LIMITED DISTRIBUTION NOTICE This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and spe...

A notion of ”communication complexity” is used to formally measure the degree to which a Boolean function is ”global”. An explicit combinatorial lower bound for this complexity measure is presented. In particular, this leads to an exp(Ω( √ n)) lower bound on the complexity of depth-restricted contact schemes computing some natural Boolean functions in NP.

This paper concerns the open problem of Lovász and Saks regarding the relationship between the communication complexity of a boolean function and the rank of the associated matrix. We first give an example exhibiting the largest gap known. We then prove two related theorems.

The model [Yao79] consists of two parties, Alice and Bob, each holding inputs x ∈ X and y ∈ Y respectively. They wish to compute a function f : X × Y → Z. Each of them have unbounded computational power, unlike as in other models of computation. However their goal is to compute the value of f(x, y) with the least amount of interaction with each other. The measure of communication between the pa...

We study classic cake-cutting problems, but in discrete models rather than using infiniteprecision real values, specifically, focusing on their communication complexity. Using general discrete simulations of classical infinite-precision protocols (Robertson-Webb and movingknife), we roughly partition the various fair-allocation problems into 3 classes: “easy” (constant number of rounds of logar...

In this paper, we study a weak version of quantum nondeterministic communication complexity, corresponding to the most natural generalization of classical nondeterminism, in which a classical proof has to be checked with probability one by a quantum protocol. Another stronger definition of quantum nondeterminism has already been extensively studied, corresponding to the view of quantum nondeter...

Deterministic, probabilistic, nondeterministic, and alternating complexity classes defined by polylogarithmic communication are considered. Main results are (1) extending work of Ja’Ja’, Prasanna Kumar, and Simon, we give a simple technique allowing translation of most known separation and containment results for complexity classes of the fixed partition model to the more difficult optimal part...

In this paper, we have studied the information complexity for the communication model involving more than two parties. A lot of work has already been done on the information complexity in two party communication model and the question of extending the definition of information complexity to the multiparty communication model was posed in [Bra12]. In this paper, we first give a definition of int...

Suppose that we are given as input an object O and we’d like to know if it has some property P . But querying the object is expensive, so we would like to do a small number of local queries on the object. Usually, deciding with certainty whether an object has a property or not will require a lot of queries. The idea of property testing is to answer an easier question, thus allowing less queries...