A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z - Other

**H**

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TR11-085
| 14th May 2011
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Yijia Chen, Joerg Flum, Moritz Müller#### Hard instances of algorithms and proof systems

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TR17-117
| 20th July 2017
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Dmitry Itsykson, Alexander Knop#### Hard satisfiable formulas for splittings by linear combinations

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TR13-151
| 7th November 2013
__

Mark Bun, Justin Thaler#### Hardness Amplification and the Approximate Degree of Constant-Depth Circuits

Revisions: 3

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TR07-102
| 4th October 2007
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Andrej Bogdanov, Muli Safra#### Hardness amplification for errorless heuristics

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TR09-072
| 3rd September 2009
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Paul Beame, Trinh Huynh#### Hardness Amplification in Proof Complexity

Revisions: 2
,
Comments: 2

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TR07-130
| 3rd December 2007
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Ronen Shaltiel, Emanuele Viola#### Hardness amplification proofs require majority

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TR05-057
| 19th May 2005
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Venkatesan Guruswami, Valentine Kabanets#### Hardness amplification via space-efficient direct products

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TR10-031
| 4th March 2010
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Christian Glaßer, Christian Reitwießner, Heinz Schmitz, Maximilian Witek#### Hardness and Approximability in Multi-Objective Optimization

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TR11-015
| 8th December 2010
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Marcel R. Ackermann, Johannes Blömer, Christoph Scholz#### Hardness and Non-Approximability of Bregman Clustering Problems

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TR06-071
| 25th April 2006
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John Hitchcock, A. Pavan#### Hardness Hypotheses, Derandomization, and Circuit Complexity

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TR09-112
| 3rd November 2009
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Davide Bilò, Luciano Gualà, Guido Proietti#### Hardness of an Asymmetric 2-player Stackelberg Network Pricing Game

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TR00-062
| 25th August 2000
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Venkatesan Guruswami, Johan Hastad, Madhu Sudan#### Hardness of approximate hypergraph coloring

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TR05-127
| 5th November 2005
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Vitaly Feldman#### Hardness of Approximate Two-level Logic Minimization and PAC Learning with Membership Queries

Revisions: 1

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TR10-053
| 28th March 2010
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Dana Moshkovitz, Subhash Khot#### Hardness of Approximately Solving Linear Equations Over Reals

Comments: 1

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TR99-029
| 31st August 1999
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Ilya Dumer, Daniele Micciancio, Madhu Sudan#### Hardness of approximating the minimum distance of a linear code

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TR06-019
| 24th November 2005
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Janka Chlebíková, Miroslav Chlebík#### Hardness of asymptotic approximation for orthogonal rectangle packing and covering problems

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TR14-051
| 12th April 2014
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Subhash Khot, Rishi Saket#### Hardness of Coloring $2$-Colorable $12$-Uniform Hypergraphs with $2^{(\log n)^{\Omega(1)}}$ Colors

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TR16-063
| 18th April 2016
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Pavel Hubacek, Eylon Yogev#### Hardness of Continuous Local Search: Query Complexity and Cryptographic Lower Bounds

Revisions: 1

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TR06-109
| 29th August 2006
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Julia Chuzhoy, Sanjeev Khanna#### Hardness of Directed Routing with Congestion

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TR06-061
| 5th May 2006
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Venkatesan Guruswami, Prasad Raghavendra#### Hardness of Learning Halfspaces with Noise

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TR17-115
| 5th July 2017
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Arnab Bhattacharyya, Suprovat Ghoshal, Rishi Saket#### Hardness of learning noisy halfspaces using polynomial thresholds

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TR06-141
| 22nd November 2006
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Venkatesan Guruswami, Kunal Talwar#### Hardness of Low Congestion Routing in Directed Graphs

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TR10-059
| 8th April 2010
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Olaf Beyersdorff, Nicola Galesi, Massimo Lauria#### Hardness of Parameterized Resolution

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TR17-147
| 3rd October 2017
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Venkatesan Guruswami, Rishi Saket#### Hardness of Rainbow Coloring Hypergraphs

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TR07-073
| 3rd August 2007
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Parikshit Gopalan, Subhash Khot, Rishi Saket#### Hardness of Reconstructing Multivariate Polynomials over Finite Fields

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TR09-020
| 2nd March 2009
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Venkatesan Guruswami, Prasad Raghavendra#### Hardness of Solving Sparse Overdetermined Linear Systems: A 3-Query PCP over Integers.

