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REPORTS > KEYWORD > COMMUNICATION COMPLEXITY:
Reports tagged with communication complexity:
TR16-168 | 2nd November 2016
Eric Blais, Clement Canonne, Tom Gur

#### Alice and Bob Show Distribution Testing Lower Bounds (They don't talk to each other anymore.)

Revisions: 1

We present a new methodology for proving distribution testing lower bounds, establishing a connection between distribution testing and the simultaneous message passing (SMP) communication model. Extending the framework of Blais, Brody, and Matulef [BBM12], we show a simple way to reduce (private-coin) SMP problems to distribution testing problems. This method ... more >>>

TR16-174 | 7th November 2016
Elchanan Mossel, Sampath Sampath Kannan, Grigory Yaroslavtsev

#### Linear Sketching over $\mathbb F_2$

We initiate a systematic study of linear sketching over $\mathbb F_2$. For a given Boolean function $f \colon \{0,1\}^n \to \{0,1\}$ a randomized $\mathbb F_2$-sketch is a distribution $\mathcal M$ over $d \times n$ matrices with elements over $\mathbb F_2$ such that $\mathcal Mx$ suffices for computing $f(x)$ with high ... more >>>

TR17-061 | 3rd April 2017
Anat Ganor, Karthik C. S.

#### Communication Complexity of Correlated Equilibrium in Two-Player Games

We show a communication complexity lower bound for finding a correlated equilibrium of a two-player game. More precisely, we define a two-player $N \times N$ game called the 2-cycle game and show that the randomized communication complexity of finding a 1/poly($N$)-approximate correlated equilibrium of the 2-cycle game is $\Omega(N)$. For ... more >>>

TR17-071 | 14th April 2017
Young Kun Ko, Arial Schvartzman

#### Bounds for the Communication Complexity of Two-Player Approximate Correlated Equilibria

Revisions: 1

In the recent paper of~\cite{BR16}, the authors show that, for any constant $10^{-15} > \varepsilon > 0$ the communication complexity of $\varepsilon$-approximate Nash equilibria in $2$-player $n \times n$ games is $n^{\Omega(\varepsilon)}$, resolving the long open problem of whether or not there exists a polylogarithmic communication protocol. In this paper ... more >>>

TR17-151 | 8th October 2017
Paul Beame, Noah Fleming, Russell Impagliazzo, Antonina Kolokolova, Denis Pankratov, Toniann Pitassi, Robert Robere

#### Stabbing Planes

Revisions: 1

We introduce and develop a new semi-algebraic proof system, called Stabbing Planes that is in the style of DPLL-based modern SAT solvers. As with DPLL, there is only one rule: the current polytope can be subdivided by
branching on an inequality and its "integer negation.'' That is, we can (nondeterministically ... more >>>

TR17-170 | 6th November 2017

#### Simulation Beats Richness: New Data-Structure Lower Bounds

We develop a technique for proving lower bounds in the setting of asymmetric communication, a model that was introduced in the famous works of Miltersen (STOC'94) and Miltersen, Nisan, Safra and Wigderson (STOC'95). At the core of our technique is a novel simulation theorem: Alice gets a $p \times n$ ... more >>>

TR17-177 | 16th November 2017
Daniel Kane, Roi Livni, Shay Moran, Amir Yehudayoff

#### On Communication Complexity of Classification Problems

Revisions: 1

This work introduces a model of distributed learning in the spirit of Yao's communication complexity model. We consider a two-party setting, where each of the players gets a list of labelled examples and they communicate in order to jointly perform some learning task. To naturally fit into the framework of ... more >>>

TR18-031 | 15th February 2018
Iftach Haitner, Noam Mazor, Rotem Oshman, Omer Reingold, Amir Yehudayoff

