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Electronic Colloquium on Computational Complexity

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All reports by Author Dor Minzer:

TR22-167 | 23rd November 2022
Mark Braverman, Subhash Khot, Dor Minzer

Parallel Repetition for the GHZ Game: Exponential Decay

We show that the value of the $n$-fold repeated GHZ game is at most $2^{-\Omega(n)}$, improving upon the polynomial bound established by Holmgren and Raz. Our result is established via a reduction to approximate subgroup type questions from additive combinatorics.

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TR22-061 | 30th April 2022
Amey Bhangale, Subhash Khot, Dor Minzer

On Approximability of Satisfiable $k$-CSPs: I

We consider the $P$-CSP problem for $3$-ary predicates $P$ on satisfiable instances. We show that under certain conditions on $P$ and a $(1,s)$ integrality gap instance of the $P$-CSP problem, it can be translated into a dictatorship vs. quasirandomness test with perfect completeness and soundness $s+\varepsilon$, for every constant $\varepsilon>0$. ... more >>>

TR21-091 | 29th June 2021
Gil Cohen, Dor Minzer, Shir Peleg, Aaron Potechin, Amnon Ta-Shma

Expander Random Walks: The General Case and Limitations

Cohen, Peri and Ta-Shma (STOC'21) considered the following question: Assume the vertices of an expander graph are labelled by $\pm 1$. What "test" functions $f : \{\pm 1\}^t \to \{\pm1 \}$ can or cannot distinguish $t$ independent samples from those obtained by a random walk? [CPTS'21] considered only balanced labelling, ... more >>>

TR20-009 | 6th February 2020
Esty Kelman, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra

Theorems of KKL, Friedgut, and Talagrand via Random Restrictions and Log-Sobolev Inequality

We give alternate proofs for three related results in analysis of Boolean functions, namely the KKL
Theorem, Friedgut’s Junta Theorem, and Talagrand’s strengthening of the KKL Theorem. We follow a
new approach: looking at the first Fourier level of the function after a suitable random restriction and
applying the Log-Sobolev ... more >>>

TR19-141 | 22nd October 2019
Mark Braverman, Subhash Khot, Dor Minzer

On Rich $2$-to-$1$ Games

We propose a variant of the $2$-to-$1$ Games Conjecture that we call the Rich $2$-to-$1$ Games Conjecture and show that it is equivalent to the Unique Games Conjecture. We are motivated by two considerations. Firstly, in light of the recent proof of the $2$-to-$1$ Games Conjecture, we hope to understand ... more >>>

TR18-078 | 23rd April 2018
Subhash Khot, Dor Minzer, Dana Moshkovitz, Muli Safra

Small Set Expansion in The Johnson Graph

This paper studies expansion properties of the (generalized) Johnson Graph. For natural numbers
t < l < k, the nodes of the graph are sets of size l in a universe of size k. Two sets are connected if
their intersection is of size t. The Johnson graph arises often ... more >>>

TR18-006 | 10th January 2018
Subhash Khot, Dor Minzer, Muli Safra

Pseudorandom Sets in Grassmann Graph have Near-Perfect Expansion

Revisions: 2

We prove that pseudorandom sets in Grassmann graph have near-perfect expansion as hypothesized in [DKKMS-2]. This completes
the proof of the $2$-to-$2$ Games Conjecture (albeit with imperfect completeness) as proposed in [KMS, DKKMS-1], along with a
contribution from [BKT].

The Grassmann graph $Gr_{global}$ contains induced subgraphs $Gr_{local}$ that are themselves ... more >>>

TR17-094 | 25th May 2017
Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra

On Non-Optimally Expanding Sets in Grassmann Graphs

The paper investigates expansion properties of the Grassmann graph,
motivated by recent results of [KMS, DKKMS] concerning hardness
of the Vertex-Cover and of the $2$-to-$1$ Games problems. Proving the
hypotheses put forward by these papers seems to first require a better
understanding of these expansion properties.

We consider the edge ... more >>>

TR16-198 | 14th December 2016
Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer, Muli Safra

Towards a Proof of the 2-to-1 Games Conjecture?

We propose a combinatorial hypothesis regarding a subspace vs. subspace agreement test, and prove that if correct it leads to a proof of the 2-to-1 Games Conjecture, albeit with imperfect completeness.

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TR15-011 | 22nd January 2015
Subhash Khot, Dor Minzer, Muli Safra

On Monotonicity Testing and Boolean Isoperimetric type Theorems

We show a directed and robust analogue of a boolean isoperimetric type theorem of Talagrand. As an application, we
give a monotonicity testing algorithm that makes $\tilde{O}(\sqrt{n}/\epsilon^2)$ non-adaptive queries to a function
$f:\{0,1\}^n \mapsto \{0,1\}$, always accepts a monotone function and rejects a function that is $\epsilon$-far from
being monotone ... more >>>

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