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An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x AND y) has polynomially related classical and quantum bounded-error complexities. We solve a…

Computational Complexity · Computer Science 2010-02-03 Alexander A. Sherstov

The level-$k$ $\ell_1$-Fourier weight of a Boolean function refers to the sum of absolute values of its level-$k$ Fourier coefficients. Fourier growth refers to the growth of these weights as $k$ grows. It has been extensively studied for…

Computational Complexity · Computer Science 2023-07-27 Uma Girish , Makrand Sinha , Avishay Tal , Kewen Wu

The \emph{rational fair consensus problem} can be informally defined as follows. Consider a network of $n$ (selfish) \emph{rational agents}, each of them initially supporting a \emph{color} chosen from a finite set $ \Sigma$. The goal is to…

Computer Science and Game Theory · Computer Science 2017-05-29 Andrea Clementi , Luciano Gualà , Guido Proietti , Giacomo Scornavacca

In the paper where he first defined Communication Complexity, Yao asks: \emph{Is computing $CC(f)$ (the 2-way communication complexity of a given function $f$) NP-complete?} The problem of deciding whether $CC(f) \le k$, when given the…

Computational Complexity · Computer Science 2025-07-15 Shuichi Hirahara , Rahul Ilango , Bruno Loff

In this paper, we show a direct product theorm in the model of two-party bounded-round public-coin randomized communication complexity. For a relation f subset of X times Y times Z (X,Y,Z are finite sets), let R^{(t), pub}_e (f) denote the…

Computational Complexity · Computer Science 2012-01-10 Rahul Jain , Attila Pereszlenyi , Penghui Yao

We consider the classical secret sharing problem in the case where all agents are selfish but rational. In recent work, Kol and Naor show that, when there are two players, in the non-simultaneous communication model, i.e. when rushing is…

Data Structures and Algorithms · Computer Science 2012-05-04 Varsha Dani , Mahnush Movahedi , Jared Saia

In this paper we study quantum nondeterminism in multiparty communication. There are three (possibly) different types of nondeterminism in quantum computation: i) strong, ii) weak with classical proofs, and iii) weak with quantum proofs.…

Computational Complexity · Computer Science 2013-08-13 Marcos Villagra , Masaki Nakanishi , Shigeru Yamashita , Yasuhiko Nakashima

Suppose, we are given a set of $n$ elements to be clustered into $k$ (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, "do two elements $u$ and $v$ belong to the same cluster?".…

Machine Learning · Statistics 2017-06-26 Arya Mazumdar , Barna Saha

There is a close relationship between the communication complexity and information complexity of communication problems, as demonstrated by results such as Shannon's noiseless source coding theorem, and the Slepian-Wolf theorem. Here, we…

Information Theory · Computer Science 2026-03-02 Gurleen Padda , Dave Touchette

The randomized query complexity $R(f)$ of a boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is famously characterized (via Yao's minimax) by the least number of queries needed to distinguish a distribution $D_0$ over $0$-inputs from a…

Computational Complexity · Computer Science 2020-02-26 Andrew Bassilakis , Andrew Drucker , Mika Göös , Lunjia Hu , Weiyun Ma , Li-Yang Tan

For a two-player imperfect-information extensive-form game (IIEFG) with $K$ time steps and a player action space of size $U$, the game tree complexity is $U^{2K}$, causing existing IIEFG solvers to struggle with large or infinite $(U,K)$,…

Computer Science and Game Theory · Computer Science 2026-03-03 Mukesh Ghimire , Lei Zhang , Zhe Xu , Yi Ren

In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and…

Computational Complexity · Computer Science 2020-09-01 Rohit Agrawal

Suppose we have randomized decision trees for an outer function $f$ and an inner function $g$. The natural approach for obtaining a randomized decision tree for the composed function $(f\circ g^n)(x^1,\ldots,x^n)=f(g(x^1),\ldots,g(x^n))$…

Computational Complexity · Computer Science 2020-06-22 Shalev Ben-David , Mika Göös , Robin Kothari , Thomas Watson

User-generated data distributions are often imbalanced across devices and labels, hampering the performance of federated learning (FL). To remedy to this non-independent and identically distributed (non-IID) data problem, in this work we…

Machine Learning · Computer Science 2020-06-11 MyungJae Shin , Chihoon Hwang , Joongheon Kim , Jihong Park , Mehdi Bennis , Seong-Lyun Kim

Given a boolean n by n matrix A we consider arithmetic circuits for computing the transformation x->Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative…

Computational Complexity · Computer Science 2013-04-24 Magnus Find , Mika Göös , Matti Järvisalo , Petteri Kaski , Mikko Koivisto , Janne H. Korhonen

The question of how much communication is required between collaborating parties to compute a function of their data is of fundamental importance in the fields of theoretical computer science and information theory. In this work, the focus…

Information Theory · Computer Science 2016-02-09 Shijin Rajakrishnan , Sundara Rajan S , Vinod Prabhakaran

XOR oblivious transfer is a universal cryptographic primitive that can be related to linear polynomial evaluation. We firstly introduce some bipartite quantum protocols for XOR oblivious transfer, which are not secure if one party cheats,…

Quantum Physics · Physics 2023-10-05 Li Yu , Jie Xu , Fuqun Wang , Chui-Ping Yang

The Minimum Circuit Size Problem for Partial Functions ($MCSP^*$) is hard assuming the Exponential Time Hypothesis (ETH) (Ilango, 2020). This breakthrough hardness result leveraged a characterization of the optimal $\{\land, \lor, \neg\}$…

Computational Complexity · Computer Science 2025-11-24 Marco Carmosino , Ngu Dang , Tim Jackman

We show a near optimal direct-sum theorem for the two-party randomized communication complexity. Let $f\subseteq X \times Y\times Z$ be a relation, $\varepsilon> 0$ and $k$ be an integer. We show,…

Information Theory · Computer Science 2020-09-04 Rahul Jain

We study an information-structure design problem (a.k.a. persuasion) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal distributions. As in the standard…

Artificial Intelligence · Computer Science 2019-08-05 Andrea Celli , Stefano Coniglio , Nicola Gatti