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TR12-182
| 24th December 2012
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Itay Berman, Iftach Haitner, Ilan Komargodski, Moni Naor#### Hardness Preserving Reductions via Cuckoo Hashing

Revisions: 2

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TR07-121
| 21st November 2007
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Zeev Dvir, Amir Shpilka, Amir Yehudayoff#### Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits

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TR04-072
| 19th August 2004
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John Hitchcock#### Hausdorff Dimension and Oracle Constructions

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TR03-034
| 17th March 2003
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Arnold Beckmann#### Height restricted constant depth LK

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TR13-074
| 9th May 2013
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Johannes Köbler, Sebastian Kuhnert, Oleg Verbitsky#### Helly Circular-Arc Graph Isomorphism is in Logspace

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TR14-178
| 5th December 2014
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Dmitry Itsykson, Alexander Knop, Dmitry Sokolov#### Heuristic time hierarchies via hierarchies for sampling distributions

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TR14-171
| 11th December 2014
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Lance Fortnow, Rahul Santhanam#### Hierarchies Against Sublinear Advice

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TR08-097
| 14th November 2008
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Oded Goldreich, Michael Krivelevich, Ilan Newman, Eyal Rozenberg#### Hierarchy Theorems for Property Testing

Revisions: 1

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TR17-157
| 13th October 2017
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Monaldo Mastrolilli#### High Degree Sum of Squares Proofs, Bienstock-Zuckerberg hierarchy and Chvatal-Gomory cuts

Revisions: 1

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TR17-089
| 11th May 2017
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Irit Dinur, Tali Kaufman#### High dimensional expanders imply agreement expanders

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TR13-053
| 4th April 2013
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Alan Guo#### High rate locally correctable codes via lifting

Revisions: 1

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TR15-068
| 21st April 2015
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Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf#### High rate locally-correctable and locally-testable codes with sub-polynomial query complexity

Revisions: 2

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TR10-148
| 23rd September 2010
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Swastik Kopparty, Shubhangi Saraf, Sergey Yekhanin#### High-rate codes with sublinear-time decoding

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TR15-110
| 8th July 2015
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Swastik Kopparty, Or Meir, Noga Ron-Zewi, Shubhangi Saraf#### High-rate Locally-testable Codes with Quasi-polylogarithmic Query Complexity

Revisions: 1

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TR10-181
| 21st November 2010
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Hamed Hatami, Shachar Lovett#### Higher-order Fourier analysis of $\mathbb{F}_p^n$ and the complexity of systems of linear forms

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TR96-055
| 22nd October 1996
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Alexander E. Andreev, Andrea E. F. Clementi, Jose' D. P. Rolim#### Hitting Properties of Hard Boolean Operators and their Consequences on BPP

Revisions: 1
,
Comments: 1

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TR95-061
| 27th November 1995
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Alexander E. Andreev, Andrea E. F. Clementi, Jose' D. P. Rolim#### Hitting sets derandomize BPP

Revisions: 1

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TR13-175
| 6th December 2013
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Venkatesan Guruswami, Chaoping Xing#### Hitting Sets for Low-Degree Polynomials with Optimal Density

Revisions: 1

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TR17-161
| 30th October 2017
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Mark Braverman, Gil Cohen, Sumegha Garg#### Hitting Sets with Near-Optimal Error for Read-Once Branching Programs

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TR13-174
| 6th December 2013
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Manindra Agrawal, Rohit Gurjar, Arpita Korwar, Nitin Saxena#### Hitting-sets for low-distance multilinear depth-$3$

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TR14-085
| 29th June 2014
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Manindra Agrawal, Rohit Gurjar, Arpita Korwar, Nitin Saxena#### Hitting-sets for ROABP and Sum of Set-Multilinear circuits

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TR05-099
| 9th September 2005
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Leslie G. Valiant#### Holographic Algorithms

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TR06-145
| 1st December 2006
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Jin-Yi Cai, Pinyan Lu#### Holographic Algorithms: From Art to Science

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TR07-020
| 11th March 2007
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Jin-Yi Cai, Pinyan Lu#### Holographic Algorithms: The Power of Dimensionality Resolved

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TR10-146
| 21st September 2010
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Ron Rothblum#### Homomorphic Encryption: from Private-Key to Public-Key

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TR14-163
| 29th November 2014
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Arnaud Durand, Meena Mahajan, Guillaume Malod, Nicolas de Rugy-Altherre, Nitin Saurabh#### Homomorphism polynomials complete for VP

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TR05-085
| 5th August 2005
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Asaf Shapira, Noga Alon#### Homomorphisms in Graph Property Testing - A Survey

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TR11-088
| 7th June 2011
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Pavel Hrubes#### How much commutativity is needed to prove polynomial identities?

