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

**Q**

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TR22-080
| 25th May 2022
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Meena Mahajan, Gaurav Sood#### QBF Merge Resolution is powerful but unnatural

Revisions: 1

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TR23-051
| 18th April 2023
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Benjamin Böhm, Olaf Beyersdorff#### QCDCL vs QBF Resolution: Further Insights

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TR21-131
| 10th September 2021
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Olaf Beyersdorff, Benjamin Böhm#### QCDCL with Cube Learning or Pure Literal Elimination - What is best?

Revisions: 1

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TR19-015
| 7th February 2019
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William Kretschmer#### QMA Lower Bounds for Approximate Counting

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TR05-129
| 30th October 2005
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Scott Aaronson#### QMA/qpoly Is Contained In PSPACE/poly: De-Merlinizing Quantum Protocols

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TR03-021
| 4th April 2003
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Mikhail Vyalyi#### QMA=PP implies that PP contains PH

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TR21-109
| 20th July 2021
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Sravanthi Chede, Anil Shukla#### QRAT Polynomially Simulates Merge Resolution.

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TR11-084
| 23rd May 2011
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Madhur Tulsiani, Julia Wolf#### Quadratic Goldreich-Levin Theorems

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TR15-205
| 15th December 2015
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Emanuele Viola#### Quadratic maps are hard to sample

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TR17-031
| 15th February 2017
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Thomas Watson#### Quadratic Simulations of Merlin-Arthur Games

Revisions: 1

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TR17-123
| 2nd August 2017
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Dmytro Gavinsky, Rahul Jain, Hartmut Klauck, Srijita Kundu, Troy Lee, Miklos Santha, Swagato Sanyal, Jevgenijs Vihrovs#### Quadratically Tight Relations for Randomized Query Complexity

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TR05-036
| 28th March 2005
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Hubie Chen#### Quantified Constraint Satisfaction, Maximal Constraint Languages, and Symmetric Polymorphisms

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TR05-024
| 8th February 2005
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Michael Bauland, Elmar Böhler, Nadia Creignou, Steffen Reith, Henning Schnoor, Heribert Vollmer#### Quantified Constraints: The Complexity of Decision and Counting for Bounded Alternation

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TR17-145
| 19th September 2017
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Roei Tell#### Quantified derandomization of linear threshold circuits

Revisions: 2

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TR18-156
| 8th September 2018
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Mark Bun, Robin Kothari, Justin Thaler#### Quantum algorithms and approximating polynomials for composed functions with shared inputs

Revisions: 2

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TR21-126
| 25th August 2021
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Yilei Chen, Qipeng Liu, Mark Zhandry#### Quantum Algorithms for Variants of Average-Case Lattice Problems via Filtering

Revisions: 1

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TR24-050
| 5th March 2024
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Omri Shmueli#### Quantum Algorithms in a Superposition of Spacetimes

Revisions: 1

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TR04-045
| 15th April 2004
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Hartmut Klauck, Robert Spalek, Ronald de Wolf#### Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs

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TR04-023
| 21st January 2004
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Yaoyun Shi#### Quantum and Classical Tradeoffs

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TR13-010
| 4th January 2013
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Yang Liu, Shengyu Zhang#### Quantum and randomized communication complexity of XOR functions in the SMP model

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TR02-013
| 30th January 2002
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Chris Pollett, Farid Ablayev, Cristopher Moore, Chris Pollett#### Quantum and Stochastic Programs of Bounded Width

Revisions: 1

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TR24-029
| 16th February 2024
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Noel Arteche, Gaia Carenini, Matthew Gray#### Quantum Automating $\mathbf{TC}^0$-Frege Is LWE-Hard

Revisions: 1

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TR03-005
| 28th December 2002
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Scott Aaronson#### Quantum Certificate Complexity

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TR99-032
| 7th July 1999
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Cristopher Moore#### Quantum Circuits: Fanout, Parity, and Counting

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TR05-003
| 23rd December 2004
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Scott Aaronson#### Quantum Computing, Postselection, and Probabilistic Polynomial-Time

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TR05-146
| 25th November 2005
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Gábor Erdèlyi, Tobias Riege, Jörg Rothe#### Quantum Cryptography: A Survey

Revisions: 2

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TR07-032
| 27th March 2007
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Pavel Pudlak#### Quantum deduction rules

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TR17-011
| 22nd January 2017
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Boaz Barak, Pravesh Kothari, David Steurer#### Quantum entanglement, sum of squares, and the log rank conjecture

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TR10-165
| 4th November 2010
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Dmytro Gavinsky, Tsuyoshi Ito#### Quantum Fingerprints that Keep Secrets

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TR06-020
| 10th February 2006
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Akinori Kawachi, Tomoyuki Yamakami#### Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding

Revisions: 1

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TR19-041
| 7th March 2019
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Srinivasan Arunachalam, Alex Bredariol Grilo, Aarthi Sundaram#### Quantum hardness of learning shallow classical circuits