#### On the Communication Complexity of Key-Agreement Protocols

Revisions: 2

Key-agreement protocols whose security is proven in the random oracle model are an important alternative to the more common public-key based key-agreement protocols. In the random oracle model, the parties and the eavesdropper have access to a shared random function (an "oracle"), but they are limited in the number of ... more >>>

TR18-043 | 22nd February 2018
Andrei Romashchenko, Marius Zimand

#### An operational characterization of mutual information in algorithmic information theory

Revisions: 2

We show that the mutual information, in the sense of Kolmogorov complexity, of any pair of strings
$x$ and $y$ is equal, up to logarithmic precision, to the length of the longest shared secret key that
two parties, one having $x$ and the complexity profile of the pair and the ... more >>>

TR18-079 | 19th April 2018
Jayadev Acharya, Clement Canonne, Himanshu Tyagi

#### Distributed Simulation and Distributed Inference

Revisions: 1

Independent samples from an unknown probability distribution $\mathbf{p}$ on a domain of size $k$ are distributed across $n$ players, with each player holding one sample. Each player can communicate $\ell$ bits to a central referee in a simultaneous message passing (SMP) model of communication to help the referee infer a ... more >>>

TR19-001 | 5th January 2019
Dmitry Itsykson, Alexander Knop, Andrei Romashchenko, Dmitry Sokolov

#### On OBDD-based algorithms and proof systems that dynamically change order of variables

In 2004 Atserias, Kolaitis and Vardi proposed OBDD-based propositional proof systems that prove unsatisfiability of a CNF formula by deduction of identically false OBDD from OBDDs representing clauses of the initial formula. All OBDDs in such proofs have the same order of variables. We initiate the study of OBDD based ... more >>>

TR19-027 | 1st March 2019
Mark Bun, Nikhil Mande, Justin Thaler

#### Sign-Rank Can Increase Under Intersection

The communication class $UPP^{cc}$ is a communication analog of the Turing Machine complexity class $PP$. It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension complexity), and is essentially the most powerful communication class against which we know how to prove lower bounds.

For a communication problem ... more >>>

TR19-101 | 24th July 2019
Amit Chakrabarti, Prantar Ghosh

#### Streaming Verification of Graph Computations via Graph Structure

We give new algorithms in the annotated data streaming setting---also known as verifiable data stream computation---for certain graph problems. This setting is meant to model outsourced computation, where a space-bounded verifier limited to sequential data access seeks to overcome its computational limitations by engaging a powerful prover, without needing to ... more >>>

TR19-103 | 7th August 2019

#### Query-to-Communication Lifting Using Low-Discrepancy Gadgets

Revisions: 2

Lifting theorems are theorems that relate the query complexity of a function $f:\left\{ 0,1 \right\}^n\to \left\{ 0,1 \right\}$ to the communication complexity of the composed function $f\circ g^n$, for some “gadget” $g:\left\{ 0,1 \right\}^b\times \left\{ 0,1 \right\}^b\to \left\{ 0,1 \right\}$. Such theorems allow transferring lower bounds from query complexity to ... more >>>

TR19-143 | 25th October 2019
Sivaramakrishnan Natarajan Ramamoorthy, Cyrus Rashtchian

#### Equivalence of Systematic Linear Data Structures and Matrix Rigidity

Recently, Dvir, Golovnev, and Weinstein have shown that sufficiently strong lower bounds for linear data structures would imply new bounds for rigid matrices. However, their result utilizes an algorithm that requires an $NP$ oracle, and hence, the rigid matrices are not explicit. In this work, we derive an equivalence between ... more >>>

TR20-021 | 21st February 2020
Rahul Ilango, Bruno Loff, Igor Carboni Oliveira

#### NP-Hardness of Circuit Minimization for Multi-Output Functions

Can we design efficient algorithms for finding fast algorithms? This question is captured by various circuit minimization problems, and algorithms for the corresponding tasks have significant practical applications. Following the work of Cook and Levin in the early 1970s, a central question is whether minimizing the circuit size of an ... more >>>