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TR12-167
| 16th November 2012
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Periklis Papakonstantinou, Charles Rackoff, Yevgeniy Vahlis#### How powerful are the DDH hard groups?

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TR17-100
| 7th June 2017
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Dakshita Khurana, Amit Sahai#### How to Achieve Non-Malleability in One or Two Rounds

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TR09-132
| 8th December 2009
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Lior Malka#### How to Achieve Perfect Simulation and a Complete Problem for Non-interactive Perfect Zero-Knowledge

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TR15-055
| 13th April 2015
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Sivaramakrishnan Natarajan Ramamoorthy, Anup Rao#### How to Compress Asymmetric Communication

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TR12-010
| 5th February 2012
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Shafi Goldwasser, Guy Rothblum#### How to Compute in the Presence of Leakage

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TR12-140
| 27th October 2012
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Mark Zhandry#### How to Construct Quantum Random Functions

Revisions: 2

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TR13-183
| 22nd December 2013
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Yael Tauman Kalai, Ran Raz, Ron Rothblum#### How to Delegate Computations: The Power of No-Signaling Proofs

Revisions: 1

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TR12-058
| 5th May 2012
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Benny Applebaum, Yuval Ishai, Eyal Kushilevitz#### How to Garble Arithmetic Circuits

Revisions: 1

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TR05-145
| 5th December 2005
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Ronen Shaltiel#### How to get more mileage from randomness extractors

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TR05-096
| 26th August 2005
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Boaz Barak, Amit Sahai#### How To Play Almost Any Mental Game Over The Net --- Concurrent Composition via Super-Polynomial Simulation

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TR09-021
| 2nd March 2009
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Konstantin Makarychev, Yury Makarychev#### How to Play Unique Games on Expanders

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TR06-144
| 21st November 2006
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Claire Kenyon-Mathieu, Warren Schudy#### How to rank with few errors: A PTAS for Weighted Feedback Arc Set on Tournaments

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TR16-023
| 23rd February 2016
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Ilan Komargodski, Moni Naor, Eylon Yogev#### How to Share a Secret, Infinitely

Revisions: 3

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TR17-112
| 27th June 2017
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Yehuda Lindell#### How To Simulate It -- A Tutorial on the Simulation Proof Technique

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TR06-025
| 19th January 2006
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Leonid Gurvits#### Hyperbolic Polynomials Approach to Van der Waerden/Schrijver-Valiant like Conjectures :\\ Sharper Bounds , Simpler Proofs and Algorithmic Applications

Yijia Chen, Joerg Flum, Moritz Müller

Assuming that the class TAUT of tautologies of propositional logic has no almost optimal algorithm, we show that every algorithm $\mathbb A$ deciding TAUT has a polynomial time computable sequence witnessing that $\mathbb A$ is not almost optimal. The result extends to every $\Pi_t^p$-complete problem with $t\ge 1$; however, we ... more >>>

Dmitry Itsykson, Alexander Knop

Itsykson and Sokolov in 2014 introduced the class of DPLL($\oplus$) algorithms that solve Boolean satisfiability problem using the splitting by linear combinations of variables modulo 2. This class extends the class of DPLL algorithms that split by variables. DPLL($\oplus$) algorithms solve in polynomial time systems of linear equations modulo two ... more >>>

Mark Bun, Justin Thaler

We establish a generic form of hardness amplification for the approximability of constant-depth Boolean circuits by polynomials. Specifically, we show that if a Boolean circuit cannot be pointwise approximated by low-degree polynomials to within constant error in a certain one-sided sense, then an OR of disjoint copies of that circuit ... more >>>

Andrej Bogdanov, Muli Safra

An errorless heuristic is an algorithm that on all inputs returns either the correct answer or the special symbol "I don't know." A central question in average-case complexity is whether every distributional decision problem in NP has an errorless heuristic scheme: This is an algorithm that, for every δ > ... more >>>

Paul Beame, Trinh Huynh

We present a generic method for converting any family of unsatisfiable CNF formulas that require large resolution rank into CNF formulas whose refutation requires large rank for proof systems that manipulate polynomials or polynomial threshold functions of degree at most $k$ (known as ${\rm Th}(k)$ proofs). Such systems include: Lovasz-Schrijver ... more >>>

