All reports in year 2023:

__
TR23-144
| 22nd September 2023
__

Lijie Chen, Shuichi Hirahara, Hanlin Ren#### Symmetric Exponential Time Requires Near-Maximum Circuit Size

__
TR23-143
| 22nd September 2023
__

Noam Mazor, Rafael Pass#### Counting Unpredictable Bits: A Simple PRG from One-way Functions

Revisions: 1

__
TR23-142
| 21st September 2023
__

Tom Gur, Wilfred Salmon, Sergii Strelchuk#### Provable Advantage in Quantum PAC Learning

__
TR23-141
| 19th September 2023
__

Nader Bshouty, Gergely Harcos#### A Tight Lower Bound of $\Omega(\log n)$ for the Estimation of the Number of Defective Items

__
TR23-140
| 20th September 2023
__

Eshan Chattopadhyay, Jesse Goodman, Mohit Gurumukhani#### Extractors for Polynomial Sources over $\mathbb{F}_2$

__
TR23-139
| 18th September 2023
__

Mrinal Kumar, Varun Ramanathan, Ramprasad Saptharishi#### Deterministic Algorithms for Low Degree Factors of Constant Depth Circuits

__
TR23-138
| 12th September 2023
__

Lianna Hambardzumyan, Toniann Pitassi, Suhail Sherif, Morgan Shirley, Adi Shraibman#### An improved protocol for ExactlyN with more than 3 players

__
TR23-137
| 10th September 2023
__

Mi-Ying Huang, Xinyu Mao, Guangxu Yang, Jiapeng Zhang#### Communication Lower Bounds of Key-Agreement Protocols via Density Increment Arguments

__
TR23-136
| 14th September 2023
__

Benny Applebaum, Oded Nir#### Advisor-Verifier-Prover Games and the Hardness of Information Theoretic Cryptography

__
TR23-135
| 14th September 2023
__

Prerona Chatterjee, Anamay Tengse#### On Annihilators of Explicit Polynomial Maps

__
TR23-134
| 14th September 2023
__

Oded Goldreich#### On the complexity of enumerating ordered sets

__
TR23-133
| 13th September 2023
__

David Ellis, Guy Kindler, Noam Lifshitz, Dor Minzer#### Product mixing in compact Lie groups

__
TR23-132
| 12th September 2023
__

Yogesh Dahiya, Meena Mahajan, Sasank Mouli#### New lower bounds for Polynomial Calculus over non-Boolean bases

__
TR23-131
| 8th September 2023
__

Meghal Gupta, Rachel Zhang#### On Interactive Coding Schemes with Adaptive Termination

__
TR23-130
| 8th September 2023
__

Eshan Chattopadhyay, Jyun-Jie Liao#### Recursive Error Reduction for Regular Branching Programs

__
TR23-129
| 21st August 2023
__

Sravanthi Chede, Leroy Chew, Balesh Kumar, Anil Shukla#### Understanding Nullstellensatz for QBFs

__
TR23-128
| 30th August 2023
__

Xue Chen, Kuan Cheng, Xin Li, Songtao Mao#### Random Shortening of Linear Codes and Application

__
TR23-127
| 30th August 2023
__

Irit Dinur, Siqi Liu, Rachel Zhang#### New Codes on High Dimensional Expanders

__
TR23-126
| 25th August 2023
__

Omar Alrabiah, Venkatesan Guruswami, Ray Li#### AG codes have no list-decoding friends: Approaching the generalized Singleton bound requires exponential alphabets

__
TR23-125
| 25th August 2023
__

Omar Alrabiah, Venkatesan Guruswami, Ray Li#### Randomly punctured Reed-Solomon codes achieve list-decoding capacity over linear-sized fields

__
TR23-124
| 24th August 2023
__

Zander Kelley, Shachar Lovett, Raghu Meka#### Explicit separations between randomized and deterministic Number-on-Forehead communication

__
TR23-123
| 21st August 2023
__

Noam Mazor#### Key-Agreement with Perfect Completeness from Random Oracles

__
TR23-122
| 9th August 2023
__

Vikraman Arvind, Abhranil Chatterjee#### On Lifting Lower Bounds for Noncommutative Circuits using Automata

__
TR23-121
| 19th August 2023
__

Theodoros Papamakarios#### Depth d Frege systems are not automatable unless P=NP

Revisions: 1

__
TR23-120
| 18th August 2023
__

Mitali Bafna, Dor Minzer#### Characterizing Direct Product Testing via Coboundary Expansion

__
TR23-119
| 18th August 2023
__

Yotam Dikstein, Irit Dinur#### Agreement theorems for high dimensional expanders in the small soundness regime: the role of covers

__
TR23-118
| 17th August 2023
__

Hugo Aaronson, Tom Gur, Ninad Rajgopal, Ron Rothblum#### Distribution-Free Proofs of Proximity

__
TR23-117
| 9th August 2023
__

François Le Gall, Yupan Liu, Qisheng Wang#### Space-bounded quantum state testing via space-efficient quantum singular value transformation

__
TR23-116
| 12th August 2023
__

Amey Bhangale, Subhash Khot, Dor Minzer#### Effective Bounds for Restricted $3$-Arithmetic Progressions in $\mathbb{F}_p^n$

__
TR23-115
| 8th August 2023
__

Abhranil Chatterjee, Mrinal Kumar, Ben Lee Volk#### Determinants vs. Algebraic Branching Programs

Revisions: 1

__
TR23-114
| 8th August 2023
__

Lijie Chen, William Hoza, Xin Lyu, Avishay Tal, Hongxun Wu#### Weighted Pseudorandom Generators via Inverse Analysis of Random Walks and Shortcutting

__
TR23-113
| 8th August 2023
__

Justin Holmgren, Ron Rothblum#### Linear-Size Boolean Circuits for Multiselection

__
TR23-112
| 30th July 2023
__

Amey Bhangale, Subhash Khot, Dor Minzer#### On Approximability of Satisfiable k-CSPs: IV

__
TR23-111
| 29th July 2023
__

Vaibhav Krishan#### $\mathit{MidBit}^+$, Torus Polynomials and Non-classical Polynomials: Equivalences for $\mathit{ACC}$ Lower Bounds

__
TR23-110
| 25th July 2023
__

Gil Cohen, Tal Yankovitz#### Asymptotically-Good RLCCs with $(\log{n})^{2+o(1)}$ Queries

__
TR23-109
| 21st July 2023
__

Pranav Bisht, Nikhil Gupta, Ilya Volkovich#### Towards Identity Testing for Sums of Products of Read-Once and Multilinear Bounded-Read Formulae

__
TR23-108
| 21st July 2023
__

Andrej Bogdanov, TsunMing Cheung, Krishnamoorthy Dinesh, John C.S. Lui#### Classical simulation of one-query quantum distinguishers

__
TR23-107
| 20th July 2023
__

Uma Girish, Ran Raz, Wei Zhan#### Quantum Logspace Computations are Verifiable

__
TR23-106
| 17th July 2023
__

Mika Göös, Ziyi Guan, Tiberiu Mosnoi#### Depth-3 Circuits for Inner Product

__
TR23-105
| 13th July 2023
__

Lijie Chen, Roei Tell, Ryan Williams#### Derandomization vs Refutation: A Unified Framework for Characterizing Derandomization

__
TR23-104
| 14th July 2023
__

Meghal Gupta, Rachel Zhang#### A Noise Resilient Transformation for Streaming Algorithms

__
TR23-103
| 12th July 2023
__

Yanyi Liu, Rafael Pass#### On One-way Functions and the Worst-case Hardness of Time-Bounded Kolmogorov Complexity

Revisions: 1

__
TR23-102
| 13th July 2023
__

Chin Ho Lee, Edward Pyne, Salil Vadhan#### On the Power of Regular and Permutation Branching Programs

__
TR23-101
| 5th July 2023
__

Renato Ferreira Pinto Jr.#### Directed Poincaré Inequalities and $L^1$ Monotonicity Testing of Lipschitz Functions

__
TR23-100
| 6th July 2023
__

Shuichi Hirahara, Mikito Nanashima#### Learning in Pessiland via Inductive Inference

__
TR23-099
| 8th July 2023
__

Sourav Chakraborty, Chandrima Kayal, Rajat Mittal, Manaswi Paraashar, Swagato Sanyal, Nitin Saurabh#### On the Composition of Randomized Query Complexity and Approximate Degree

Revisions: 1

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TR23-098
| 5th July 2023
__

Andrej Bogdanov, Pravesh Kothari, Alon Rosen#### Public-Key Encryption, Local Pseudorandom Generators, and the Low-Degree Method

__
TR23-097
| 2nd July 2023
__

Joshua Cook, Ron D. Rothblum#### Efficient Interactive Proofs for Non-Deterministic Bounded Space

Revisions: 1

__
TR23-096
| 28th June 2023
__

Huacheng Yu, Wei Zhan#### Randomized vs. Deterministic Separation in Time-Space Tradeoffs of Multi-Output Functions

__
TR23-095
| 21st June 2023
__

David Heath, Vladimir Kolesnikov, Rafail Ostrovsky#### Tri-State Circuits: A Circuit Model that Captures RAM

__
TR23-094
| 29th June 2023
__

Lijie Chen, Roei Tell#### New ways of studying the BPP = P conjecture

__
TR23-093
| 29th June 2023
__

Vinayak Kumar, Geoffrey Mon#### Relaxed Local Correctability from Local Testing

__
TR23-092
| 28th June 2023
__

Swastik Kopparty, Vishvajeet N#### Extracting Mergers and Projections of Partitions

__
TR23-091
| 18th June 2023
__

Benny Applebaum, Amos Beimel, Yuval Ishai, Eyal Kushilevitz, Tianren Liu, Vinod Vaikuntanathan#### Succinct Computational Secret Sharing