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TR20-066
| 28th April 2020
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Scott Aaronson, Shalev Ben-David, Robin Kothari, Avishay Tal#### Quantum Implications of Huang's Sensitivity Theorem

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TR05-038
| 10th April 2005
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Ran Raz#### Quantum Information and the PCP Theorem

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TR20-185
| 1st December 2020
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Srinivasan Arunachalam, Alex Grilo, Tom Gur, Igor Oliveira, Aarthi Sundaram#### Quantum learning algorithms imply circuit lower bounds

Revisions: 1

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TR23-173
| 15th November 2023
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Louis Golowich, Venkatesan Guruswami#### Quantum Locally Recoverable Codes

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TR18-201
| 30th November 2018
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Anurag Anshu, Naresh Boddu, Dave Touchette#### Quantum Log-Approximate-Rank Conjecture is also False

Comments: 1

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TR20-087
| 8th June 2020
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Uma Girish, Ran Raz, Wei Zhan#### Quantum Logspace Algorithm for Powering Matrices with Bounded Norm

Revisions: 2

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TR23-107
| 20th July 2023
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Uma Girish, Ran Raz, Wei Zhan#### Quantum Logspace Computations are Verifiable

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TR18-087
| 20th April 2018
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Kun He, Qian Li, Xiaoming Sun, Jiapeng Zhang#### Quantum Lov{\'a}sz Local Lemma: Shearer's Bound is Tight

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TR18-137
| 7th August 2018
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Scott Aaronson#### Quantum Lower Bound for Approximate Counting Via Laurent Polynomials

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TR14-109
| 14th August 2014
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Aran Nayebi, Scott Aaronson, Aleksandrs Belovs, Luca Trevisan#### Quantum lower bound for inverting a permutation with advice

Revisions: 1

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TR02-072
| 12th November 2002
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Scott Aaronson#### Quantum Lower Bound for Recursive Fourier Sampling

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TR19-062
| 18th April 2019
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Scott Aaronson, Robin Kothari, William Kretschmer, Justin Thaler#### Quantum Lower Bounds for Approximate Counting via Laurent Polynomials

Revisions: 2

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TR96-003
| 4th December 1995
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Alexei Kitaev#### Quantum measurements and the Abelian Stabilizer Problem

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TR21-116
| 10th August 2021
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Nai-Hui Chia, Chi-Ning Chou, Jiayu Zhang, Ruizhe Zhang#### Quantum Meets the Minimum Circuit Size Problem

Revisions: 1

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TR12-024
| 25th March 2012
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Scott Aaronson, Paul Christiano#### Quantum Money from Hidden Subspaces

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TR14-151
| 13th November 2014
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Debajyoti Bera#### Quantum One-Sided Exact Error Algorithms

Revisions: 2

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TR10-143
| 19th September 2010
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Bo'az Klartag, Oded Regev#### Quantum One-Way Communication is Exponentially Stronger Than Classical Communication

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TR18-105
| 30th May 2018
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Joseph Fitzsimons, Zhengfeng Ji, Thomas Vidick, Henry Yuen#### Quantum proof systems for iterated exponential time, and beyond

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TR09-102
| 21st October 2009
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Andrew Drucker, Ronald de Wolf#### Quantum Proofs for Classical Theorems

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TR21-068
| 8th May 2021
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Marcel Dall'Agnol, Tom Gur, Subhayan Roy Moulik, Justin Thaler#### Quantum Proofs of Proximity

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TR08-086
| 9th July 2008
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Vikraman Arvind, Partha Mukhopadhyay#### Quantum Query Complexity of Multilinear Identity Testing

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TR19-136
| 23rd September 2019
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Sourav Chakraborty, Arkadev Chattopadhyay, Nikhil Mande, Manaswi Paraashar#### Quantum Query-to-Communication Simulation Needs a Logarithmic Overhead

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TR07-013
| 6th February 2007
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Andris Ambainis, Joseph Emerson#### Quantum t-designs: t-wise independence in the quantum world

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TR22-029
| 27th February 2022
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Anthony Leverrier, Gilles Zémor#### Quantum Tanner codes

Revisions: 2

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TR24-011
| 24th January 2024
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Paul Beame, Niels Kornerup#### Quantum Time-Space Tradeoffs for Matrix Problems

Revisions: 1

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TR06-055
| 10th April 2006
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Scott Aaronson, Greg Kuperberg#### Quantum Versus Classical Proofs and Advice

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TR22-177
| 7th December 2022
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Vahid Reza Asadi, Alexander Golovnev, Tom Gur, Igor Shinkar, Sathyawageeswar Subramanian#### Quantum Worst-Case to Average-Case Reductions for All Linear Problems

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TR12-136
| 26th October 2012
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Dan Boneh, Mark Zhandry#### Quantum-Secure Message Authentication Codes

Revisions: 2

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TR16-001
| 9th January 2016
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Eli Ben-Sasson, Alessandro Chiesa, Ariel Gabizon, Madars Virza#### Quasi-Linear Size Zero Knowledge from Linear-Algebraic PCPs