Ronen Shaltiel, Emanuele Viola

Hardness amplification is the fundamental task of

converting a $\delta$-hard function $f : {0,1}^n ->

{0,1}$ into a $(1/2-\eps)$-hard function $Amp(f)$,

where $f$ is $\gamma$-hard if small circuits fail to

compute $f$ on at least a $\gamma$ fraction of the

inputs. Typically, $\eps,\delta$ are small (and

$\delta=2^{-k}$ captures the case ...
more >>>

Venkatesan Guruswami, Valentine Kabanets

We prove a version of the derandomized Direct Product Lemma for

deterministic space-bounded algorithms. Suppose a Boolean function

$g:\{0,1\}^n\to\{0,1\}$ cannot be computed on more than $1-\delta$

fraction of inputs by any deterministic time $T$ and space $S$

algorithm, where $\delta\leq 1/t$ for some $t$. Then, for $t$-step

walks $w=(v_1,\dots, v_t)$ ...
more >>>

Christian Glaßer, Christian Reitwießner, Heinz Schmitz, Maximilian Witek

We systematically study the hardness and the approximability of combinatorial multi-objective NP optimization problems (multi-objective problems, for short).

We define solution notions that precisely capture the typical algorithmic tasks in multi-objective optimization. These notions inherit polynomial-time Turing reducibility from multivalued functions, which allows us to compare the solution notions and ... more >>>

Marcel R. Ackermann, Johannes Blömer, Christoph Scholz

We prove the computational hardness of three k-clustering problems using an (almost) arbitrary Bregman divergence as dissimilarity measure: (a) The Bregman k-center problem, where the objective is to find a set of centers that minimizes the maximum dissimilarity of any input point towards its closest center, and (b) the Bregman ... more >>>

John Hitchcock, A. Pavan

We consider hypotheses about nondeterministic computation that

have been studied in different contexts and shown to have interesting

consequences:

1. The measure hypothesis: NP does not have p-measure 0.

2. The pseudo-NP hypothesis: there is an NP language that can be

distinguished from any DTIME(2^n^epsilon) language by an ...
more >>>

Davide Bilò, Luciano Gualà, Guido Proietti

Consider a communication network represented by a directed graph $G=(V,E)$ of $n$ nodes and $m$ edges. Assume that edges in $E$ are

partitioned into two sets: a set $C$ of edges with a fixed

non-negative real cost, and a set $P$ of edges whose \emph{price} should instead be set by ...
more >>>

Venkatesan Guruswami, Johan Hastad, Madhu Sudan

We introduce the notion of covering complexity of a probabilistic

verifier. The covering complexity of a verifier on a given input is

the minimum number of proofs needed to ``satisfy'' the verifier on

every random string, i.e., on every random string, at least one of the

given proofs must be ...
more >>>

Vitaly Feldman

Producing a small DNF expression consistent with given data is a

classical problem in computer science that occurs in a number of forms and

has numerous applications. We consider two standard variants of this

problem. The first one is two-level logic minimization or finding a minimal

more >>>

Dana Moshkovitz, Subhash Khot

In this paper, we consider the problem of approximately solving a

system of homogeneous linear equations over reals, where each

equation contains at most three variables.

Since the all-zero assignment always satisfies all the equations

exactly, we restrict the assignments to be ``non-trivial". Here is

an informal statement of our ...
more >>>

Ilya Dumer, Daniele Micciancio, Madhu Sudan

We show that the minimum distance of a linear code (or

equivalently, the weight of the lightest codeword) is

not approximable to within any constant factor in random polynomial

time (RP), unless NP equals RP.

Under the stronger assumption that NP is not contained in RQP

(random ...
more >>>

Janka Chlebíková, Miroslav Chlebík

Recently Bansal and Sviridenko (Proc. of the 15th SODA'04, 189-196)

proved that for

2-dimensional Orthogonal Rectangle

Bin Packing without rotations allowed there is no asymptotic PTAS, unless P=NP. We show that similar

approximation hardness results hold for several rectangle packing and covering problems even if rotations by ninety

more >>>

Subhash Khot, Rishi Saket

We show that it is quasi-NP-hard to color $2$-colorable $12$-uniform hypergraphs with $2^{(\log n)^{\Omega(1) }}$ colors where $n$ is the number of vertices. Previously, Guruswami et al. [GHHSV14] showed that it is quasi-NP-hard to color $2$-colorable $8$-uniform hypergraphs with $2^{2^{\Omega(\sqrt{\log \log n})}}$ colors. Their result is obtained by composing a ... more >>>