__
TR23-090
| 15th June 2023
__

Itay Cohen, Roy Roth, Amnon Ta-Shma#### HDX Condensers

__
TR23-089
| 15th June 2023
__

Louis Golowich#### New Explicit Constant-Degree Lossless Expanders

__
TR23-088
| 1st June 2023
__

Parker Newton, Silas Richelson, Chase Wilson#### A High Dimensional Goldreich-Levin Theorem

__
TR23-087
| 9th June 2023
__

Benny Applebaum, Oded Nir, Benny Pinkas#### How to Recover a Secret with $O(n)$ Additions

Revisions: 1

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TR23-086
| 8th June 2023
__

Dmitry Sokolov#### Random $(\log n)$-CNF are Hard for Cutting Planes (Again)

__
TR23-085
| 4th June 2023
__

Ari Karchmer#### Average-Case PAC-Learning from Nisan's Natural Proofs

Revisions: 1

__
TR23-084
| 31st May 2023
__

Itai Dinur#### Time-Space Lower Bounds for Bounded-Error Computation in the Random-Query Model

__
TR23-083
| 2nd June 2023
__

Srinivasan A, Uma Girish#### Trade-offs between Entanglement and Communication

__
TR23-082
| 1st June 2023
__

Ryan Williams#### Self-Improvement for Circuit-Analysis Problems

__
TR23-081
| 1st June 2023
__

Noga Amit, Guy Rothblum#### Constant-Round Arguments from One-Way Functions

__
TR23-080
| 1st June 2023
__

Halley Goldberg, Valentine Kabanets#### Improved Learning from Kolmogorov Complexity

__
TR23-079
| 31st May 2023
__

Russell Impagliazzo, Valentine Kabanets, Ilya Volkovich#### Mutual Empowerment between Circuit Obfuscation and Circuit Minimization

__
TR23-078
| 30th May 2023
__

Or Meir#### Toward Better Depth Lower Bounds: A KRW-like theorem for Strong Composition

Revisions: 3

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TR23-077
| 25th May 2023
__

Nir Bitansky, Chethan Kamath, Omer Paneth, Ron Rothblum, Prashant Nalini Vasudevan#### Batch Proofs are Statistically Hiding

Revisions: 2

__
TR23-076
| 24th May 2023
__

Lijie Chen, Zhenjian Lu, Igor Carboni Oliveira, Hanlin Ren, Rahul Santhanam#### Polynomial-Time Pseudodeterministic Construction of Primes

__
TR23-075
| 17th May 2023
__

Abhranil Chatterjee, Sumanta Ghosh, Rohit Gurjar, Roshan Raj#### Border Complexity of Symbolic Determinant under Rank One Restriction

__
TR23-074
| 14th May 2023
__

Abhibhav Garg, Rafael Mendes de Oliveira, Shir Peleg, Akash Sengupta#### Radical Sylvester-Gallai Theorem for Tuples of Quadratics

__
TR23-073
| 15th May 2023
__

Xi Chen, Yuhao Li, Mihalis Yannakakis#### Reducing Tarski to Unique Tarski (in the Black-box Model)

__
TR23-072
| 18th May 2023
__

Yeyuan Chen, Yizhi Huang, Jiatu Li, Hanlin Ren#### Range Avoidance, Remote Point, and Hard Partial Truth Tables via Satisfying-Pairs Algorithms

__
TR23-071
| 8th May 2023
__

Yuval Filmus, Itai Leigh, Artur Riazanov, Dmitry Sokolov#### Sampling and Certifying Symmetric Functions

__
TR23-070
| 9th May 2023
__

Shuichi Hirahara, Zhenjian Lu, Hanlin Ren#### Bounded Relativization

__
TR23-069
| 11th May 2023
__

Bruno Pasqualotto Cavalar, Igor Carboni Oliveira#### Constant-depth circuits vs. monotone circuits

__
TR23-068
| 10th May 2023
__

Ben Davis, Robert Robere#### Colourful TFNP and Propositional Proofs

Revisions: 1

__
TR23-067
| 7th May 2023
__

Guy Goldberg#### Linear Relaxed Locally Decodable and Correctable Codes Do Not Need Adaptivity and Two-Sided Error

__
TR23-066
| 4th May 2023
__

Klim Efremenko, Gillat Kol, Dmitry Paramonov, Raghuvansh Saxena#### Protecting Single-Hop Radio Networks from Message Drops

__
TR23-065
| 4th May 2023
__

Louis Golowich#### From Grassmannian to Simplicial High-Dimensional Expanders

__
TR23-064
| 3rd May 2023
__

Oded Goldreich#### On the Lower Bound on the Length of Relaxed Locally Decodable Codes

__
TR23-063
| 2nd May 2023
__

Jacobo Toran, Florian Wörz#### Cutting Planes Width and the Complexity of Graph Isomorphism Refutations

__
TR23-062
| 2nd May 2023
__

Benny Applebaum, Eliran Kachlon#### Conflict Checkable and Decodable Codes and Their Applications

__
TR23-061
| 2nd May 2023
__

Abhimanyu Choudhury, Meena Mahajan#### Dependency schemes in CDCL-based QBF solving: a proof-theoretic study

__
TR23-060
| 17th April 2023
__

Sagnik Saha, Nikolaj Schwartzbach, Prashant Nalini Vasudevan#### The Planted $k$-SUM Problem: Algorithms, Lower Bounds, Hardness Amplification, and Cryptography

__
TR23-058
| 23rd April 2023
__

Xin Li, Yan Zhong#### Explicit Directional Affine Extractors and Improved Hardness for Linear Branching Programs

__
TR23-057
| 27th April 2023
__

Iddo Tzameret, Luming Zhang#### Stretching Demi-Bits and Nondeterministic-Secure Pseudorandomness

__
TR23-056
| 26th April 2023
__

Geoffrey Mon, Dana Moshkovitz, Justin Oh#### Approximate Locally Decodable Codes with Constant Query Complexity and Nearly Optimal Rate

__
TR23-055
| 20th April 2023
__

Amey Bhangale, Subhash Khot, Dor Minzer#### On Approximability of Satisfiable $k$-CSPs: II

Revisions: 1

__
TR23-054
| 20th April 2023
__

Amey Bhangale, Subhash Khot, Dor Minzer#### On Approximability of Satisfiable $k$-CSPs: III

__
TR23-053
| 19th April 2023
__

Leroy Chew#### Proof Simulation via Round-based Strategy Extraction for QBF

__
TR23-052
| 19th April 2023
__

Noah Fleming, Vijay Ganesh, Antonina Kolokolova, Chunxiao Li, Marc Vinyals#### Limits of CDCL Learning via Merge Resolution

__
TR23-051
| 18th April 2023
__

Benjamin Böhm, Olaf Beyersdorff#### QCDCL vs QBF Resolution: Further Insights

__
TR23-050
| 18th April 2023
__

Manasseh Ahmed, TsunMing Cheung, Hamed Hatami, Kusha Sareen#### Communication complexity of half-plane membership

__
TR23-049
| 17th April 2023
__

Mika Göös, Artur Riazanov, Anastasia Sofronova, Dmitry Sokolov#### Top-Down Lower Bounds for Depth-Four Circuits

__
TR23-048
| 4th April 2023
__

Hadley Black, Deeparnab Chakrabarty, C. Seshadhri#### A $d^{1/2+o(1)}$ Monotonicity Tester for Boolean Functions on $d$-Dimensional Hypergrids

__
TR23-047
| 2nd April 2023
__

Hunter Monroe#### Ruling Out Short Proofs of Unprovable Sentences is Hard

__
TR23-046
| 13th April 2023
__

Yizhi Huang, Rahul Ilango, Hanlin Ren#### NP-Hardness of Approximating Meta-Complexity: A Cryptographic Approach

__
TR23-045
| 13th April 2023
__

Vinayak Kumar#### Tight Correlation Bounds for Circuits Between AC0 and TC0

Revisions: 1

__
TR23-044
| 28th March 2023
__

Sourav Chakraborty, Chandrima Kayal, Manaswi Paraashar#### Separations between Combinatorial Measures for Transitive Functions

__
TR23-043
| 9th April 2023
__

Yotam Dikstein, Irit Dinur#### Coboundary and cosystolic expansion without dependence on dimension or degree

__
TR23-042
| 3rd April 2023
__

Johan Håstad#### On small-depth Frege proofs for PHP

__
TR23-041
| 1st April 2023
__

Lila Fontes, Sophie Laplante, Mathieu Lauriere, Alexandre Nolin#### The communication complexity of functions with large outputs

__
TR23-040
| 28th March 2023
__

Edward Pyne, Ran Raz, Wei Zhan#### Certified Hardness vs. Randomness for Log-Space

__
TR23-039
| 28th March 2023
__

Arkadev Chattopadhyay, Yogesh Dahiya, Meena Mahajan#### Query Complexity of Search Problems

Revisions: 1

__
TR23-038
| 28th March 2023
__

Rahul Ilango, Jiatu Li, Ryan Williams#### Indistinguishability Obfuscation, Range Avoidance, and Bounded Arithmetic

__
TR23-037
| 28th March 2023
__

Shuichi Hirahara#### Capturing One-Way Functions via NP-Hardness of Meta-Complexity

__
TR23-036
| 27th March 2023
__

Dean Doron, Roei Tell#### Derandomization with Minimal Memory Footprint

__
TR23-035
| 22nd March 2023
__

Shuichi Hirahara, Rahul Ilango, Zhenjian Lu, Mikito Nanashima, Igor Carboni Oliveira#### A Duality Between One-Way Functions and Average-Case Symmetry of Information

