Communication is a bottleneck in many distributed computations. In VLSI, communication constraints dictate lower bounds on the performance of chips. The two-processor information transfer model measures the communication requirements to compute functions. We study the unbounded error probabilistic version of this model. Because of its weak notion of correct output, we believe that this model me...

A hallmark of human communication is vocal turn taking. Until recently, turn taking was thought to be unique to humans but new data indicate that marmosets, a new world monkey, take turns when vocalizing too.

We initiate the theory of communication complexity of individual inputs held by the agents, rather than worst-case or average-case. We consider total, partial, and partially correct protocols, one-way versus two-way, with (not in this version) and without help bits.

In the setting of communication complexity, two distributed parties want to compute a function depending on both their inputs, using as little communication as possible. The required communication can sometimes be signiicantly lowered if we allow the parties the use of quantum communication. We survey the main results of the young area of quantum communication complexity: its relation to telepo...

Can quantum communication be more efficient than its classical counterpart? Holevo’s theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits—unless the two parties are entangled, in which case twice as many classical bits can be communicated but no more. In apparent contradiction, there are distributed computational task...

This paper surveys the field of quantum communication complexity. Some interesting recent results are collected concerning relations to classical communication, lower bound methods, one-way communication, and applications of quantum communication complexity.

one way a d two way complexities differ by a t most 1 certain functions like equality and the verification of Hamming distance have upper bounds that are considerably PO, and Pi have unlimited local computing better than their counterparts in deterministic, nondeterministic, or power, and the ability to realize an arbitrary bounded error probabilistic model there exists a function which require...

In this essay, we give a basic introduction to the exciting eld of communication complexity. Communication complexity was rst formalized by Yao in 1979 [3]. e context is easy enough to understand: two parties (usually named Alice and Bob) wish to compute the value of some function f of two variables. Alice knows the value of one of the variables, while Bob knows the value of the other. How mu...

We propose a model. LPRAM. for parallel random access machines uith local memon, that captures bcth the communication and computational requirements in parallel computation. For this model. n? present se\cral interesting resuk including the following: Two n x n matkez can be multiplied in Of n’/p) computation time and O( n“/p’ ‘) communication steps using p processors (for p = Ot n ‘/log’ ’ n) ...

This thesis discusses the connection between the nonlocal behavior of quantum mechanics and the communication complexity of distributed computations. The first three chapters provide an introduction to quantum information theory with an emphasis on the description of entangled systems. The next chapter looks at how to measure the complexity of distributed computations. This is expressed by the ...