Pavel Hubacek, Eylon Yogev

Local search proved to be an extremely useful tool when facing hard optimization problems (e.g. via the simplex algorithm, simulated annealing, or genetic algorithms). Although powerful, it has its limitations: there are functions for which exponentially many queries are needed to find a local optimum. In many contexts the optimization ... more >>>

Julia Chuzhoy, Sanjeev Khanna

Given a graph G and a collection of source-sink pairs in G, what is the least integer c such that each source can be connected by a path to its sink, with at most c paths going through an edge? This is known as the congestion minimization problem, and the ... more >>>

Venkatesan Guruswami, Prasad Raghavendra

Learning an unknown halfspace (also called a perceptron) from

labeled examples is one of the classic problems in machine learning.

In the noise-free case, when a halfspace consistent with all the

training examples exists, the problem can be solved in polynomial

time using linear programming. ...
more >>>

Arnab Bhattacharyya, Suprovat Ghoshal, Rishi Saket

We prove the hardness of weakly learning halfspaces in the presence of adversarial noise using polynomial threshold functions (PTFs). In particular, we prove that for any constants $d \in \mathbb{Z}^+$ and $\epsilon > 0$, it is NP-hard to decide: given a set of $\{-1,1\}$-labeled points in $\mathbb{R}^n$ whether (YES Case) ... more >>>

Venkatesan Guruswami, Kunal Talwar

We prove a strong inapproximability result for routing on directed

graphs with low congestion. Given as input a directed graph on $N$

vertices and a set of source-destination pairs that can be connected

via edge-disjoint paths, we prove that it is hard, assuming NP

doesn't have $n^{O(\log\log n)}$ time randomized ...
more >>>

Olaf Beyersdorff, Nicola Galesi, Massimo Lauria

Parameterized Resolution and, moreover, a general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider (FOCS'07). In that paper, Dantchev et al. show a complexity gap in tree-like Parameterized Resolution for propositional formulas arising from translations of first-order principles.

We broadly investigate Parameterized Resolution obtaining the following ...
more >>>

Venkatesan Guruswami, Rishi Saket

A hypergraph is $k$-rainbow colorable if there exists a vertex coloring using $k$ colors such that each hyperedge has all the $k$ colors. Unlike usual hypergraph coloring, rainbow coloring becomes harder as the number of colors increases. This work studies the rainbow colorability of hypergraphs which are guaranteed to be ... more >>>

Parikshit Gopalan, Subhash Khot, Rishi Saket

We study the polynomial reconstruction problem for low-degree

multivariate polynomials over finite fields. In the GF[2] version of this problem, we are given a set of points on the hypercube and target values $f(x)$ for each of these points, with the promise that there is a polynomial over GF[2] of ...
more >>>

Venkatesan Guruswami, Prasad Raghavendra

A classic result due to Hastad established that for every constant \eps > 0, given an overdetermined system of linear equations over a finite field \F_q where each equation depends on exactly 3 variables and at least a fraction (1-\eps) of the equations can be satisfied, it is NP-hard to ... more >>>

Itay Berman, Iftach Haitner, Ilan Komargodski, Moni Naor

A common method for increasing the usability and uplifting the security of pseudorandom function families (PRFs) is to ``hash" the inputs into a smaller domain before applying the PRF. This approach, known as ``Levin's trick", is used to achieve ``PRF domain extension" (using a short, e.g., fixed, input length PRF ... more >>>

Zeev Dvir, Amir Shpilka, Amir Yehudayoff

In this paper we show that lower bounds for bounded depth arithmetic circuits imply derandomization of polynomial identity testing for bounded depth arithmetic circuits. More formally, if there exists an explicit polynomial f(x_1,...,x_m) that cannot be computed by a depth d arithmetic circuit of small size then there exists ... more >>>

John Hitchcock

Bennett and Gill (1981) proved that P^A != NP^A relative to a

random oracle A, or in other words, that the set

O_[P=NP] = { A | P^A = NP^A }

has Lebesgue measure 0. In contrast, we show that O_[P=NP] has

Hausdorff dimension 1.