__
TR23-034
| 24th March 2023
__

Oded Goldreich#### On teaching the approximation method for circuit lower bounds

Revisions: 1

__
TR23-033
| 24th March 2023
__

Sumanta Ghosh, Prahladh Harsha, Simao Herdade, Mrinal Kumar, Ramprasad Saptharishi#### Fast Numerical Multivariate Multipoint Evaluation

Revisions: 1

__
TR23-032
| 24th March 2023
__

Vishwas Bhargava, Shubhangi Saraf, Ilya Volkovich#### Linear Independence, Alternants and Applications

__
TR23-031
| 23rd March 2023
__

Benny Applebaum, Eliran Kachlon, Arpita Patra#### The Round Complexity of Statistical MPC with Optimal Resiliency

__
TR23-030
| 21st March 2023
__

Jan Krajicek#### A proof complexity conjecture and the Incompleteness theorem

__
TR23-029
| 18th March 2023
__

Nicollas Sdroievski, Dieter van Melkebeek#### Instance-Wise Hardness versus Randomness Tradeoffs for Arthur-Merlin Protocols

__
TR23-028
| 15th March 2023
__

Rahul Santhanam#### An Algorithmic Approach to Uniform Lower Bounds

__
TR23-027
| 8th March 2023
__

Joseph Zalewski#### Some Lower Bounds Related to the Missing String Problem

__
TR23-026
| 15th March 2023
__

Shuichi Hirahara, Nobutaka Shimizu#### Hardness Self-Amplification: Simplified, Optimized, and Unified

__
TR23-025
| 10th March 2023
__

Vikraman Arvind, Pushkar Joglekar#### Multivariate to Bivariate Reduction for Noncommutative Polynomial Factorization

__
TR23-024
| 9th March 2023
__

Mark Bun, Nadezhda Voronova#### Approximate degree lower bounds for oracle identification problems

Revisions: 1

__
TR23-023
| 13th March 2023
__

Xin Li#### Two Source Extractors for Asymptotically Optimal Entropy, and (Many) More

Revisions: 1

__
TR23-022
| 11th March 2023
__

Jiatu Li, Igor Carboni Oliveira#### Unprovability of strong complexity lower bounds in bounded arithmetic

__
TR23-021
| 9th March 2023
__

Karthik Gajulapalli, Alexander Golovnev, Satyajeet Nagargoje, Sidhant Saraogi#### Range Avoidance for Constant-Depth Circuits: Hardness and Algorithms

Revisions: 2

__
TR23-020
| 3rd March 2023
__

Scott Aaronson, Shih-Han Hung#### Certified Randomness from Quantum Supremacy

__
TR23-019
| 2nd March 2023
__

Pooya Hatami, William Hoza#### Theory of Unconditional Pseudorandom Generators

Revisions: 2

__
TR23-018
| 1st March 2023
__

Qipeng Liu, Ran Raz, Wei Zhan#### Memory-Sample Lower Bounds for Learning with Classical-Quantum Hybrid Memory

__
TR23-017
| 21st February 2023
__

Deepanshu Kush, Shubhangi Saraf#### Near-Optimal Set-Multilinear Formula Lower Bounds

__
TR23-016
| 22nd February 2023
__

Yuval Filmus, Edward Hirsch, Artur Riazanov, Alexander Smal, Marc Vinyals#### Proving Unsatisfiability with Hitting Formulas

__
TR23-015
| 20th February 2023
__

Scott Aaronson, Harry Buhrman, William Kretschmer#### A Qubit, a Coin, and an Advice String Walk Into a Relational Problem

__
TR23-014
| 16th February 2023
__

Tameem Choudhury, Karteek Sreenivasaiah#### Depth-3 Circuit Lower Bounds for k-OV

__
TR23-013
| 7th February 2023
__

Noam Mazor#### A Lower Bound on the Share Size in Evolving Secret Sharing

Revisions: 1

__
TR23-012
| 16th February 2023
__

Yogesh Dahiya, Vignesh K, Meena Mahajan, Karteek Sreenivasaiah#### Linear threshold functions in decision lists, decision trees, and depth-2 circuits

__
TR23-011
| 13th February 2023
__

Mikhail Dektiarev, Nikolay Vereshchagin#### Half-duplex communication complexity with adversary? can be less than the classical communication complexity

__
TR23-010
| 13th February 2023
__

Per Austrin, Kilian Risse#### Sum-of-Squares Lower Bounds for the Minimum Circuit Size Problem

__
TR23-009
| 14th February 2023
__

Hervé Fournier, Nutan Limaye, Guillaume Malod, Srikanth Srinivasan, Sébastien Tavenas#### Towards Optimal Depth-Reductions for Algebraic Formulas

__
TR23-008
| 2nd February 2023
__

Ond?ej Ježil#### Limits of structures and Total NP Search Problems

__
TR23-007
| 3rd February 2023
__

Jan Krajicek#### Extended Nullstellensatz proof systems

__
TR23-006
| 20th January 2023
__

Nader Bshouty#### Superpolynomial Lower Bounds for Learning Monotone Classes

Revisions: 1

__
TR23-005
| 13th January 2023
__

Paul Beame, Niels Kornerup#### Cumulative Memory Lower Bounds for Randomized and Quantum Computation

Revisions: 2

__
TR23-004
| 13th January 2023
__

Yinan Li, Youming Qiao, Avi Wigderson, Yuval Wigderson, Chuanqi Zhang#### On linear-algebraic notions of expansion

__
TR23-003
| 11th January 2023
__

Shachar Lovett, Jiapeng Zhang#### Streaming Lower Bounds and Asymmetric Set-Disjointness

__
TR23-002
| 5th January 2023
__

Noga Alon, Olivier Bousquet, Kasper Green Larsen, Shay Moran, Shlomo Moran#### Diagonalization Games

Revisions: 2

__
TR23-001
| 5th January 2023
__

Prerona Chatterjee, Pavel Hrubes#### New Lower Bounds against Homogeneous Non-Commutative Circuits

Lijie Chen, Shuichi Hirahara, Hanlin Ren

We show that there is a language in $\mathrm{S}_2\mathrm{E}/_1$ (symmetric exponential time with one bit of advice) with circuit complexity at least $2^n/n$. In particular, the above also implies the same near-maximum circuit lower bounds for the classes $\Sigma_2\mathrm{E}$, $(\Sigma_2\mathrm{E}\cap\Pi_2\mathrm{E})/_1$, and $\mathrm{ZPE}^{\mathrm{NP}}/_1$. Previously, only "half-exponential" circuit lower bounds for these ... more >>>

Noam Mazor, Rafael Pass

A central result in the theory of Cryptography, by Hastad, Imagliazzo, Luby and Levin [SICOMP’99], demonstrates that the existence one-way functions (OWF) implies the existence of pseudo-random generators (PRGs). Despite the fundamental importance of this result, and several elegant improvements/simplifications, analyses of constructions of PRGs from OWFs remain complex (both ... more >>>

Tom Gur, Wilfred Salmon, Sergii Strelchuk

We revisit the problem of characterising the complexity of Quantum PAC learning, as introduced by Bshouty and Jackson [SIAM J. Comput.

1998, 28, 1136–1153]. Several quantum advantages have been demonstrated in this setting, however, none are generic: they apply to particular concept classes and typically only work when the distribution ...
more >>>

Nader Bshouty, Gergely Harcos

Let $X$ be a set of items of size $n$ , which may contain some defective items denoted by $I$, where $I \subseteq X$. In group testing, a {\it test} refers to a subset of items $Q \subset X$. The test outcome is $1$ (positive) if $Q$ contains at least ... more >>>

Eshan Chattopadhyay, Jesse Goodman, Mohit Gurumukhani

We explicitly construct the first nontrivial extractors for degree $d \ge 2$ polynomial sources over $\mathbb{F}_2^n$. Our extractor requires min-entropy $k\geq n - \frac{\sqrt{\log n}}{(d\log \log n)^{d/2}}$. Previously, no constructions were known, even for min-entropy $k\geq n-1$. A key ingredient in our construction is an input reduction lemma, which allows ... more >>>

Mrinal Kumar, Varun Ramanathan, Ramprasad Saptharishi

For every constant $d$, we design a subexponential time deterministic algorithm that takes as input a multivariate polynomial $f$ given as a constant depth algebraic circuit over the field of rational numbers, and outputs all irreducible factors of $f$ of degree at most $d$ together with their respective multiplicities. Moreover, ... more >>>

Lianna Hambardzumyan, Toniann Pitassi, Suhail Sherif, Morgan Shirley, Adi Shraibman

The ExactlyN problem in the number-on-forehead (NOF) communication setting asks $k$ players, each of whom can see every input but their own, if the $k$ input numbers add up to $N$. Introduced by Chandra, Furst and Lipton in 1983, ExactlyN is important for its role in understanding the strength of ... more >>>

Mi-Ying Huang, Xinyu Mao, Guangxu Yang, Jiapeng Zhang

Constructing key-agreement protocols in the random oracle model (ROM) is a viable method to assess the feasibility of developing public-key cryptography within Minicrypt. Unfortunately, as shown by Impagliazzo and Rudich (STOC 1989) and Barak and Mahmoody (Crypto 2009), such protocols can only guarantee limited security: any $\ell$-query protocol can be ... more >>>

Benny Applebaum, Oded Nir

A major open problem in information-theoretic cryptography is to obtain a super-polynomial lower bound for the communication complexity of basic cryptographic tasks. This question is wide open even for very powerful non-interactive primitives such as private information retrieval (or locally-decodable codes), general secret sharing schemes, conditional disclosure of secrets, and ... more >>>

Prerona Chatterjee, Anamay Tengse

We study the algebraic complexity of annihilators of polynomials maps. In particular, when a polynomial map is `encoded by' a small algebraic circuit, we show that the coefficients of an annihilator of the map can be computed in PSPACE. Even when the underlying field is that of reals or complex ... more >>>

Oded Goldreich

We consider the complexity of enumerating ordered sets, defined as solving the following type of a computational problem: For a predetermined ordered set, given $i\in\N$, one is required to answer with the $i^{th}$ member of the set (according to the predetermined order).