Revisions: 1

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TR17-135
| 10th September 2017
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Ramprasad Saptharishi, Anamay Tengse#### Quasi-polynomial Hitting Sets for Circuits with Restricted Parse Trees

Revisions: 1

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TR12-113
| 7th September 2012
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Manindra Agrawal, Chandan Saha, Nitin Saxena#### Quasi-polynomial Hitting-set for Set-depth-$\Delta$ Formulas

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TR19-090
| 27th June 2019
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Ronen Shaltiel, Swastik Kopparty, Jad Silbak#### Quasilinear time list-decodable codes for space bounded channels

Revisions: 2

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TR12-115
| 11th September 2012
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Michael Forbes, Amir Shpilka#### Quasipolynomial-time Identity Testing of Non-Commutative and Read-Once Oblivious Algebraic Branching Programs

Revisions: 1

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TR22-091
| 2nd July 2022
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Harm Derksen, Emanuele Viola#### Quasirandom groups enjoy interleaved mixing

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TR12-002
| 4th January 2012
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Akinori Kawachi, Benjamin Rossman, Osamu Watanabe#### Query Complexity and Error Tolerance of Witness Finding Algorithms

Revisions: 3

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TR10-126
| 12th August 2010
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Thomas Watson#### Query Complexity in Errorless Hardness Amplification

Revisions: 2

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TR20-133
| 8th September 2020
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Noga Ron-Zewi, Ronen Shaltiel, Nithin Varma#### Query complexity lower bounds for local list-decoding and hard-core predicates (even for small rate and huge lists)

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TR10-067
| 14th April 2010
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Sourav Chakraborty, Eldar Fischer, Arie Matsliah#### Query Complexity Lower Bounds for Reconstruction of Codes

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TR20-108
| 19th July 2020
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Arijit Bishnu, Arijit Ghosh, Gopinath Mishra, Manaswi Paraashar#### Query Complexity of Global Minimum Cut

Revisions: 1

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TR22-158
| 18th November 2022
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Ivan Hu, Andrew Morgan, Dieter van Melkebeek#### Query Complexity of Inversion Minimization on Trees

Revisions: 1

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TR12-063
| 17th May 2012
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Raghav Kulkarni, Miklos Santha#### Query complexity of matroids

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TR23-039
| 28th March 2023
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Arkadev Chattopadhyay, Yogesh Dahiya, Meena Mahajan#### Query Complexity of Search Problems

Revisions: 1

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TR10-173
| 9th November 2010
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Yeow Meng Chee, Tao Feng, San Ling, Huaxiong Wang, Liang Feng Zhang#### Query-Efficient Locally Decodable Codes

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TR17-053
| 22nd March 2017
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Mika Göös, Toniann Pitassi, Thomas Watson#### Query-to-Communication Lifting for BPP

Revisions: 1

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TR17-024
| 16th February 2017
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Mika Göös, Pritish Kamath, Toniann Pitassi, Thomas Watson#### Query-to-Communication Lifting for P^NP

Revisions: 1

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TR19-103
| 7th August 2019
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Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, Toniann Pitassi#### Query-to-Communication Lifting Using Low-Discrepancy Gadgets

Revisions: 2

Meena Mahajan, Gaurav Sood

The Merge Resolution proof system (M-Res) for QBFs, proposed by Beyersdorff et al. in 2019, explicitly builds partial strategies inside refutations. The original motivation for this approach was to overcome the limitations encountered in long-distance Q-Resolution proof system (LD-Q-Res), where the syntactic side-conditions, while prohibiting all unsound resolutions, also end ... more >>>

Benjamin Böhm, Olaf Beyersdorff

We continue the investigation on the relations of QCDCL and QBF resolution systems. In particular, we introduce QCDCL versions that tightly characterise QU-Resolution and (a slight variant of) long-distance Q-Resolution. We show that most QCDCL variants - parameterised by different policies for decisions, unit propagations and reductions -- lead to ... more >>>

Olaf Beyersdorff, Benjamin Böhm

Quantified conflict-driven clause learning (QCDCL) is one of the main approaches for solving quantified Boolean formulas (QBF). We formalise and investigate several versions of QCDCL that include cube learning and/or pure-literal elimination, and formally compare the resulting solving models via proof complexity techniques. Our results show that almost all of ... more >>>

William Kretschmer

We prove a query complexity lower bound for $QMA$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $SBP^A \not\subset QMA^A$, resolving an open problem of Aaronson [2]. Our proof uses the polynomial method to ... more >>>

Scott Aaronson

This paper introduces a new technique for removing existential quantifiers

over quantum states. Using this technique, we show that there is no way

to pack an exponential number of bits into a polynomial-size quantum

state, in such a way that the value of any one of those bits ...
more >>>

Mikhail Vyalyi

We consider possible equality QMA=PP and give an argument

against it. Namely, this equality implies that PP contains PH. The argument is based on the strong form of Toda's theorem and

the strengthening of the proof for inclusion $QMA\subseteq PP$ due to Kitaev and Watrous.

