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Electronic Colloquium on Computational Complexity

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All reports by Author Gillat Kol:

TR17-093 | 22nd May 2017
Klim Efremenko, Gillat Kol, Raghuvansh Saxena

Interactive Coding Over the Noisy Broadcast Channel

A set of $n$ players, each holding a private input bit, communicate over a noisy broadcast channel. Their mutual goal is for all players to learn all inputs. At each round one of the players broadcasts a bit to all the other players, and the bit received by each player ... more >>>

TR16-113 | 22nd July 2016
Gillat Kol, Ran Raz, Avishay Tal

Time-Space Hardness of Learning Sparse Parities

We define a concept class ${\cal F}$ to be time-space hard (or memory-samples hard) if any learning algorithm for ${\cal F}$ requires either a memory of size super-linear in $n$ or a number of samples super-polynomial in $n$, where $n$ is the length of one sample.

A recent work shows ... more >>>

TR15-168 | 18th October 2015
Gillat Kol

Interactive Compression for Product Distributions

We study the interactive compression problem: Given a two-party communication protocol with small information cost, can it be compressed so that the total number of bits communicated is also small? We consider the case where the parties have inputs that are independent of each other, and give a simulation protocol ... more >>>

TR14-113 | 27th August 2014
Anat Ganor, Gillat Kol, Ran Raz

Exponential Separation of Information and Communication for Boolean Functions

We show an exponential gap between communication complexity and information complexity for boolean functions, by giving an explicit example of a partial function with information complexity $\leq O(k)$, and distributional communication complexity $\geq 2^k$. This shows that a communication protocol for a partial boolean function cannot always be compressed to ... more >>>

TR14-046 | 8th April 2014
Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

Approximate Nonnegative Rank is Equivalent to the Smooth Rectangle Bound

We consider two known lower bounds on randomized communication complexity: The smooth rectangle bound and the logarithm of the approximate non-negative rank. Our main result is that they are the same up to a multiplicative constant and a small additive term.
The logarithm of the nonnegative rank is known to ... more >>>

TR13-079 | 2nd June 2013
Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

Direct Sum Fails for Zero Error Average Communication

We show that in the model of zero error communication complexity, direct sum fails for average communication complexity as well as for external information cost. Our example also refutes a version of a conjecture by Braverman et al. that in the zero error case amortized communication complexity equals external information ... more >>>

TR13-001 | 2nd January 2013
Gillat Kol, Ran Raz

Interactive Channel Capacity

Revisions: 1

We study the interactive channel capacity of an $\epsilon$-noisy channel. The interactive channel capacity $C(\epsilon)$ is defined as the minimal ratio between the communication complexity of a problem (over a non-noisy channel), and the communication complexity of the same problem over the binary symmetric channel with noise rate $\epsilon$, where ... more >>>

TR12-088 | 7th July 2012
Irit Dinur, Gillat Kol

Covering CSPs

We study the covering complexity of constraint satisfaction problems (CSPs). The covering number of a CSP instance C, denoted $\nu(C)$, is the smallest number of assignments to the variables, such that each constraint is satisfied by at least one of the assignments. This covering notion describes situations in which we ... more >>>

TR11-122 | 14th September 2011
Gillat Kol, Ran Raz

Competing Provers Protocols for Circuit Evaluation

Let $C$ be a (fan-in $2$) Boolean circuit of size $s$ and depth $d$, and let $x$ be an input for $C$. Assume that a verifier that knows $C$ but doesn't know $x$ can access the low degree extension of $x$ at one random point. Two competing provers try to ... more >>>

TR09-138 | 14th December 2009
Gillat Kol, Ran Raz

Bounds on 2-Query Locally Testable Codes with Affine Tests

We study Locally Testable Codes (LTCs) that can be tested by making two queries to the tested word using an affine test. That is, we consider LTCs over a finite field F, with codeword testers that only use tests of the form $av_i + bv_j = c$, where v is ... more >>>

TR09-128 | 29th November 2009
Gillat Kol, Ran Raz

Locally Testable Codes Analogues to the Unique Games Conjecture Do Not Exist

The Unique Games Conjecture (UGC) is possibly the most important open problem in the research of PCPs and hardness of approximation. The conjecture is a strengthening of the PCP Theorem, predicting the existence of a special type of PCP verifiers: 2-query verifiers that only make unique tests. Moreover, the UGC ... more >>>

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