Our focus is on countable sets such as ... more >>>

David Ellis, Guy Kindler, Noam Lifshitz, Dor Minzer

If $G$ is a group, we say a subset $S$ of $G$ is product-free if the equation $xy=z$ has no solutions with $x,y,z \in S$. For $D \in \mathbb{N}$, a group $G$ is said to be $D$-quasirandom if the minimal dimension of a nontrivial complex irreducible representation of $G$ is ... more >>>

Yogesh Dahiya, Meena Mahajan, Sasank Mouli

In this paper, we obtain new size lower bounds for proofs in the

Polynomial Calculus (PC) proof system, in two different settings.

1. When the Boolean variables are encoded using $\pm 1$ (as opposed

to $0,1$): We establish a lifting theorem using an asymmetric gadget

$G$, showing ...
more >>>

Meghal Gupta, Rachel Zhang

In interactive coding, Alice and Bob wish to compute some function $f$ of their individual private inputs $x$ and $y$. They do this by engaging in an interactive protocol to jointly compute $f(x,y)$. The goal is to do this in an error-resilient way, such that even given some fraction of ... more >>>

Eshan Chattopadhyay, Jyun-Jie Liao

In a recent work, Chen, Hoza, Lyu, Tal and Wu (FOCS 2023) showed an improved error reduction framework for the derandomization of regular read-once branching programs (ROBPs). Their result is based on a clever modification to the inverse Laplacian perspective of space-bounded derandomization, which was originally introduced by Ahmadinejad, Kelner, ... more >>>

Sravanthi Chede, Leroy Chew, Balesh Kumar, Anil Shukla

QBF proof systems are routinely adapted from propositional logic along with adjustments for the new quantifications. Existing are two main successful frameworks, the reduction and expansion frameworks, inspired by QCDCL [Zhang et al. ICCAD.'2002] and CEGAR solving [Janota et al. Artif. Intell.'2016] respectively. However, the reduction framework, while immensely useful ... more >>>

Xue Chen, Kuan Cheng, Xin Li, Songtao Mao

Random linear codes (RLCs) are well known to have nice combinatorial properties and near-optimal parameters in many different settings. However, getting explicit constructions matching the parameters of RLCs is challenging, and RLCs are hard to decode efficiently. This motivated several previous works to study the problem of partially derandomizing RLCs, ... more >>>

Irit Dinur, Siqi Liu, Rachel Zhang

We describe a new family of symmetric error-correcting codes with low-density parity-check matrices (LDPC).

Our codes can be described in two seemingly different ways. First, in relation to Reed-Muller codes: our codes are functions on a subset of $\mathbb{F}^n$ whose restrictions to a prescribed set of affine lines has low ... more >>>

Omar Alrabiah, Venkatesan Guruswami, Ray Li

A simple, recently observed generalization of the classical Singleton bound to list-decoding asserts that rate $R$ codes are not list-decodable using list-size $L$ beyond an error fraction $\frac{L}{L+1} (1-R)$ (the Singleton bound being the case of $L=1$, i.e., unique decoding). We prove that in order to approach this bound for ... more >>>

Omar Alrabiah, Venkatesan Guruswami, Ray Li

Reed-Solomon codes are a classic family of error-correcting codes consisting of evaluations of low-degree polynomials over a finite field on some sequence of distinct field elements. They are widely known for their optimal unique-decoding capabilities, but their list-decoding capabilities are not fully understood. Given the prevalence of Reed-Solomon codes, a ... more >>>

Zander Kelley, Shachar Lovett, Raghu Meka

We study the power of randomness in the Number-on-Forehead (NOF) model in communication complexity. We construct an explicit 3-player function $f:[N]^3 \to \{0,1\}$, such that: (i) there exist a randomized NOF protocol computing it that sends a constant number of bits; but (ii) any deterministic or nondeterministic NOF protocol computing ... more >>>

Noam Mazor

In the Random Oracle Model (ROM) all parties have oracle access to a common random function, and the parties are limited in the number of queries they can make to the oracle. The Merkle’s Puzzles protocol, introduced by Merkle [CACM ’78], is a key-agreement protocol in the ROM with a ... more >>>

Vikraman Arvind, Abhranil Chatterjee

We revisit the main result of Carmosino et al \cite{CILM18} which shows that an $\Omega(n^{\omega/2+\epsilon})$ size noncommutative arithmetic circuit size lower bound (where $\omega$ is the matrix multiplication exponent) for a constant-degree $n$-variate polynomial family $(g_n)_n$, where each $g_n$ is a noncommutative polynomial, can be ``lifted'' to an exponential size ... more >>>

Theodoros Papamakarios

We show that for any integer $d>0$, depth $d$ Frege systems are NP-hard to automate. Namely, given a set $S$ of depth $d$ formulas, it is NP-hard to find a depth $d$ Frege refutation of $S$ in time polynomial in the size of the shortest such a refutation. This extends ... more >>>

Mitali Bafna, Dor Minzer

A $d$-dimensional simplicial complex $X$ is said to support a direct product tester if any locally consistent function defined on its $k$-faces (where $k\ll d$) necessarily come from a function over its vertices. More precisely, a direct product tester has a distribution $\mu$ over pairs of $k$-faces $(A,A')$, and given ... more >>>

Yotam Dikstein, Irit Dinur

Given a family X of subsets of [n] and an ensemble of local functions $\{f_s:s\to\Sigma \;|\; s\in X\}$, an agreement test is a randomized property tester that is supposed to test whether there is some global function $G:[n]\to\Sigma$ such that $f_s=G|_s$ for many sets $s$. For example, the V-test chooses ... more >>>

Hugo Aaronson, Tom Gur, Ninad Rajgopal, Ron Rothblum

Motivated by the fact that input distributions are often unknown in advance, distribution-free property testing considers a setting in which the algorithmic task is to accept functions $f : [n] \to \{0,1\}$ having a certain property $\Pi$ and reject functions that are $\varepsilon$-far from $\Pi$, where the distance is measured ... more >>>

François Le Gall, Yupan Liu, Qisheng Wang

Driven by exploring the power of quantum computation with a limited number of qubits, we present a novel complete characterization for space-bounded quantum computation, which encompasses settings with one-sided error (unitary coRQL) and two-sided error (BQL), approached from a quantum (mixed) state testing perspective:

- The first family of natural ...
more >>>

Amey Bhangale, Subhash Khot, Dor Minzer

For a prime $p$, a restricted arithmetic progression in $\mathbb{F}_p^n$ is a triplet of vectors $x, x+a, x+2a$ in which the common difference $a$ is a non-zero element from $\{0,1,2\}^n$. What is the size of the largest $A\subseteq \mathbb{F}_p^n$ that is free of restricted arithmetic progressions? We show that the ... more >>>

Abhranil Chatterjee, Mrinal Kumar, Ben Lee Volk

We show that for every homogeneous polynomial of degree $d$, if it has determinantal complexity at most $s$, then it can be computed by a homogeneous algebraic branching program (ABP) of size at most $O(d^5s)$. Moreover, we show that for \textit{most} homogeneous polynomials, the width of the resulting homogeneous ABP ... more >>>

Lijie Chen, William Hoza, Xin Lyu, Avishay Tal, Hongxun Wu

A weighted pseudorandom generator (WPRG) is a generalization of a pseudorandom generator (PRG) in which, roughly speaking, probabilities are replaced with weights that are permitted to be positive or negative. We present new explicit constructions of WPRGs that fool certain classes of standard-order read-once branching programs. In particular, our WPRGs ... more >>>

Justin Holmgren, Ron Rothblum

We study the circuit complexity of the multiselection problem: given an input string $x \in \{0,1\}^n$ along with indices $i_1,\dots,i_q \in [n]$, output $(x_{i_1},\dots,x_{i_q})$. A trivial lower bound for the circuit size is the input length $n + q \cdot \log(n)$, but the straightforward construction has size $\Theta(q \cdot n)$.

... more >>>Amey Bhangale, Subhash Khot, Dor Minzer

We prove a stability result for general $3$-wise correlations over distributions satisfying mild connectivity properties. More concretely, we show that if $\Sigma,\Gamma$ and $\Phi$ are alphabets of constant size, and $\mu$ is a pairwise connected distribution over $\Sigma\times\Gamma\times\Phi$ with no $(\mathbb{Z},+)$ embeddings in which the probability of each atom is ... more >>>

Vaibhav Krishan

We give a conversion from non-classical polynomials to $\mathit{MidBit}^+$ circuits and vice-versa. This conversion, along with previously known results, shows that torus polynomials, non-classical polynomials and $\mathit{MidBit}^+$ circuits can all be converted to each other. Therefore lower bounds against any of these models lead to lower bounds against all three ... more >>>

Gil Cohen, Tal Yankovitz

Recently, Kumar and Mon reached a significant milestone by constructing asymptotically good relaxed locally correctable codes (RLCCs) with poly-logarithmic query complexity. Specifically, they constructed $n$-bit RLCCs with $O(\log^{69}n)$ queries. This significant advancement relies on a clever reduction to locally testable codes (LTCs), capitalizing on recent breakthrough works in LTCs.