Sravanthi Chede, Anil Shukla

Merge Resolution (MRes [Beyersdorff et al. J. Autom. Reason.'2021] ) is a refutational proof system for quantified Boolean formulas (QBF). Each line of MRes consists of clauses with only existential literals, together with information of countermodels stored as merge maps. As a result, MRes has strategy extraction by design. The ... more >>>

Madhur Tulsiani, Julia Wolf

Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin algorithm can be viewed as an algorithmic analogue of such a decomposition as it ... more >>>

Emanuele Viola

This note proves the existence of a quadratic GF(2) map

$p : \{0,1\}^n \to \{0,1\}$ such that no constant-depth circuit

of size $\poly(n)$ can sample the distribution $(u,p(u))$

for uniform $u$.

Thomas Watson

The known proofs of $\text{MA}\subseteq\text{PP}$ incur a quadratic overhead in the running time. We prove that this quadratic overhead is necessary for black-box simulations; in particular, we obtain an oracle relative to which $\text{MA-TIME}(t)\not\subseteq\text{P-TIME}(o(t^2))$. We also show that 2-sided-error Merlin--Arthur games can be simulated by 1-sided-error Arthur--Merlin games with quadratic ... more >>>

Dmytro Gavinsky, Rahul Jain, Hartmut Klauck, Srijita Kundu, Troy Lee, Miklos Santha, Swagato Sanyal, Jevgenijs Vihrovs

Let $f:\{0,1\}^n \rightarrow \{0,1\}$ be a Boolean function. The certificate complexity $C(f)$ is a complexity measure that is quadratically tight for the zero-error randomized query complexity $R_0(f)$: $C(f) \leq R_0(f) \leq C(f)^2$. In this paper we study a new complexity measure that we call expectational certificate complexity $EC(f)$, which is ... more >>>

Hubie Chen

The constraint satisfaction problem (CSP) is a convenient framework for modelling search problems; the CSP involves deciding, given a set of constraints on variables, whether or not there is an assignment to the variables satisfying all of the constraints. This paper is concerned with the quantified constraint satisfaction problem (QCSP), ... more >>>

Michael Bauland, Elmar Böhler, Nadia Creignou, Steffen Reith, Henning Schnoor, Heribert Vollmer

We consider constraint satisfaction problems parameterized by the set of allowed constraint predicates. We examine the complexity of quantified constraint satisfaction problems with a bounded number of quantifier alternations and the complexity of the associated counting problems. We obtain classification results that completely solve the Boolean case, and we show ... more >>>

Roei Tell

One of the prominent current challenges in complexity theory is the attempt to prove lower bounds for $TC^0$, the class of constant-depth, polynomial-size circuits with majority gates. Relying on the results of Williams (2013), an appealing approach to prove such lower bounds is to construct a non-trivial derandomization algorithm for ... more >>>

Mark Bun, Robin Kothari, Justin Thaler

We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be a Boolean function and consider a function $F$ obtained by applying $f$ to conjunctions of possibly overlapping subsets of $n$ variables. If $f$ has quantum query complexity $Q(f)$, we give ... more >>>

Yilei Chen, Qipeng Liu, Mark Zhandry

We show polynomial-time quantum algorithms for the following problems:

(*) Short integer solution (SIS) problem under the infinity norm, where the public matrix is very wide, the modulus is a polynomially large prime, and the bound of infinity norm is set to be half of the modulus minus a ...
more >>>

Omri Shmueli

Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the universe grows, so does our ability to use it for computation. A natural question ... more >>>

Hartmut Klauck, Robert Spalek, Ronald de Wolf

A strong direct product theorem says that if we want to compute

k independent instances of a function, using less than k times

the resources needed for one instance, then our overall success

probability will be exponentially small in k.

We establish such theorems for the classical as well as ...
more >>>

Yaoyun Shi

We initiate the study of quantifying the quantumness of

a quantum circuit by the number of gates that do not preserve

the computational basis, as a means to understand the nature

of quantum algorithmic speedups.

Intuitively, a reduction in the quantumness requires

an increase in the amount of classical computation, ...
more >>>

Yang Liu, Shengyu Zhang

Communication complexity of XOR functions $f (x \oplus y)$ has attracted increasing attention in recent years, because of its connections to Fourier analysis, and its exhibition of exponential separations between classical and quantum communication complexities of total functions.However, the complexity of certain basic functions still seems elusive especially in the ... more >>>

Chris Pollett, Farid Ablayev, Cristopher Moore, Chris Pollett

We prove upper and lower bounds on the power of quantum and stochastic

branching programs of bounded width. We show any NC^1 language can

be accepted exactly by a width-2 quantum branching program of

polynomial length, in contrast to the classical case where width 5 is

necessary unless \NC^1=\ACC. ...
more >>>

Noel Arteche, Gaia Carenini, Matthew Gray

We prove the first hardness results against efficient proof search by quantum algorithms. We show that under Learning with Errors (LWE), the standard lattice-based cryptographic assumption, no quantum algorithm can weakly automate $\mathbf{TC}^0$-Frege. This extends the line of results of Kraí?ek and Pudlák (Information and Computation, 1998), Bonet, Pitassi, and ... more >>>

