All reports by Author Gillat Kol:

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TR17-093
| 22nd May 2017
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Klim Efremenko, Gillat Kol, Raghuvansh Saxena#### Interactive Coding Over the Noisy Broadcast Channel

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TR16-113
| 22nd July 2016
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Gillat Kol, Ran Raz, Avishay Tal#### Time-Space Hardness of Learning Sparse Parities

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TR15-168
| 18th October 2015
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Gillat Kol#### Interactive Compression for Product Distributions

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TR15-165
| 14th October 2015
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Ran Gelles, Bernhard Haeupler, Gillat Kol, Noga Ron-Zewi, Avi Wigderson#### Towards Optimal Deterministic Coding for Interactive Communication

Revisions: 1

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TR15-088
| 31st May 2015
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Anat Ganor, Gillat Kol, Ran Raz#### Exponential Separation of Communication and External Information

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TR14-113
| 27th August 2014
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Anat Ganor, Gillat Kol, Ran Raz#### Exponential Separation of Information and Communication for Boolean Functions

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TR14-049
| 11th April 2014
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Anat Ganor, Gillat Kol, Ran Raz#### Exponential Separation of Information and Communication

Revisions: 1

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TR14-046
| 8th April 2014
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Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff#### Approximate Nonnegative Rank is Equivalent to the Smooth Rectangle Bound

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TR13-079
| 2nd June 2013
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Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff#### Direct Sum Fails for Zero Error Average Communication

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TR13-001
| 2nd January 2013
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Gillat Kol, Ran Raz#### Interactive Channel Capacity

Revisions: 1

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

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TR11-122
| 14th September 2011
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Gillat Kol, Ran Raz#### Competing Provers Protocols for Circuit Evaluation

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TR09-138
| 14th December 2009
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Gillat Kol, Ran Raz#### Bounds on 2-Query Locally Testable Codes with Affine Tests

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TR09-128
| 29th November 2009
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Gillat Kol, Ran Raz#### Locally Testable Codes Analogues to the Unique Games Conjecture Do Not Exist

Klim Efremenko, Gillat Kol, Raghuvansh Saxena

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 >>>

Gillat Kol, Ran Raz, Avishay Tal

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 >>>

Gillat Kol

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 >>>

Ran Gelles, Bernhard Haeupler, Gillat Kol, Noga Ron-Zewi, Avi Wigderson

We study \emph{efficient, deterministic} interactive coding schemes that simulate any interactive protocol both under random and adversarial errors, and can achieve a constant communication rate independent of the protocol length.

For channels that flip bits independently with probability~$\epsilon<1/2$, our coding scheme achieves a communication rate of $1 - O(\sqrt{H({\epsilon})})$ and ... more >>>

Anat Ganor, Gillat Kol, Ran Raz

We show an exponential gap between communication complexity and external information complexity, by analyzing a communication task suggested as a candidate by Braverman [Bra13]. Previously, only a separation of communication complexity and internal information complexity was known [GKR14,GKR15].

More precisely, we obtain an explicit example of a search problem with ... more >>>

Anat Ganor, Gillat Kol, Ran Raz

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 >>>

Anat Ganor, Gillat Kol, Ran Raz

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

Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

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 ...
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Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

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 >>>

Gillat Kol, Ran Raz

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 >>>

Irit Dinur, Gillat Kol

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 >>>

Gillat Kol, Ran Raz

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 >>>

Gillat Kol, Ran Raz

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 >>>

Gillat Kol, Ran Raz

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 >>>