... more >>>

Arnold Beckmann

Height restricted constant depth LK is a natural restriction of

Gentzen's propositional proof system LK. A sequence of LK-formulas

has polylogarithmic-height restricted depth-d-LK proofs iff the

n-th formula in the sequence possesses LK-proofs where cut-formulas

are of depth d+1 with small bottom fanin

and of ...
more >>>

Johannes Köbler, Sebastian Kuhnert, Oleg Verbitsky

We present logspace algorithms for the canonical labeling problem and the representation problem of Helly circular-arc (HCA) graphs. The first step is a reduction to canonical labeling and representation of interval intersection matrices. In a second step, the Delta trees employed in McConnell's linear time representation algorithm for interval matrices ... more >>>

Dmitry Itsykson, Alexander Knop, Dmitry Sokolov

We give a new simple proof of the time hierarchy theorem for heuristic BPP originally proved by Fortnow and Santhanam [FS04] and then simplified and improved by Pervyshev [P07]. In the proof we use a hierarchy theorem for sampling distributions recently proved by Watson [W13]. As a byproduct we get ... more >>>

Lance Fortnow, Rahul Santhanam

We strengthen the non-deterministic time hierarchy theorem of

\cite{Cook72, Seiferas-Fischer-Meyer78, Zak83} to show that the lower bound

holds against sublinear advice. More formally, we show that for any constants

$c$ and $d$ such that $1 \leq c < d$, there is a language in $\NTIME(n^d)$

which is not in $\NTIME(n^c)/n^{1/d}$. ...
more >>>

Oded Goldreich, Michael Krivelevich, Ilan Newman, Eyal Rozenberg

Referring to the query complexity of property testing,

we prove the existence of a rich hierarchy of corresponding

complexity classes. That is, for any relevant function $q$,

we prove the existence of properties that have testing

complexity Theta(q).

Such results are proven in three standard

domains often considered in property ...
more >>>

Monaldo Mastrolilli

Chvatal-Gomory (CG) cuts and the Bienstock-Zuckerberg hierarchy capture useful linear programs that the standard bounded degree Lasserre/Sum-of-Squares (SOS) hierarchy fails to capture.

In this paper we present a novel polynomial time SOS hierarchy for 0/1 problems with a custom subspace of high degree polynomials (not the standard subspace of low-degree ... more >>>

Irit Dinur, Tali Kaufman

We show that high dimensional expanders imply derandomized direct product tests, with a number of subsets that is *linear* in the size of the universe.

Direct product tests belong to a family of tests called agreement tests that are important components in PCP constructions and include, for example, low degree ... more >>>

Alan Guo

We present a general framework for constructing high rate error correcting codes that are locally correctable (and hence locally decodable if linear) with a sublinear number of queries, based on lifting codes with respect to functions on the coordinates. Our approach generalizes the lifting of affine-invariant codes of Guo, Kopparty, ... more >>>

Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf

In this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs and LTCs with block length $n$, constant rate (which can even be taken arbitrarily close to 1), constant ... more >>>

Swastik Kopparty, Shubhangi Saraf, Sergey Yekhanin

Locally decodable codes are error-correcting codes that admit efficient decoding algorithms; any bit of the original message can be recovered by looking at only a small number of locations of a corrupted codeword. The tradeoff between the rate of a code and the locality/efficiency of its decoding algorithms has been ... more >>>

Swastik Kopparty, Or Meir, Noga Ron-Zewi, Shubhangi Saraf

An error correcting code is said to be \emph{locally testable} if

there is a test that checks whether a given string is a codeword,

or rather far from the code, by reading only a small number of symbols

of the string. Locally testable codes (LTCs) are both interesting

in their ...
more >>>

Hamed Hatami, Shachar Lovett

In this article we are interested in the density of small linear structures (e.g. arithmetic progressions) in subsets $A$ of the group $\mathbb{F}_p^n$. It is possible to express these densities as certain analytic averages involving $1_A$, the indicator function of $A$. In the higher-order Fourier analytic approach, the function $1_A$ ... more >>>

Alexander E. Andreev, Andrea E. F. Clementi, Jose' D. P. Rolim

We present the first worst-case hardness conditions

on the circuit complexity of EXP functions which are

sufficient to obtain P=BPP. In particular, we show that

from such hardness conditions it is possible to construct

quick Hitting Sets Generators with logarithmic prize.

...
more >>>

Alexander E. Andreev, Andrea E. F. Clementi, Jose' D. P. Rolim

We show that hitting sets can derandomize any BPP-algorithm.