Scott Aaronson

Given a Boolean function f, we study two natural generalizations of the certificate complexity C(f): the randomized certificate complexity RC(f) and the quantum certificate complexity QC(f). Using Ambainis' adversary method, we exactly characterize QC(f) as the square root of RC(f). We then use this result to prove the new relation ... more >>>

Cristopher Moore

We propose definitions of $\QAC^0$, the quantum analog of the

classical class $\AC^0$ of constant-depth circuits with AND and OR

gates of arbitrary fan-in, and $\QACC^0[q]$, the analog of the class

$\ACC^0[q]$ where $\Mod_q$ gates are also allowed. We show that it is

possible to make a `cat' state on ...
more >>>

Scott Aaronson

I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic Polynomial-Time. Using this result, I show that several simple changes to the axioms ... more >>>

Gábor Erdèlyi, Tobias Riege, Jörg Rothe

We survey some results in quantum cryptography. After a brief

introduction to classical cryptography, we provide the physical and

mathematical background needed and present some fundamental protocols

from quantum cryptography, including quantum key distribution and

quantum bit commitment protocols.

Pavel Pudlak

We define propositional quantum Frege proof systems and compare it

with classical Frege proof systems.

Boaz Barak, Pravesh Kothari, David Steurer

For every constant $\epsilon>0$, we give an $\exp(\tilde{O}(\sqrt{n}))$-time algorithm for the $1$ vs $1-\epsilon$ Best Separable State (BSS) problem of distinguishing, given an $n^2\times n^2$ matrix $M$ corresponding to a quantum measurement, between the case that there is a separable (i.e., non-entangled) state $\rho$ that $M$ accepts with probability $1$, ... more >>>

Dmytro Gavinsky, Tsuyoshi Ito

We introduce a new type of cryptographic primitive that we call hiding fingerprinting. No classical fingerprinting scheme is hiding. We construct quantum hiding fingerprinting schemes and argue their optimality.

more >>>Akinori Kawachi, Tomoyuki Yamakami

We present three new quantum hardcore functions for any quantum one-way function. We also give a "quantum" solution to Damgard's question (CRYPTO'88) on his pseudorandom generator by proving the quantum hardcore property of his generator, which has been unknown to have the classical hardcore property.

Our technical tool is ...
more >>>

Srinivasan Arunachalam, Alex Bredariol Grilo, Aarthi Sundaram

In this paper we study the quantum learnability of constant-depth classical circuits under the uniform distribution and in the distribution-independent framework of PAC learning. In order to attain our results, we establish connections between quantum learning and quantum-secure cryptosystems. We then achieve the following results.

1) Hardness of learning ... more >>>

Scott Aaronson, Shalev Ben-David, Robin Kothari, Avishay Tal

Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$, the deterministic query complexity, $D(f)$, is at most quartic in the quantum query complexity, $Q(f)$: $D(f) = O(Q(f)^4)$. This matches the known separation (up to log factors) due to Ambainis, Balodis, Belovs, Lee, ... more >>>

Ran Raz

We show how to encode $2^n$ (classical) bits $a_1,...,a_{2^n}$

by a single quantum state $|\Psi \rangle$ of size $O(n)$ qubits,

such that:

for any constant $k$ and any $i_1,...,i_k \in \{1,...,2^n\}$,

the values of the bits $a_{i_1},...,a_{i_k}$ can be retrieved

from $|\Psi \rangle$ by a one-round Arthur-Merlin interactive ...
more >>>

Srinivasan Arunachalam, Alex Grilo, Tom Gur, Igor Oliveira, Aarthi Sundaram

We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathrm{C}$ be a class of polynomial-size concepts, and suppose that $\mathrm{C}$ can be PAC-learned with membership queries under the uniform distribution with error $1/2 - \gamma$ by a time $T$ quantum algorithm. ... more >>>

Louis Golowich, Venkatesan Guruswami

Classical locally recoverable codes, which permit highly efficient recovery from localized errors as well as global recovery from larger errors, provide some of the most useful codes for distributed data storage in practice. In this paper, we initiate the study of quantum locally recoverable codes (qLRCs). In the long ... more >>>

Anurag Anshu, Naresh Boddu, Dave Touchette

In a recent breakthrough result, Chattopadhyay, Mande and Sherif [ECCC TR18-17] showed an exponential separation between the log approximate rank and randomized communication complexity of a total function $f$, hence refuting the log approximate rank conjecture of Lee and Shraibman [2009]. We provide an alternate proof of their randomized communication ... more >>>

Uma Girish, Ran Raz, Wei Zhan

We give a quantum logspace algorithm for powering contraction matrices, that is, matrices with spectral norm at most 1. The algorithm gets as an input an arbitrary $n\times n$ contraction matrix $A$, and a parameter $T \leq poly(n)$ and outputs the entries of $A^T$, up to (arbitrary) polynomially small additive ... more >>>