TR20-048 | 16th April 2020
Shachar Lovett, Raghu Meka, Jiapeng Zhang

#### Improved lifting theorems via robust sunflowers

Lifting theorems are a generic way to lift lower bounds in query complexity to lower bounds in communication complexity, with applications in diverse areas, such as combinatorial optimization, proof complexity, game theory. Lifting theorems rely on a gadget, where smaller gadgets give stronger lower bounds. However, existing proof techniques are ... more >>>

TR20-100 | 6th July 2020
Amit Chakrabarti, Prantar Ghosh, Justin Thaler

#### Streaming Verification for Graph Problems: Optimal Tradeoffs and Nonlinear Sketches

We study graph computations in an enhanced data streaming setting, where a space-bounded client reading the edge stream of a massive graph may delegate some of its work to a cloud service. We seek algorithms that allow the client to verify a purported proof sent by the cloud service that ... more >>>

TR20-111 | 24th July 2020
Ian Mertz, Toniann Pitassi

#### Lifting: As Easy As 1,2,3

Revisions: 1

Query-to-communication lifting theorems translate lower bounds on query complexity to lower bounds for the corresponding communication model. In this paper, we give a simplified proof of deterministic lifting (in both the tree-like and dag-like settings). Whereas previous proofs used sophisticated Fourier analytic techniques, our proof uses elementary counting together with ... more >>>

TR20-114 | 22nd July 2020
Anup Bhattacharya, Sourav Chakraborty, Arijit Ghosh, Gopinath Mishra, Manaswi Paraashar

#### Disjointness through the Lens of Vapnik–Chervonenkis Dimension: Sparsity and Beyond

The disjointness problem - where Alice and Bob are given two subsets of $\{1, \dots, n\}$ and they have to check if their sets intersect - is a central problem in the world of communication complexity. While both deterministic and randomized communication complexities for this problem are known to be ... more >>>

TR20-119 | 1st August 2020
Nikhil Mande, Swagato Sanyal

#### On parity decision trees for Fourier-sparse Boolean functions

We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Our contributions are as follows. Let $f : \mathbb{F}_2^n \to \{-1, 1\}$ be a Boolean function with Fourier support ... more >>>

TR21-006 | 18th January 2021
Susanna de Rezende, Jakob Nordström, Marc Vinyals

#### How Limited Interaction Hinders Real Communication (and What It Means for Proof and Circuit Complexity)

We obtain the first true size-space trade-offs for the cutting planes proof system, where the upper bounds hold for size and total space for derivations with constant-size coefficients, and the lower bounds apply to length and formula space (i.e., number of inequalities in memory) even for derivations with exponentially large ... more >>>

TR21-027 | 24th February 2021
Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh Saxena, Zhao Song, Huacheng Yu

#### Almost Optimal Super-Constant-Pass Streaming Lower Bounds for Reachability

We give an almost quadratic $n^{2-o(1)}$ lower bound on the space consumption of any $o(\sqrt{\log n})$-pass streaming algorithm solving the (directed) $s$-$t$ reachability problem. This means that any such algorithm must essentially store the entire graph. As corollaries, we obtain almost quadratic space lower bounds for additional fundamental problems, including ... more >>>

TR21-051 | 8th April 2021
Klim Efremenko, Gillat Kol, Raghuvansh Saxena

#### Binary Interactive Error Resilience Beyond $1/8$ (or why $(1/2)^3 > 1/8$)

Interactive error correcting codes are codes that encode a two party communication protocol to an error-resilient protocol that succeeds even if a constant fraction of the communicated symbols are adversarially corrupted, at the cost of increasing the communication by a constant factor. What is the largest fraction of corruptions that ... more >>>

TR21-065 | 5th May 2021
Nikhil Mande, Swagato Sanyal

#### One-way communication complexity and non-adaptive decision trees

Revisions: 1

We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the Inner Product on a constant number of inputs. Let $IP$ denote Inner Product on ... more >>>