This gives a positive answer to a fundamental open question in

probabilistic algorithms. More precisely, we present a polynomial

time deterministic algorithm which uses any given hitting set

to approximate the fractions of 1's in the ...
more >>>

Venkatesan Guruswami, Chaoping Xing

We give a length-efficient puncturing of Reed-Muller codes which preserves its distance properties. Formally, for the Reed-Muller code encoding $n$-variate degree-$d$ polynomials over ${\mathbb F}_q$ with $q \ge \Omega(d/\delta)$, we present an explicit (multi)-set $S \subseteq {\mathbb F}_q^n$ of size $N=\mathrm{poly}(n^d/\delta)$ such that every nonzero polynomial vanishes on at most ... more >>>

Mark Braverman, Gil Cohen, Sumegha Garg

Nisan (Combinatorica'92) constructed a pseudorandom generator for length $n$, width $n$ read-once branching programs (ROBPs) with error $\varepsilon$ and seed length $O(\log^2{n} + \log{n} \cdot \log(1/\varepsilon))$. A major goal in complexity theory is to reduce the seed length, hopefully, to the optimal $O(\log{n}+\log(1/\varepsilon))$, or to construct improved hitting sets, as ... more >>>

Manindra Agrawal, Rohit Gurjar, Arpita Korwar, Nitin Saxena

The depth-$3$ model has recently gained much importance, as it has become a stepping-stone to understanding general arithmetic circuits. Its restriction to multilinearity has known exponential lower bounds but no nontrivial blackbox identity tests. In this paper we take a step towards designing such hitting-sets. We define a notion of ... more >>>

Manindra Agrawal, Rohit Gurjar, Arpita Korwar, Nitin Saxena

We give a $n^{O(\log n)}$-time ($n$ is the input size) blackbox polynomial identity testing algorithm for unknown-order read-once oblivious algebraic branching programs (ROABP). The best time-complexity known for this class was $n^{O(\log^2 n)}$ due to Forbes-Saptharishi-Shpilka (STOC 2014), and that too only for multilinear ROABP. We get rid of their ... more >>>

Leslie G. Valiant

Complexity theory is built fundamentally on the notion of efficient

reduction among computational problems. Classical

reductions involve gadgets that map solution fragments of one problem to

solution fragments of another in one-to-one, or

possibly one-to-many, fashion. In this paper we propose a new kind of

reduction that allows for gadgets ...
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Jin-Yi Cai, Pinyan Lu

We develop the theory of holographic algorithms. We give

characterizations of algebraic varieties of realizable

symmetric generators and recognizers on the basis manifold,

and a polynomial time decision algorithm for the

simultaneous realizability problem.

Using the general machinery we are able to give

unexpected holographic algorithms for

some counting problems, ...
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Jin-Yi Cai, Pinyan Lu

Valiant's theory of holographic algorithms is a novel methodology

to achieve exponential speed-ups in computation. A fundamental

parameter in holographic algorithms is the dimension of the linear basis

vectors.

We completely resolve the problem of the power of higher dimensional

bases. We prove that 2-dimensional bases are universal for

holographic ...
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Ron Rothblum

We show that any private-key encryption scheme that is weakly

homomorphic with respect to addition modulo 2, can be transformed

into a public-key encryption scheme. The homomorphic feature

referred to is a minimalistic one; that is, the length of a

homomorphically generated encryption should be independent of the

number of ...
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Arnaud Durand, Meena Mahajan, Guillaume Malod, Nicolas de Rugy-Altherre, Nitin Saurabh

The VP versus VNP question, introduced by Valiant, is probably the most important open question in algebraic complexity theory. Thanks to completeness results, a variant of this question, VBP versus VNP, can be succinctly restated as asking whether the permanent of a generic matrix can be written as a determinant ... more >>>

Asaf Shapira, Noga Alon

Property-testers are fast randomized algorithms for distinguishing

between graphs (and other combinatorial structures) satisfying a

certain property, from those that are far from satisfying it. In

many cases one can design property-testers whose running time is in

fact {\em independent} of the size of the input. In this paper we

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Pavel Hrubes

Let $f$ be a non-commutative polynomial such that $f=0$ if we assume that the variables in $f$ commute. Let $Q(f)$ be the smallest $k$ such that there exist polynomials $g_1,g_1', g_2, g_2',\dots, g_k, g_k' $ with \[f\in I([g_1,g_1'], [g_2, g_2'],\dots, [g_k, g_k'] )\,,\]

where $[g,h]=gh-hg$. Then $Q(f)\leq {n\choose 2}$, where ...
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Periklis Papakonstantinou, Charles Rackoff, Yevgeniy Vahlis

The question whether Identity-Based Encryption (IBE) can be based on the Decisional Diffie-Hellman (DDH) assumption is one of the most prominent questions in Cryptography related to DDH. We study limitations on the use of the DDH assumption in cryptographic constructions, and show that it is impossible to construct a secure ... more >>>