Uma Girish, Ran Raz, Wei Zhan

In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an information-theoretically secure) streaming proof with a quantum logspace prover and a classical logspace verifier. The prover provides a polynomial-length proof that is streamed to ... more >>>

Kun He, Qian Li, Xiaoming Sun, Jiapeng Zhang

Lov{\'a}sz Local Lemma (LLL) is a very powerful tool in combinatorics and probability theory to show the possibility of avoiding all ``bad" events under some ``weakly dependent" condition. Over the last decades, the algorithmic aspect of LLL has also attracted lots of attention in theoretical computer science \cite{moser2010constructive, kolipaka2011moser, harvey2015algorithmic}. ... more >>>

Scott Aaronson

We consider the following problem: estimate the size of a nonempty set $S\subseteq\left[ N\right] $, given both quantum queries to a membership oracle for $S$, and a device that generates equal superpositions $\left\vert S\right\rangle $ over $S$ elements. We show that, if $\left\vert S\right\vert $ is neither too large nor ... more >>>

Aran Nayebi, Scott Aaronson, Aleksandrs Belovs, Luca Trevisan

Given a random permutation $f: [N] \to [N]$ as a black box and $y \in [N]$, we want to output $x = f^{-1}(y)$. Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on the permutation but \emph{not} on ... more >>>

Scott Aaronson

We revisit the oft-neglected 'recursive Fourier sampling' (RFS) problem, introduced by Bernstein and Vazirani to prove an oracle separation between BPP and BQP. We show that the known quantum algorithm for RFS is essentially optimal, despite its seemingly wasteful need to uncompute information. This implies that, to place BQP outside ... more >>>

Scott Aaronson, Robin Kothari, William Kretschmer, Justin Thaler

This paper proves new limitations on the power of quantum computers to solve approximate counting---that is, multiplicatively estimating the size of a nonempty set $S\subseteq [N]$.

Given only a membership oracle for $S$, it is well known that approximate counting takes $\Theta(\sqrt{N/|S|})$ quantum queries. But what if a quantum algorithm ... more >>>

Alexei Kitaev

We present a polynomial quantum algorithm for the Abelian stabilizer problem

which includes both factoring and the discrete logarithm. Thus we extend famous

Shor's results. Our method is based on a procedure for measuring an eigenvalue

of a unitary operator. Another application of this

procedure is a polynomial ...
more >>>

Nai-Hui Chia, Chi-Ning Chou, Jiayu Zhang, Ruizhe Zhang

In this work, we initiate the study of the Minimum Circuit Size Problem (MCSP) in the quantum setting. MCSP is a problem to compute the circuit complexity of Boolean functions. It is a fascinating problem in complexity theory---its hardness is mysterious, and a better understanding of its hardness can have ... more >>>

Scott Aaronson, Paul Christiano

Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. We propose the first quantum money scheme that is (1) public-key, meaning that anyone can verify a banknote as genuine, not only the bank that ... more >>>

Debajyoti Bera

We define a complexity class for randomized algorithms with one-sided error that is exactly equal to a constant (unlike the usual definitions, in which the error is only bounded above or below by a constant). We show that the corresponding quantum classes (one each for a different error probability) are ... more >>>

Bo'az Klartag, Oded Regev

In STOC 1999, Raz presented a (partial) function for which there is a quantum protocol

communicating only $O(\log n)$ qubits, but for which any classical (randomized, bounded-error) protocol requires $\poly(n)$ bits of communication. That quantum protocol requires two rounds of communication. Ever since Raz's paper it was open whether the ...
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Joseph Fitzsimons, Zhengfeng Ji, Thomas Vidick, Henry Yuen

We show that any language in nondeterministic time $\exp(\exp(\cdots\exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical polynomial-time verifier and a constant number of quantum entangled provers, with completeness $1$ and soundness $1 - \exp(-C\exp(\cdots\exp(n)))$, ... more >>>

Andrew Drucker, Ronald de Wolf

Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and the quantum toolbox they use.

more >>>Marcel Dall'Agnol, Tom Gur, Subhayan Roy Moulik, Justin Thaler

We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof and are required to accept inputs having a property $\Pi$ and reject ... more >>>

Vikraman Arvind, Partha Mukhopadhyay

Motivated by the quantum algorithm in \cite{MN05} for testing

commutativity of black-box groups, we study the following problem:

Given a black-box finite ring $R=\angle{r_1,\cdots,r_k}$ where

$\{r_1,r_2,\cdots,r_k\}$ is an additive generating set for $R$ and a

multilinear polynomial $f(x_1,\cdots,x_m)$ over $R$ also accessed as

a ...
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Sourav Chakraborty, Arkadev Chattopadhyay, Nikhil Mande, Manaswi Paraashar

Buhrman, Cleve and Wigderson (STOC'98) observed that for every Boolean function $f : \{-1, 1\}^n \to \{-1, 1\}$ and $\bullet : \{-1, 1\}^2 \to \{-1, 1\}$ the two-party bounded-error quantum communication complexity of $(f \circ \bullet)$ is $O(Q(f) \log n)$, where $Q(f)$ is the bounded-error quantum query complexity of $f$. ... more >>>

Andris Ambainis, Joseph Emerson

A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate quantum t-designs for arbitrary t.