TR21-068 | 8th May 2021
Marcel Dall'Agnol, Tom Gur, Subhayan Roy Moulik, Justin Thaler

#### Quantum Proofs of Proximity

We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof and are required to accept inputs having a property $\Pi$ and reject ... more >>>

TR21-100 | 11th July 2021
Christian Ikenmeyer, Balagopal Komarath, Nitin Saurabh

#### Karchmer-Wigderson Games for Hazard-free Computation

We present a Karchmer-Wigderson game to study the complexity of hazard-free formulas. This new game is both a generalization of the monotone Karchmer-Wigderson game and an analog of the classical Boolean Karchmer-Wigderson game. Therefore, it acts as a bridge between the existing monotone and general games.

Using this game, we ... more >>>

TR21-127 | 30th August 2021
Ron D. Rothblum, Michael Ezra

#### Small Circuits Imply Efficient Arthur-Merlin Protocols

Revisions: 1

The inner product function $\langle x,y \rangle = \sum_i x_i y_i \bmod 2$ can be easily computed by a (linear-size) ${AC}^0(\oplus)$ circuit: that is, a constant depth circuit with AND, OR and parity (XOR) gates. But what if we impose the restriction that the parity gates can only be on ... more >>>

TR21-181 | 30th December 2021
Oded Goldreich

#### The KW Games as a Teaser

This is a purely pedagogical text.
We advocate using KW-games as a teaser (or riddle'') for a complexity theoretic course.
In particular, stating the KW-game for a familiar NP-complete problem such as 3-Colorability and asking to prove that it requires more than polylogarithmic communication poses a seemingly tractable question ... more >>>

TR22-016 | 15th February 2022
Artur Ignatiev, Ivan Mihajlin, Alexander Smal

#### Super-cubic lower bound for generalized Karchmer-Wigderson games

In this paper, we prove a super-cubic lower bound on the size of a communication protocol for generalized Karchmer-Wigderson game for some explicit function $f: \{0,1\}^n\to \{0,1\}^{\log n}$. Lower bounds for original Karchmer-Wigderson games correspond to De Morgan formula lower bounds, thus the best known size lower bound is cubic. ... more >>>

TR22-019 | 17th February 2022
Guangxu Yang, Jiapeng Zhang

#### Simulation Methods in Communication Lower Bounds, Revisited

The notion of lifting theorems is a generic method to lift hardness of one-party functions to two-party lower bounds in communication model. It has many applications in different areas such as proof complexity, game theory, combinatorial optimization. Among many lifting results, a central idea is called Raz-McKenize simulation (FOCS 1997). ... more >>>

TR22-050 | 12th April 2022
Klim Efremenko, Bernhard Haeupler, Yael Kalai, Pritish Kamath, Gillat Kol, Nicolas Resch, Raghuvansh Saxena

#### Circuits Resilient to Short-Circuit Errors

Given a Boolean circuit $C$, we wish to convert it to a circuit $C'$ that computes the same function as $C$ even if some of its gates suffer from adversarial short circuit errors, i.e., their output is replaced by the value of one of their inputs [KLM97]. Can we ... more >>>

TR22-118 | 23rd August 2022
Huacheng Yu

#### Strong XOR Lemma for Communication with Bounded Rounds

In this paper, we prove a strong XOR lemma for bounded-round two-player randomized communication. For a function $f:\mathcal{X}\times \mathcal{Y}\rightarrow\{0,1\}$, the $n$-fold XOR function $f^{\oplus n}:\mathcal{X}^n\times \mathcal{Y}^n\rightarrow\{0,1\}$ maps $n$ input pairs $(X_1,\ldots,X_n,Y_1,\ldots,Y_n)$ to the XOR of the $n$ output bits $f(X_1,Y_1)\oplus \cdots \oplus f(X_n, Y_n)$. We prove that if every ... more >>>

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