With ... more >>>

Pranav Bisht, Nikhil Gupta, Ilya Volkovich

An arithmetic formula is an arithmetic circuit where each gate has fan-out one. An \emph{arithmetic read-once formula} (ROF in short) is an arithmetic formula where each input variable labels at most one leaf. In this paper we present several efficient blackbox \emph{polynomial identity testing} (PIT) algorithms for some classes of ... more >>>

Andrej Bogdanov, TsunMing Cheung, Krishnamoorthy Dinesh, John C.S. Lui

We study the relative advantage of classical and quantum distinguishers of bounded query complexity over $n$-bit strings, focusing on the case of a single quantum query. A construction of Aaronson and Ambainis (STOC 2015) yields a pair of distributions that is $\epsilon$-distinguishable by a one-query quantum algorithm, but $O(\epsilon k/\sqrt{n})$-indistinguishable ... 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 >>>

Mika Göös, Ziyi Guan, Tiberiu Mosnoi

What is the $\Sigma_3^2$-circuit complexity (depth 3, bottom-fanin 2) of the $2n$-bit inner product function? The complexity is known to be exponential $2^{\alpha_n n}$ for some $\alpha_n=\Omega(1)$. We show that the limiting constant $\alpha=\limsup \alpha_n$ satisfies

\[

0.847... ~\leq~ \alpha ~\leq~ 0.965...\ .

\]

Determining $\alpha$ is one of the ...
more >>>

Lijie Chen, Roei Tell, Ryan Williams

We establish an equivalence between two algorithmic tasks: *derandomization*, the deterministic simulation of probabilistic algorithms; and *refutation*, the deterministic construction of inputs on which a given probabilistic algorithm fails to compute a certain hard function.

We prove that refuting low-space probabilistic streaming algorithms that try to compute functions $f\in\mathcal{FP}$ ... more >>>

Meghal Gupta, Rachel Zhang

In a streaming algorithm, Bob receives an input $x \in \{0,1\}^n$ via a stream and must compute a function $f$ in low space. However, this function may be fragile to errors in the input stream. In this work, we investigate what happens when the input stream is corrupted. Our main ... more >>>

Yanyi Liu, Rafael Pass

Whether one-way functions (OWF) exist is arguably the most important

problem in Cryptography, and beyond. While lots of candidate

constructions of one-way functions are known, and recently also

problems whose average-case hardness characterize the existence of

OWFs have been demonstrated, the question of

whether there exists some \emph{worst-case hard problem} ...
more >>>

Chin Ho Lee, Edward Pyne, Salil Vadhan

We give new upper and lower bounds on the power of several restricted classes of arbitrary-order read-once branching programs (ROBPs) and standard-order ROBPs (SOBPs) that have received significant attention in the literature on pseudorandomness for space-bounded computation.

Regular SOBPs of length $n$ and width $\lfloor w(n+1)/2\rfloor$ can exactly simulate general ... more >>>

Renato Ferreira Pinto Jr.

We study the connection between directed isoperimetric inequalities and monotonicity testing. In recent years, this connection has unlocked breakthroughs for testing monotonicity of functions defined on discrete domains. Inspired the rich history of isoperimetric inequalities in continuous settings, we propose that studying the relationship between directed isoperimetry and monotonicity in ... more >>>

Shuichi Hirahara, Mikito Nanashima

Pessiland is one of Impagliazzo's five possible worlds in which NP is hard on average, yet no one-way function exists. This world is considered the most pessimistic because it offers neither algorithmic nor cryptographic benefits.

In this paper, we develop a unified framework for constructing strong learning algorithms ... more >>>

Sourav Chakraborty, Chandrima Kayal, Rajat Mittal, Manaswi Paraashar, Swagato Sanyal, Nitin Saurabh

For any Boolean functions $f$ and $g$, the question whether $\text{R}(f\circ g) = \tilde{\Theta}(\text{R}(f) \cdot \text{R}(g))$, is known as the composition question for the randomized query complexity. Similarly, the composition question for the approximate degree asks whether $\widetilde{\text{deg}}(f\circ g) = \tilde{\Theta}(\widetilde{\text{deg}}(f)\cdot\widetilde{\text{deg}}(g))$. These questions are two of the most important and ... more >>>

Andrej Bogdanov, Pravesh Kothari, Alon Rosen

The low-degree method postulates that no efficient algorithm outperforms low-degree polynomials in certain hypothesis-testing tasks. It has been used to understand computational indistinguishability in high-dimensional statistics.

We explore the use of the low-degree method in the context of cryptography. To this end, we apply it in the design and analysis ... more >>>

Joshua Cook, Ron D. Rothblum

The celebrated $\mathbf{IP}=\mathbf{PSPACE}$ Theorem gives an efficient interactive proof for any bounded-space algorithm. In this work we study interactive proofs for non-deterministic bounded space computations. While Savitch's Theorem shows that nondeterministic bounded-space algorithms can be simulated by deterministic bounded-space algorithms, this simulation has a quadratic overhead. We give interactive protocols ... more >>>

Huacheng Yu, Wei Zhan

We prove the first polynomial separation between randomized and deterministic time-space tradeoffs of multi-output functions. In particular, we present a total function that on the input of $n$ elements in $[n]$, outputs $O(n)$ elements, such that:

- There exists a randomized oblivious algorithm with space $O(\log n)$, time $O(n\log n)$ ... more >>>

David Heath, Vladimir Kolesnikov, Rafail Ostrovsky

We introduce tri-state circuits (TSCs). TSCs form a natural model of computation that, to our knowledge, has not been considered by theorists. The model captures a surprising combination of simplicity and power. TSCs are simple in that they allow only three wire values ($0$,$1$, and undefined – $Z$) and three ... more >>>

Lijie Chen, Roei Tell

What's new in the world of derandomization? Questions about pseudorandomness and derandomization have been driving progress in complexity theory for many decades. In this survey we will describe new approaches to the $\mathcal{BPP}=\mathcal{P}$ conjecture from recent years, as well as new questions, algorithmic approaches, and ways of thinking. For example: ... more >>>

Vinayak Kumar, Geoffrey Mon

We cement the intuitive connection between relaxed local correctability and local testing by presenting a concrete framework for building a relaxed locally correctable code from any family of linear locally testable codes with sufficiently high rate. When instantiated using the locally testable codes of Dinur et al. (STOC 2022), this ... more >>>

Swastik Kopparty, Vishvajeet N

We study the problem of extracting randomness from somewhere random sources, and related combinatorial phenomena: partition analogues of Shearer's lemma on projections.

A somewhere-random source is a tuple $(X_1, \ldots, X_t)$ of (possibly correlated) $\{0,1\}^n$-valued random variables $X_i$ where for some unknown $i \in [t]$, $X_i$ is guaranteed to be ... more >>>

Benny Applebaum, Amos Beimel, Yuval Ishai, Eyal Kushilevitz, Tianren Liu, Vinod Vaikuntanathan

A secret-sharing scheme enables a dealer to share a secret $s$ among $n$ parties such that only authorized subsets of parties, specified by a monotone access structure $f:\{0,1\}^n\to\{0,1\}$, can reconstruct $s$ from their shares. Other subsets of parties learn nothing about $s$.

The question of minimizing the (largest) share size ... more >>>

Itay Cohen, Roy Roth, Amnon Ta-Shma

More than twenty years ago, Capalbo, Reingold, Vadhan and Wigderson gave the first (and up to date only) explicit construction of a bipartite expander with almost full combinatorial expansion. The construction incorporates zig-zag ideas together with extractor technology, and is rather complicated. We give an alternative construction that builds upon ... more >>>

Louis Golowich

We present a new explicit construction of onesided bipartite lossless expanders of constant degree, with arbitrary constant ratio between the sizes of the two vertex sets. Our construction is simpler to state and analyze than the prior construction of Capalbo, Reingold, Vadhan, and Wigderson (2002).

We construct our ... more >>>

Parker Newton, Silas Richelson, Chase Wilson

In this work we prove a high dimensional analogue of the beloved Goldreich-Levin theorem (STOC 1989). We consider the following algorithmic problem: given oracle access to a function $f:\mathbb{Z}_q^m\rightarrow\mathbb{Z}_q^n$ such that ${\rm Prob}_{{\bf x}\sim\mathbb{Z}_q^m}\bigl[f({\bf x})={\bf Ax}\bigr]\geq\varepsilon$ for some ${\bf A}\in\mathbb{Z}_q^{n\times m}$ and $\varepsilon>0$, recover ${\bf A}$ (or a list of ... more >>>

Benny Applebaum, Oded Nir, Benny Pinkas

Threshold cryptography is typically based on the idea of secret-sharing a private-key $s\in F$ ``in the exponent'' of some cryptographic group $G$, or more generally, encoding $s$ in some linearly homomorphic domain. In each invocation of the threshold system (e.g., for signing or decrypting) an ``encoding'' of the secret is ... more >>>

Dmitry Sokolov

The random $\Delta$-CNF model is one of the most important distribution over $\Delta\text{-}\mathrm{SAT}$ instances. It is closely connected to various areas of computer science, statistical physics, and is a benchmark for satisfiability algorithms. Fleming, Pankratov, Pitassi, and Robere and independently Hrubes and Pudlak showed that when $\Delta = \Theta(\log n)$, ... more >>>

Ari Karchmer

Carmosino et al. (2016) demonstrated that natural proofs of circuit lower bounds imply algorithms for learning circuits with membership queries over the uniform distribution. Indeed, they exercised this implication to obtain a quasi-polynomial time learning algorithm for ${AC}^0[p]$ circuits, for any prime $p$, by leveraging the existing natural proofs from ... more >>>

Itai Dinur

The random-query model was introduced by Raz and Zhan at ITCS 2020 as a new model of space-bounded computation. In this model, a branching program of length $T$ and width $2^{S}$ attempts to compute a function $f:\{0,1\}^n \rightarrow \{0,1 \}$. However, instead of receiving direct access to the input bits ... more >>>

Srinivasan A, Uma Girish

We study the advantages of quantum communication models over classical communication models that are equipped with a limited number of qubits of entanglement. In this direction, we give explicit partial functions on $n$ bits for which reducing the entanglement increases the classical communication complexity exponentially. Our separations are as follows. ... more >>>

Ryan Williams

Many results in fine-grained complexity reveal intriguing consequences from solving various SAT problems even slightly faster than exhaustive search. We prove a ``self-improving'' (or ``bootstrapping'') theorem for Circuit-SAT, $\#$Circuit-SAT, and its fully-quantified version: solving one of these problems faster for ``large'' circuit sizes implies a significant speed-up for ``smaller'' circuit ... more >>>

Noga Amit, Guy Rothblum

We study the following question: what cryptographic assumptions are needed for obtaining constant-round computationally-sound argument systems? We focus on argument systems with almost-linear verification time for subclasses of $\mathbf{P}$, such as depth-bounded computations.

