All reports in year 2018:

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TR18-010
| 14th January 2018
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Alexander A. Sherstov#### Algorithmic polynomials

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TR18-009
| 9th January 2018
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Saikrishna Badrinarayanan, Yael Kalai, Dakshita Khurana, Amit Sahai, Daniel Wichs#### Non-Interactive Delegation for Low-Space Non-Deterministic Computation

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TR18-008
| 10th January 2018
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Tom Gur, Igor Shinkar#### An Entropy Lower Bound for Non-Malleable Extractors

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TR18-007
| 9th January 2018
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Lior Gishboliner, Asaf Shapira#### A Generalized Turan Problem and its Applications

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TR18-006
| 10th January 2018
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Subhash Khot, Dor Minzer, Muli Safra#### Pseudorandom Sets in Grassmann Graph have Near-Perfect Expansion

Revisions: 1

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TR18-005
| 9th January 2018
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Deeparnab Chakrabarty, C. Seshadhri#### Adaptive Boolean Monotonicity Testing in Total Influence Time

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TR18-004
| 3rd January 2018
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Aayush Ojha, Raghunath Tewari#### Circuit Complexity of Bounded Planar Cutwidth Graph Matching

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TR18-003
| 2nd January 2018
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Roei Tell#### Proving that prBPP=prP is as hard as "almost" proving that P \ne NP

Revisions: 1

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TR18-002
| 31st December 2017
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Constantinos Daskalakis, Gautam Kamath, John Wright#### Which Distribution Distances are Sublinearly Testable?

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TR18-001
| 2nd January 2018
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Tim Roughgarden#### Complexity Theory, Game Theory, and Economics

Alexander A. Sherstov

The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in learning theory, differential privacy, and algorithm design in general. Nearly all known upper bounds on approximate degree ... more >>>

Saikrishna Badrinarayanan, Yael Kalai, Dakshita Khurana, Amit Sahai, Daniel Wichs

We construct a delegation scheme for verifying non-deterministic computations, with complexity proportional only to the non-deterministic space of the computation. Specifi cally, letting $n$ denote the input length, we construct a delegation scheme for any language veri fiable in non-deterministic time and space $(T(n);S(n))$ with communication complexity $poly(S(n))$, verifi er ... more >>>

Tom Gur, Igor Shinkar

A (k,\eps)-non-malleable extractor is a function nmExt : {0,1}^n x {0,1}^d -> {0,1} that takes two inputs, a weak source X~{0,1}^n of min-entropy k and an independent uniform seed s in {0,1}^d, and outputs a bit nmExt(X, s) that is \eps-close to uniform, even given the seed s and the ... more >>>

Lior Gishboliner, Asaf Shapira

Our first theorem in this papers is a hierarchy theorem for the query complexity of testing graph properties with $1$-sided error; more precisely, we show that for every super-polynomial $f$, there is a graph property whose 1-sided-error query complexity is $f(\Theta(1/\varepsilon))$. No result of this type was previously known for ... more >>>

Subhash Khot, Dor Minzer, Muli Safra

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 >>>

Deeparnab Chakrabarty, C. Seshadhri

The problem of testing monotonicity

of a Boolean function $f:\{0,1\}^n \to \{0,1\}$ has received much attention

recently. Denoting the proximity parameter by $\varepsilon$, the best tester is the non-adaptive $\widetilde{O}(\sqrt{n}/\varepsilon^2)$ tester

of Khot-Minzer-Safra (FOCS 2015). Let $I(f)$ denote the total influence

of $f$. We give an adaptive tester whose running ...
more >>>

Aayush Ojha, Raghunath Tewari

Recently, perfect matching in bounded planar cutwidth bipartite graphs

$BGGM$ was shown to be in ACC$^0$ by Hansen et al.. They also conjectured that

the problem is in AC$^0$.

In this paper, we disprove their conjecture by showing that the problem is

not in AC$^0[p^{\alpha}]$ for every prime $p$. ...
more >>>

Roei Tell

We show that any proof that $promise\textrm{-}\mathcal{BPP}=promise\textrm{-}\mathcal{P}$ necessitates proving circuit lower bounds that almost yield that $\mathcal{P}\ne\mathcal{NP}$. More accurately, we show that if $promise\textrm{-}\mathcal{BPP}=promise\textrm{-}\mathcal{P}$, then for essentially any super-constant function $f(n)=\omega(1)$ it holds that $NTIME[n^{f(n)}]\not\subseteq\mathcal{P}/\mathrm{poly}$. The conclusion of the foregoing conditional statement cannot be improved (to conclude that $\mathcal{NP}\not\subseteq\mathcal{P}/\mathrm{poly}$) without ... more >>>

Constantinos Daskalakis, Gautam Kamath, John Wright

Given samples from an unknown distribution $p$ and a description of a distribution $q$, are $p$ and $q$ close or far? This question of "identity testing" has received significant attention in the case of testing whether $p$ and $q$ are equal or far in total variation distance. However, in recent ... more >>>

Tim Roughgarden

This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19-23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity.

The goal of this mini-course is twofold: (i) to explain how complexity ... more >>>