set disjointness problem. Such techniques may “hide” important aspects of the original problem. Intuitively, search is a much simpler task: while set disjointness is hard even for NP, successful search necessarily results in a short witness, which makes it easy for NP. According...

Preface The best algorithm designers prove both possibility and impossibility results — both upper and lower bounds. For example, every serious computer scientist knows a collection of canonical NP-complete problems and how to reduce them to other problems of interest. Communication complexity offers a clean theory that is extremely useful for proving lower bounds for lots of different fundamen...

One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet there are ways of conveying information with exponentially fewer qubits than possible classically [2, 21]. Moreover, these methods have a very simple structure—they involve little interaction between the communicating p...

In this paper we study the gap between the logarithm of the rank of a matrix and its communication complexity. The main contribution of the paper relies on the algebraic interpretation of some methods which yield non constant gaps by combining, mainly via tensor products, matrices with constant gap.

Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics, and did not take into account all the possibilities that physically-realizable computing devices offer in ...

The communication complexity of a two-variable function f (x , y) is the number of information bits two communicators need to exchange to compute f when, initially, each knows only one of the variables. There are several communication-complexity measures corresponding to whether 1) the worst case or average number of bits is considered, 2) computation errors are allowed or not, and 3) randomiza...