Kilian's celebrated work [STOC 1992] provides such 4-message arguments for $\mathbf{P}$ (actually, for $\mathbf{NP}$) using collision-resistant hash ...
more >>>

Halley Goldberg, Valentine Kabanets

Carmosino, Impagliazzo, Kabanets, and Kolokolova (CCC, 2016) showed that the existence of natural properties in the sense of Razborov and Rudich (JCSS, 1997) implies PAC learning algorithms in the sense of Valiant (Comm. ACM, 1984), for boolean functions in $\P/\poly$, under the uniform distribution and with membership queries. It is ... more >>>

Russell Impagliazzo, Valentine Kabanets, Ilya Volkovich

We study close connections between Indistinguishability Obfuscation ($IO$) and the Minimum Circuit Size Problem ($MCSP$), and argue that algorithms for one of $MCSP$ or $IO$ would empower the other one. Some of our main results are:

\begin{itemize}

\item If there exists a perfect (imperfect) $IO$ that is computationally secure ...
more >>>

Or Meir

One of the major open problems in complexity theory is proving super-logarithmic lower bounds on the depth of circuits (i.e., $\mathbf{P}\not\subseteq \mathbf{NC}^{1}$). Karchmer, Raz, and Wigderson (Computational Complexity 5(3/4), 1995) suggested to approach this problem by proving that depth complexity of a composition of functions $f \diamond g$ is roughly ... more >>>

Nir Bitansky, Chethan Kamath, Omer Paneth, Ron Rothblum, Prashant Nalini Vasudevan

Batch proofs are proof systems that convince a verifier that $x_1,\dots, x_t \in L$, for some $NP$ language $L$, with communication that is much shorter than sending the $t$ witnesses. In the case of statistical soundness (where the cheating prover is unbounded but honest prover is efficient), interactive batch proofs ... more >>>

Lijie Chen, Zhenjian Lu, Igor Carboni Oliveira, Hanlin Ren, Rahul Santhanam

A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open problem whether prime numbers can be pseudodeterministically constructed in polynomial time.

... more >>>Abhranil Chatterjee, Sumanta Ghosh, Rohit Gurjar, Roshan Raj

VBP is the class of polynomial families that can be computed by the determinant of a symbolic matrix of the form $A_0 + \sum_{i=1}^n A_ix_i$ where the size of each $A_i$ is polynomial in the number of variables (equivalently, computable by polynomial-sized algebraic branching programs (ABP)). A major open problem ... more >>>

Abhibhav Garg, Rafael Mendes de Oliveira, Shir Peleg, Akash Sengupta

We prove a higher codimensional radical Sylvester-Gallai type theorem for quadratic polynomials, simultaneously generalizing [Han65, Shp20]. Hansen's theorem is a high-dimensional version of the classical Sylvester-Gallai theorem in which the incidence condition is given by high-dimensional flats instead of lines. We generalize Hansen's theorem to the setting of quadratic forms ... more >>>

Xi Chen, Yuhao Li, Mihalis Yannakakis

We study the problem of finding a Tarski fixed point over the $k$-dimensional grid $[n]^k$. We give a black-box reduction from the Tarski problem to the same problem with an additional promise that the input function has a unique fixed point. It implies that the Tarski problem and the unique ... more >>>

Yeyuan Chen, Yizhi Huang, Jiatu Li, Hanlin Ren

The *range avoidance problem*, denoted as $\mathcal{C}$-$\rm Avoid$, asks to find a non-output of a given $\mathcal{C}$-circuit $C:\{0,1\}^n\to\{0,1\}^\ell$ with stretch $\ell>n$. This problem has recently received much attention in complexity theory for its connections with circuit lower bounds and other explicit construction problems. Inspired by the Algorithmic Method for circuit ... more >>>

Yuval Filmus, Itai Leigh, Artur Riazanov, Dmitry Sokolov

A circuit $\mathcal{C}$ samples a distribution $\mathbf{X}$ with an error $\epsilon$ if the statistical distance between the output of $\mathcal{C}$ on the uniform input and $\mathbf{X}$ is $\epsilon$. We study the hardness of sampling a uniform distribution over the set of $n$-bit strings of Hamming weight $k$ denoted by $\mathbf{U}^n_k$ ... more >>>

Shuichi Hirahara, Zhenjian Lu, Hanlin Ren

Relativization is one of the most fundamental concepts in complexity theory, which explains the difficulty of resolving major open problems. In this paper, we propose a weaker notion of relativization called *bounded relativization*. For a complexity class $C$, we say that a statement is *$C$-relativizing* if the statement holds relative ... more >>>

Bruno Pasqualotto Cavalar, Igor Carboni Oliveira

We establish new separations between the power of monotone and general (non-monotone) Boolean circuits:

- For every $k \geq 1$, there is a monotone function in ${\rm AC^0}$ (constant-depth poly-size circuits) that requires monotone circuits of depth $\Omega(\log^k n)$. This significantly extends a classical result of Okol'nishnikova (1982) and Ajtai ... more >>>

Ben Davis, Robert Robere

Recent work has shown that many of the standard TFNP classes — such as PLS, PPADS, PPAD, SOPL, and EOPL — have corresponding proof systems in propositional proof complexity, in the sense that a total search problem is in the class if and only if the totality of the problem ... more >>>

Guy Goldberg

Relaxed locally decodable codes (RLDCs) are error-correcting codes in which individual bits of the message can be recovered by querying only a few bits from a noisy codeword.

Unlike standard (non-relaxed) decoders, a relaxed one is allowed to output a ``rejection'' symbol, indicating that the decoding failed.

To prevent the ...
more >>>

Klim Efremenko, Gillat Kol, Dmitry Paramonov, Raghuvansh Saxena

Single-hop radio networks (SHRN) are a well studied abstraction of communication over a wireless channel. In this model, in every round, each of the $n$ participating parties may decide to broadcast a message to all the others, potentially causing collisions. We consider the SHRN model in the presence of stochastic ... more >>>

Louis Golowich

In this paper, we present a new construction of simplicial complexes of subpolynomial degree with arbitrarily good local spectral expansion. Previously, the only known high-dimensional expanders (HDXs) with arbitrarily good expansion and less than polynomial degree were based on one of two constructions, namely Ramanujan complexes and coset complexes. ... more >>>

Oded Goldreich

We revisit the known proof of the lower bound on the length of relaxed locally decodable codes, providing an arguably simpler exposition that yields a slightly better lower bound for the non-adaptive case and a weaker bound in the general case.

Recall that a locally decodable code is an error ... more >>>

Jacobo Toran, Florian Wörz

The width complexity measure plays a central role in Resolution and other propositional proof systems like Polynomial Calculus (under the name of degree). The study of width lower bounds is the most extended method for proving size lower bounds, and it is known that for these systems, proofs with small ... more >>>

Benny Applebaum, Eliran Kachlon

Let $C$ be an error-correcting code over a large alphabet $q$ of block length $n$, and assume that, a possibly corrupted, codeword $c$ is distributively stored among $n$ servers where the $i$th entry is being held by the $i$th server. Suppose that every pair of servers publicly announce whether the ... more >>>

Abhimanyu Choudhury, Meena Mahajan

We formalize the notion of proof systems obtained by adding normal dependency schemes into the QCDCL proof system underlying algorithms for solving Quantified Boolean Formulas, by exploring the addition of the dependency schemes via two approaches: one as a preprocessing tool, and second in propagation and learnings in the QCDCL ... more >>>

Sagnik Saha, Nikolaj Schwartzbach, Prashant Nalini Vasudevan

In the average-case $k$-SUM problem, given $r$ integers chosen uniformly at random from $\{0,\ldots,M-1\}$, the objective is to find a set of $k$ numbers that sum to $0$ modulo $M$ (this set is called a ``solution''). In the related $k$-XOR problem, given $k$ uniformly random Boolean vectors of length $\log{M}$, ... more >>>

Xin Li, Yan Zhong

Affine extractors give some of the best-known lower bounds for various computational models, such as AC$^0$ circuits, parity decision trees, and general Boolean circuits. However, they are not known to give strong lower bounds for read-once branching programs (ROBPs). In a recent work, Gryaznov, Pudl\'{a}k, and Talebanfard (CCC' 22) introduced ... more >>>

Iddo Tzameret, Luming Zhang

We develop the theory of cryptographic nondeterministic-secure pseudorandomness beyond the point reached by Rudich's original work (Rudich 1997), and apply it to draw new consequences in average-case complexity and proof complexity. Specifically, we show the following:

?*Demi-bit stretch*: Super-bits and demi-bits are variants of cryptographic pseudorandom generators which are ... more >>>