We then show that an ... more >>>

Anthony Leverrier, Gilles Zémor

Tanner codes are long error correcting codes obtained from short codes and a graph, with bits on the edges and parity-check constraints from the short codes enforced at the vertices of the graph. Combining good short codes together with a spectral expander graph yields the celebrated expander codes of Sipser ... more >>>

Paul Beame, Niels Kornerup

We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra problems---including matrix-vector product, matrix inversion, matrix multiplication and powering---existing ... more >>>

Scott Aaronson, Greg Kuperberg

This paper studies whether quantum proofs are more powerful than

classical proofs, or in complexity terms, whether QMA=QCMA. We prove

two results about this question. First, we give a "quantum oracle

separation" between QMA and QCMA. More concretely, we show that any

quantum algorithm needs order sqrt(2^n/(m+1)) queries to find ...
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Vahid Reza Asadi, Alexander Golovnev, Tom Gur, Igor Shinkar, Sathyawageeswar Subramanian

We study the problem of designing worst-case to average-case reductions for quantum algorithms. For all linear problems, we provide an explicit and efficient transformation of quantum algorithms that are only correct on a small (even sub-constant) fraction of their inputs into ones that are correct on all inputs. This stands ... more >>>

Dan Boneh, Mark Zhandry

We construct the first Message Authentication Codes (MACs) that are existentially unforgeable against a quantum chosen message attack. These chosen message attacks model a quantum adversary’s ability to obtain the MAC on a superposition of messages of its choice. We begin by showing that a quantum secure PRF is sufficient ... more >>>

Eli Ben-Sasson, Alessandro Chiesa, Ariel Gabizon, Madars Virza

The seminal result that every language having an interactive proof also has a zero-knowledge interactive proof assumes the existence of one-way functions. Ostrovsky and Wigderson (ISTCS 1993) proved that this assumption is necessary: if one-way functions do not exist, then only languages in BPP have zero-knowledge interactive proofs.

Ben-Or et ... more >>>

Ramprasad Saptharishi, Anamay Tengse

We study the class of non-commutative Unambiguous circuits or Unique-Parse-Tree (UPT) circuits, and a related model of Few-Parse-Trees (FewPT) circuits (which were recently introduced by Lagarde, Malod and Perifel [LMP16] and Lagarde, Limaye and Srinivasan [LLS17]) and give the following constructions:

• An explicit hitting set of quasipolynomial size for ...
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Manindra Agrawal, Chandan Saha, Nitin Saxena

We call a depth-$4$ formula $C$ $\textit{ set-depth-4}$ if there exists a (unknown) partition $X_1\sqcup\cdots\sqcup X_d$ of the variable indices $[n]$ that the top product layer respects, i.e. $C(\mathbf{x})=\sum_{i=1}^k {\prod_{j=1}^{d} {f_{i,j}(\mathbf{x}_{X_j})}}$ $ ,$ where $f_{i,j}$ is a $\textit{sparse}$ polynomial in $\mathbb{F}[\mathbf{x}_{X_j}]$. Extending this definition to any depth - we call ... more >>>

Ronen Shaltiel, Swastik Kopparty, Jad Silbak

We consider codes for space bounded channels. This is a model for communication under noise that was studied by Guruswami and Smith (J. ACM 2016) and lies between the Shannon (random) and Hamming (adversarial) models. In this model, a channel is a space bounded procedure that reads the codeword in ... more >>>

Michael Forbes, Amir Shpilka

We study the problem of obtaining efficient, deterministic, black-box polynomial identity testing (PIT) algorithms for read-once oblivious algebraic branching programs (ABPs). This class has an efficient, deterministic, white-box polynomial identity testing algorithm (due to Raz and Shpilka), but prior to this work had no known such black-box algorithm. Here we ... more >>>

Harm Derksen, Emanuele Viola

Let $G$ be a group such that any non-trivial representation has dimension

at least $d$. Let $X=(X_{1},X_{2},\ldots,X_{t})$ and $Y=(Y_{1},Y_{2},\ldots,Y_{t})$

be distributions over $G^{t}$. Suppose that $X$ is independent from

$Y$. We show that for any $g\in G$ we have

\[

\left|\mathbb{P}[X_{1}Y_{1}X_{2}Y_{2}\cdots X_{t}Y_{t}=g]-1/|G|\right|\le\frac{|G|^{2t-1}}{d^{t-1}}\sqrt{\mathbb{E}_{h\in G^{t}}X(h)^{2}}\sqrt{\mathbb{E}_{h\in G^{t}}Y(h)^{2}}.