Dakshita Khurana, Amit Sahai

Despite over 25 years of research on non-malleable commitments in the plain model, their round complexity has remained open. The goal of achieving non-malleable commitment protocols with only one or two rounds has been especially elusive. Pass (TCC 2013, CC 2016) captured this difficulty by proving important impossibility results regarding ... more >>>

Lior Malka

Perfect zero-knowledge (PZK) proofs have been constructed in various settings and they are

also interesting from a complexity theoretic perspective. Yet, virtually nothing is known about them. This is in contrast to statistical zero-knowledge proofs, where many general results have been proved using an array of tools, none of which ...
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Sivaramakrishnan Natarajan Ramamoorthy, Anup Rao

We study the relationship between communication and information in 2-party communication protocols when the information is asymmetric. If $I^A$ denotes the number of bits of information revealed by the first party, $I^B$ denotes the information revealed by the second party, and $C$ is the number of bits of communication in ... more >>>

Shafi Goldwasser, Guy Rothblum

We address the following problem: how to execute any algorithm P, for an unbounded number of executions, in the presence of an adversary who observes partial information on the internal state of the computation during executions. The security guarantee is that the adversary learns nothing, beyond P's input/output behavior.

This ... more >>>

Mark Zhandry

In the presence of a quantum adversary, there are two possible definitions of security for a pseudorandom function. The first, which we call standard-security, allows the adversary to be quantum, but requires queries to the function to be classical. The second, quantum-security, allows the adversary to query the function on ... more >>>

Yael Tauman Kalai, Ran Raz, Ron Rothblum

We construct a 1-round delegation scheme (i.e., argument-system) for every language computable in time t=t(n), where the running time of the prover is poly(t) and the running time of the verifier is n*polylog(t). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. ... more >>>

Benny Applebaum, Yuval Ishai, Eyal Kushilevitz

Yao's garbled circuit construction transforms a boolean circuit $C:\{0,1\}^n\to\{0,1\}^m$

into a ``garbled circuit'' $\hat{C}$ along with $n$ pairs of $k$-bit keys, one for each

input bit, such that $\hat{C}$ together with the $n$ keys

corresponding to an input $x$ reveal $C(x)$ and no additional information about $x$.

The garbled circuit ...
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Ronen Shaltiel

Let $\cal C$ be a class of distributions over $\B^n$. A deterministic randomness extractor for $\cal C$ is a function $E:\B^n \ar \B^m$ such that for any $X$ in $\cal C$ the distribution $E(X)$ is statistically close to the uniform distribution. A long line of research deals with explicit constructions ... more >>>

Boaz Barak, Amit Sahai

We construct a secure protocol for any multi-party functionality

that remains secure (under a relaxed definition of security) when

executed concurrently with multiple copies of itself and other

protocols. We stress that we do *not* use any assumptions on

existence of trusted parties, common reference string, honest

majority or synchronicity ...
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Konstantin Makarychev, Yury Makarychev

In this note we improve a recent result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders.

Given a (1 - epsilon)-satisfiable instance of Unique Games with the constraint graph G, our algorithm finds an assignments satisfying at least a (1 - C ... more >>>

Claire Kenyon-Mathieu, Warren Schudy

Suppose you ran a chess tournament, everybody played everybody, and you wanted to use the results to rank everybody. Unless you were really lucky, the results would not be acyclic, so you could not just sort the players by who beat whom. A natural objective is to find a ranking ... more >>>

Ilan Komargodski, Moni Naor, Eylon Yogev

Secret sharing schemes allow a dealer to distribute a secret piece of information among several parties so that any qualified subset of parties can reconstruct the secret, while every unqualified subset of parties learns nothing about the secret. The collection of qualified subsets is called an access structure. The best ... more >>>

Yehuda Lindell

One of the most fundamental notions of cryptography is that of \emph{simulation}. It stands behind the concepts of semantic security, zero knowledge, and security for multiparty computation. However, writing a simulator and proving security via the use of simulation is a non-trivial task, and one that many newcomers to the ... more >>>

Leonid Gurvits

Let $p(x_1,...,x_n) = p(X) , X \in R^{n}$ be a homogeneous polynomial of degree $n$ in $n$ real variables ,

$e = (1,1,..,1) \in R^n$ be a vector of all ones . Such polynomial $p$ is

called $e$-hyperbolic if for all real vectors $X \in R^{n}$ the univariate polynomial

equation ...
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