Geoffrey Mon, Dana Moshkovitz, Justin Oh

We present simple constructions of good approximate locally decodable codes (ALDCs) in the presence of a $\delta$-fraction of errors for $\delta<1/2$. In a standard locally decodable code $C \colon \Sigma_1^k \to \Sigma_2^n$, there is a decoder $M$ that on input $i \in [k]$ correctly outputs the $i$-th symbol of a ... more >>>

Amey Bhangale, Subhash Khot, Dor Minzer

Let $\Sigma$ be an alphabet and $\mu$ be a distribution on $\Sigma^k$ for some $k \geq 2$. Let $\alpha > 0$ be the minimum probability of a tuple in the support of $\mu$ (denoted by $supp(\mu)$). Here, the support of $\mu$ is the set of all tuples in $\Sigma^k$ that ... more >>>

Amey Bhangale, Subhash Khot, Dor Minzer

In this paper we study functions on the Boolean hypercube that have the property that after applying certain random restrictions, the restricted function is correlated to a linear function with non-negligible probability. If the given function is correlated with a linear function then this property clearly holds. Furthermore, the property ... more >>>

Leroy Chew

The proof complexity of Quantified Boolean Formulas (QBF) relates to both QBF solving and OBF certification. One method to p-simulate a QBF proof system is by formalising the soundness of its strategy extraction in propositional logic. In this work we illustrate how to use extended QBF Frege to simulate LD-Q(Drrs)-Res, ... more >>>

Noah Fleming, Vijay Ganesh, Antonina Kolokolova, Chunxiao Li, Marc Vinyals

In their seminal work, Atserias et al. and independently Pipatsrisawat and Darwiche in 2009 showed that CDCL solvers can simulate resolution proofs with polynomial overhead. However, previous work does not address the tightness of the simulation, i.e., the question of how large this overhead needs to be. In this paper, ... 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 >>>

Manasseh Ahmed, TsunMing Cheung, Hamed Hatami, Kusha Sareen

We study the randomized communication complexity of the following problem. Alice receives the integer coordinates of a point in the plane, and Bob receives the integer parameters of a half-plane, and their goal is to determine whether Alice's point belongs to Bob's half-plane.

This communication task corresponds to determining ... more >>>

Mika Göös, Artur Riazanov, Anastasia Sofronova, Dmitry Sokolov

We present a top-down lower-bound method for depth-$4$ boolean circuits. In particular, we give a new proof of the well-known result that the parity function requires depth-$4$ circuits of size exponential in $n^{1/3}$. Our proof is an application of robust sunflowers and block unpredictability.

more >>>Hadley Black, Deeparnab Chakrabarty, C. Seshadhri

Monotonicity testing of Boolean functions on the hypergrid, $f:[n]^d \to \{0,1\}$, is a classic topic in property testing. Determining the non-adaptive complexity of this problem is an important open question. For arbitrary $n$, [Black-Chakrabarty-Seshadhri, SODA 2020] describe a tester with query complexity $\widetilde{O}(\varepsilon^{-4/3}d^{5/6})$. This complexity is independent of $n$, but ... more >>>

Hunter Monroe

If no optimal propositional proof system exists, we (and independently Pudlák) prove that ruling out length $t$ proofs of any unprovable sentence is hard. This mapping from unprovable to hard-to-prove sentences powerfully translates facts about noncomputability into complexity theory. For instance, because proving string $x$ is Kolmogorov random ($x{\in}R$) is ... more >>>

Yizhi Huang, Rahul Ilango, Hanlin Ren

It is a long-standing open problem whether the Minimum Circuit Size Problem ($\mathrm{MCSP}$) and related meta-complexity problems are NP-complete. Even for the rare cases where the NP-hardness of meta-complexity problems are known, we only know very weak hardness of approximation.

In this work, we prove NP-hardness of approximating meta-complexity with ... more >>>

Vinayak Kumar

We initiate the study of generalized $AC^0$ circuits comprised of arbitrary unbounded fan-in gates which only need to be constant over inputs of Hamming weight $\ge k$ (up to negations of the input bits), which we denote $GC^0(k)$. The gate set of this class includes biased LTFs like the $k$-$OR$ ... more >>>

Sourav Chakraborty, Chandrima Kayal, Manaswi Paraashar

The role of symmetry in Boolean functions $f:\{0,1\}^n \to \{0,1\}$ has been extensively studied in complexity theory.

For example, symmetric functions, that is, functions that are invariant under the action of $S_n$ is an important class of functions in the study of Boolean functions.

A function $f:\{0,1\}^n \to \{0,1\}$ ...
more >>>

Yotam Dikstein, Irit Dinur

We give new bounds on the cosystolic expansion constants of several families of high dimensional expanders, and the known coboundary expansion constants of order complexes of homogeneous geometric lattices, including the spherical building of $SL_n(F_q)$. The improvement applies to the high dimensional expanders constructed by Lubotzky, Samuels and Vishne, and ... more >>>

Johan Håstad

We study Frege proofs for the one-to-one graph Pigeon Hole Principle

defined on the $n\times n$ grid where $n$ is odd.

We are interested in the case where each formula

in the proof is a depth $d$ formula in the basis given by

$\land$, $\lor$, and $\neg$. We prove that ...
more >>>

Lila Fontes, Sophie Laplante, Mathieu Lauriere, Alexandre Nolin

We study the two-party communication complexity of functions with large outputs, and show that the communication complexity can greatly vary depending on what output model is considered. We study a variety of output models, ranging from the open model, in which an external observer can compute the outcome, to the ... more >>>

Edward Pyne, Ran Raz, Wei Zhan

Let $\mathcal{L}$ be a language that can be decided in linear space and let $\epsilon >0$ be any constant. Let $\mathcal{A}$ be the exponential hardness assumption that for every $n$, membership in $\mathcal{L}$ for inputs of length~$n$ cannot be decided by circuits of size smaller than $2^{\epsilon n}$.

We ...
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 >>>

Rahul Ilango, Jiatu Li, Ryan Williams

The range avoidance problem (denoted by Avoid) asks to find a string outside of the range of a given circuit $C:\{0,1\}^n\to\{0,1\}^m$, where $m>n$. Although at least half of the strings of length $m$ are correct answers, it is not clear how to deterministically find one. Recent results of Korten (FOCS'21) ... more >>>

Shuichi Hirahara

A one-way function is a function that is easy to compute but hard to invert *on average*. We establish the first characterization of a one-way function by *worst-case* hardness assumptions, by introducing a natural meta-computational problem whose NP-hardness (and the worst-case hardness of NP) characterizes the existence of a one-way ... more >>>

Dean Doron, Roei Tell

Existing proofs that deduce BPL=L from circuit lower bounds convert randomized algorithms into deterministic algorithms with large constant overhead in space. We study space-bounded derandomization with minimal footprint, and ask what is the minimal possible space overhead for derandomization.

We show that $BPSPACE[S] \subseteq DSPACE[c \cdot S]$ for $c \approx ...
more >>>

Shuichi Hirahara, Rahul Ilango, Zhenjian Lu, Mikito Nanashima, Igor Carboni Oliveira

Symmetry of Information (SoI) is a fundamental property of Kolmogorov complexity that relates the complexity of a pair of strings and their conditional complexities. Understanding if this property holds in the time-bounded setting is a longstanding open problem. In the nineties, Longpré and Mocas (1993) and Longpré and Watanabe (1995) ... more >>>

Oded Goldreich

This text provides a basic presentation of the the approximation method of Razborov (Matematicheskie Zametki, 1987) and its application by Smolensky (19th STOC, 1987) for proving lower bounds on the size of ${\cal AC}^0[p]$-circuits that compute sums mod~$q$ (for primes $q\neq p$).

The textbook presentations of the latter result ...
more >>>

Sumanta Ghosh, Prahladh Harsha, Simao Herdade, Mrinal Kumar, Ramprasad Saptharishi

We design nearly-linear time numerical algorithms for the problem of multivariate multipoint evaluation over the fields of rational, real and complex numbers. We consider both \emph{exact} and \emph{approximate} versions of the algorithm. The input to the algorithms are (1) coefficients of an $m$-variate polynomial $f$ with degree $d$ in each ... more >>>

Vishwas Bhargava, Shubhangi Saraf, Ilya Volkovich

We develop a new technique for analyzing linear independence of multivariate polynomials. One of our main technical contributions is a \emph{Small Witness for Linear Independence} (SWLI) lemma which states the following.

If the polynomials $f_1,f_2, \ldots, f_k \in \F[X]$ over $X=\{x_1, \ldots, x_n\}$ are $\F$-linearly independent then there exists ...
more >>>

Benny Applebaum, Eliran Kachlon, Arpita Patra

In STOC 1989, Rabin and Ben-Or (RB) established an important milestone in the fields of cryptography and distributed computing by showing that every functionality can be computed with statistical (information-theoretic) security in the presence of an active (aka Byzantine) rushing adversary that controls up to half of the parties. We ... more >>>

Jan Krajicek

Given a sound first-order p-time theory $T$ capable of formalizing syntax of

first-order logic we define a p-time function $g_T$ that stretches all inputs by one

bit and we use its properties to show that $T$ must be incomplete. We leave it as an

open problem whether ...
more >>>

Nicollas Sdroievski, Dieter van Melkebeek

A fundamental question in computational complexity asks whether probabilistic polynomial-time algorithms can be simulated deterministically with a small overhead in time (the BPP vs. P problem). A corresponding question in the realm of interactive proofs asks whether Arthur-Merlin protocols can be simulated nondeterministically with a small overhead in time (the ... more >>>

Rahul Santhanam

We propose a new family of circuit-based sampling tasks, such that non-trivial algorithmic solutions to certain tasks from this family imply frontier uniform lower bounds such as ``NP is not in uniform ACC^0" and ``NP does not have uniform polynomial-size depth-two threshold circuits". Indeed, the most general versions of our ... more >>>

Joseph Zalewski

We prove that a $O(k \log k)$-probe local algorithm for $k$-Missing String presented by Vyas and Williams is asymptotically optimal among a certain class of algorithms for this problem. The best lower bound we are aware of for the general case is still $\Omega(k)$.

more >>>Shuichi Hirahara, Nobutaka Shimizu

Strong (resp. weak) average-case hardness refers to the properties of a computational problem in which a large (resp. small) fraction of instances are hard to solve. We develop a general framework for proving hardness self-amplification, that is, the equivalence between strong and weak average-case hardness. Using this framework, we prove ... more >>>

Vikraman Arvind, Pushkar Joglekar

Based on a theorem of Bergman we show that multivariate noncommutative polynomial factorization is deterministic polynomial-time reducible to the factorization of bivariate noncommutative polynomials. More precisely, we show the following:

(1) In the white-box setting, given an n-variate noncommutative polynomial f in F over a field F (either a ... more >>>

Mark Bun, Nadezhda Voronova

The approximate degree of a Boolean function is the minimum degree of real polynomial that approximates it pointwise. For any Boolean function, its approximate degree serves as a lower bound on its quantum query complexity, and generically lifts to a quantum communication lower bound for a related function.