\]

Our results generalize, improve, and ...
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Akinori Kawachi, Benjamin Rossman, Osamu Watanabe

We propose an abstract framework for studying search-to-decision reductions for NP. Specifically, we study the following witness finding problem: for a hidden nonempty set $W\subseteq\{0,1\}^n$, the goal is to output a witness in $W$ with constant probability by making randomized queries of the form ``is $Q\cap W$ nonempty?''\ where $Q\subseteq\{0,1\}^n$. ... more >>>

Thomas Watson

An errorless circuit for a boolean function is one that outputs the correct answer or ``don't know'' on each input (and never outputs the wrong answer). The goal of errorless hardness amplification is to show that if $f$ has no size $s$ errorless circuit that outputs ``don't know'' on at ... more >>>

Noga Ron-Zewi, Ronen Shaltiel, Nithin Varma

A binary code $\text{Enc}:\{0,1\}^k \rightarrow \{0,1\}^n$ is $(\frac{1}{2}-\varepsilon,L)$-list decodable if for every $w \in \{0,1\}^n$, there exists a set $\text{List}(w)$ of size at most $L$, containing all messages $m \in \{0,1\}^k$ such that the relative Hamming distance between $\text{Enc}(m)$ and $w$ is at most $\frac{1}{2}-\varepsilon$.

A $q$-query local list-decoder is ...
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Sourav Chakraborty, Eldar Fischer, Arie Matsliah

We investigate the problem of {\em local reconstruction}, as defined by Saks and Seshadhri (2008), in the context of error correcting codes.

The first problem we address is that of {\em message reconstruction}, where given oracle access to a corrupted encoding $w \in \zo^n$ of some message $x \in \zo^k$ ... more >>>

Arijit Bishnu, Arijit Ghosh, Gopinath Mishra, Manaswi Paraashar

In this work, we resolve the query complexity of global minimum cut problem for a graph by designing a randomized algorithm for approximating the size of minimum cut in a graph, where the graph can be accessed through local queries like \textsc{Degree}, \textsc{Neighbor}, and \textsc{Adjacency} queries.

Given $\epsilon \in (0,1)$, ... more >>>

Ivan Hu, Andrew Morgan, Dieter van Melkebeek

We consider the following computational problem: Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the well-known problem of counting inversions in arrays originated in mathematical psychology. It ... more >>>

Raghav Kulkarni, Miklos Santha

Let $\mathcal{M}$ be a bridgeless matroid on ground set $\{1,\ldots, n\}$ and $f_{\mathcal{M}}: \{0,1\}^n \to \{0, 1\}$ be the indicator function of its independent sets. A folklore fact is that $f_\mathcal{M}$ is ``evasive," i.e., $D(f_\mathcal{M}) = n$ where $D(f)$ denotes the deterministic decision tree complexity of $f.$ Here we prove ... more >>>

Arkadev Chattopadhyay, Yogesh Dahiya, Meena Mahajan

We relate various complexity measures like sensitivity, block sensitivity, certificate complexity for multi-output functions to the query complexities of such functions. Using these relations, we improve upon the known relationship between pseudo-deterministic query complexity and deterministic query complexity for total search problems: We show that pseudo-deterministic query complexity is at ... more >>>

Yeow Meng Chee, Tao Feng, San Ling, Huaxiong Wang, Liang Feng Zhang

A $k$-query locally decodable code (LDC)

$\textbf{C}:\Sigma^{n}\rightarrow \Gamma^{N}$ encodes each message $x$ into

a codeword $\textbf{C}(x)$ such that each symbol of $x$ can be probabilistically

recovered by querying only $k$ coordinates of $\textbf{C}(x)$, even after a

constant fraction of the coordinates have been corrupted.

Yekhanin (2008)

constructed a $3$-query LDC ...
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Mika Göös, Toniann Pitassi, Thomas Watson

For any $n$-bit boolean function $f$, we show that the randomized communication complexity of the composed function $f\circ g^n$, where $g$ is an index gadget, is characterized by the randomized decision tree complexity of $f$. In particular, this means that many query complexity separations involving randomized models (e.g., classical vs.\ ... more >>>

Mika Göös, Pritish Kamath, Toniann Pitassi, Thomas Watson

We prove that the $\text{P}^{\small\text{NP}}$-type query complexity (alternatively, decision list width) of any boolean function $f$ is quadratically related to the $\text{P}^{\small\text{NP}}$-type communication complexity of a lifted version of $f$. As an application, we show that a certain "product" lower bound method of Impagliazzo and Williams (CCC 2010) fails to ... more >>>

Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, Toniann Pitassi

Lifting theorems are theorems that relate the query complexity of a function $f:\left\{ 0,1 \right\}^n\to \left\{ 0,1 \right\}$ to the communication complexity of the composed function $f\circ g^n$, for some “gadget” $g:\left\{ 0,1 \right\}^b\times \left\{ 0,1 \right\}^b\to \left\{ 0,1 \right\}$. Such theorems allow transferring lower bounds from query complexity to ... more >>>