We ... more >>>

Xin Li

A long line of work in the past two decades or so established close connections between several different pseudorandom objects and applications, including seeded or seedless non-malleable extractors, two source extractors, (bipartite) Ramsey graphs, privacy amplification protocols with an active adversary, non-malleable codes and many more. These connections essentially show ... more >>>

Jiatu Li, Igor Carboni Oliveira

While there has been progress in establishing the unprovability of complexity statements in lower fragments of bounded arithmetic, understanding the limits of Jerabek's theory $\textbf{APC}_1$ (2007) and of higher levels of Buss's hierarchy $\textbf{S}^i_2$ (1986) has been a more elusive task. Even in the more restricted setting of Cook's theory ... more >>>

Karthik Gajulapalli, Alexander Golovnev, Satyajeet Nagargoje, Sidhant Saraogi

Range Avoidance (AVOID) is a total search problem where, given a Boolean circuit $C\colon\{0,1\}^n\to\{0,1\}^m$, $m>n$, the task is to find a $y\in\{0,1\}^m$ outside the range of $C$. For an integer $k\geq 2$, $NC^0_k$-AVOID is a special case of AVOID where each output bit of $C$ depends on at most $k$ ... more >>>

Scott Aaronson, Shih-Han Hung

We propose an application for near-term quantum devices: namely, generating cryptographically certified random bits, to use (for example) in proof-of-stake cryptocurrencies. Our protocol repurposes the existing "quantum supremacy" experiments, based on random circuit sampling, that Google and USTC have successfully carried out starting in 2019. We show that, whenever the ... more >>>

Pooya Hatami, William Hoza

This is a survey of unconditional *pseudorandom generators* (PRGs). A PRG uses a short, truly random seed to generate a long, "pseudorandom" sequence of bits. To be more specific, for each restricted model of computation (e.g., bounded-depth circuits or read-once branching programs), we would like to design a PRG that ... more >>>

Qipeng Liu, Ran Raz, Wei Zhan

In a work by Raz (J. ACM and FOCS 16), it was proved that any algorithm for parity learning on $n$ bits requires either $\Omega(n^2)$ bits of classical memory or an exponential number (in~$n$) of random samples. A line of recent works continued that research direction and showed that for ... more >>>

Deepanshu Kush, Shubhangi Saraf

The seminal work of Raz (J. ACM 2013) as well as the recent breakthrough results by Limaye, Srinivasan, and Tavenas (FOCS 2021, STOC 2022) have demonstrated a potential avenue for obtaining lower bounds for general algebraic formulas, via strong enough lower bounds for set-multilinear formulas.

In this paper, we make ... more >>>

Yuval Filmus, Edward Hirsch, Artur Riazanov, Alexander Smal, Marc Vinyals

Hitting formulas have been studied in many different contexts at least since [Iwama 1989]. A hitting formula is a set of Boolean clauses such that any two of the clauses cannot be simultaneously falsified. [Peitl and Szeider 2022] conjectured that the family of unsatisfiable hitting formulas should contain the hardest ... more >>>

Scott Aaronson, Harry Buhrman, William Kretschmer

Relational problems (those with many possible valid outputs) are different from decision problems, but it is easy to forget just how different. This paper initiates the study of FBQP/qpoly, the class of relational problems solvable in quantum polynomial-time with the help of polynomial-sized quantum advice, along with its analogues for ... more >>>

Tameem Choudhury, Karteek Sreenivasaiah

The 2-Orthogonal Vectors (2-OV) problem is the following: given two tuples $A$ and $B$ of $n$ vectors each of dimension $d$, decide if there exists a vector $u\in A$, and $v\in B$ such that $u$ and $v$ are orthogonal. This problem, and its generalization $k$-OV defined analogously for $k$ tuples, ... more >>>

Noam Mazor

Secret sharing schemes allow sharing a secret between a set of parties in a way that ensures that only authorized subsets of the parties learn the secret. Evolving secret sharing schemes (Komargodski, Naor, and Yogev [TCC ’16]) allow achieving this end in a scenario where the parties arrive in an ... more >>>

Yogesh Dahiya, Vignesh K, Meena Mahajan, Karteek Sreenivasaiah

We show that polynomial-size constant-rank linear decision trees (LDTs) can be converted to polynomial-size depth-2 threshold circuits LTF$\circ$LTF. An intermediate construct is polynomial-size decision lists that query a conjunction of a constant number of linear threshold functions (LTFs); we show that these are equivalent to polynomial-size exact linear decision lists ... more >>>

Mikhail Dektiarev, Nikolay Vereshchagin

Half-duplex communication complexity with adversary was defined in [Hoover, K., Impagliazzo, R., Mihajlin, I., Smal, A. V. Half-Duplex Communication Complexity, ISAAC 2018.] Half-duplex communication protocols generalize classical protocols defined by Andrew Yao in [Yao, A. C.-C. Some Complexity Questions Related to Distributive Computing (Preliminary Report), STOC 1979]. It has been ... more >>>

Per Austrin, Kilian Risse

We prove lower bounds for the Minimum Circuit Size Problem (MCSP) in the Sum-of-Squares (SoS) proof system. Our main result is that for every Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}$, SoS requires degree $\Omega(s^{1-\epsilon})$ to prove that $f$ does not have circuits of size $s$ (for any $s > \text{poly}(n)$). ... more >>>

Hervé Fournier, Nutan Limaye, Guillaume Malod, Srikanth Srinivasan, Sébastien Tavenas

Classical results of Brent, Kuck and Maruyama (IEEE Trans. Computers 1973) and Brent (JACM 1974) show that any algebraic formula of size s can be converted to one of depth O(log s) with only a polynomial blow-up in size. In this paper, we consider a fine-grained version of this result ... more >>>

Ond?ej Ježil

For a class of finite graphs, we define a limit object relative to some computationally restricted class of functions. The properties of the limit object then reflect how a computationally restricted viewer "sees" a generic instance from the class. The construction uses Krají?ek's forcing with random variables [7]. We prove ... more >>>

Jan Krajicek

For a finite set $\cal F$ of polynomials over a fixed finite prime field of size $p$ containing all polynomials $x^2 - x$, a Nullstellensatz proof of the unsolvability of the system

$$

f = 0\ ,\ \mbox{ all } f \in {\cal F}

$$

is a linear combination ...
more >>>

Nader Bshouty

Koch, Strassle, and Tan [SODA 2023], show that, under the randomized exponential time hypothesis, there is no distribution-free PAC-learning algorithm that runs in time $n^{\tilde O(\log\log s)}$ for the classes of $n$-variable size-$s$ DNF, size-$s$ Decision Tree, and $\log s$-Junta by DNF (that returns a DNF hypothesis). Assuming a natural ... more >>>

Paul Beame, Niels Kornerup

Cumulative memory---the sum of space used over the steps of a computation---is a fine-grained measure of time-space complexity that is a more accurate measure of cost for algorithms with infrequent spikes in memory usage in the context of technologies such as cloud computing that allow dynamic allocation and de-allocation of ... more >>>

Yinan Li, Youming Qiao, Avi Wigderson, Yuval Wigderson, Chuanqi Zhang

A fundamental fact about bounded-degree graph expanders is that three notions of expansion---vertex expansion, edge expansion, and spectral expansion---are all equivalent. In this paper, we study to what extent such a statement is true for linear-algebraic notions of expansion.

There are two well-studied notions of linear-algebraic expansion, namely dimension expansion ... more >>>

Shachar Lovett, Jiapeng Zhang

Frequency estimation in data streams is one of the classical problems in streaming algorithms. Following much research, there are now almost matching upper and lower bounds for the trade-off needed between the number of samples and the space complexity of the algorithm, when the data streams are adversarial. However, in ... more >>>

Noga Alon, Olivier Bousquet, Kasper Green Larsen, Shay Moran, Shlomo Moran

We study several variants of a combinatorial game which is based on Cantor's diagonal argument. The game is between two players called Kronecker and Cantor. The names of the players are motivated by the known fact that Leopold Kronecker did not appreciate Georg Cantor's arguments about the infinite, and even ... more >>>

Prerona Chatterjee, Pavel Hrubes

We give several new lower bounds on size of homogeneous non-commutative circuits. We present an explicit homogeneous bivariate polynomial of degree $d$ which requires homogeneous non-commutative circuit of size $\Omega(d/\log d)$. For an $n$-variate polynomial with $n>1$, the result can be improved to $\Omega(nd)$, if $d\leq n$, or $\Omega(nd \frac{\log ... more >>>