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- research-articleApril 2024
Faster Modular Composition
Journal of the ACM (JACM), Volume 71, Issue 2Article No.: 11, Pages 1–79https://doi.org/10.1145/3638349A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by n, the algorithm uses O(n1.43) field operations, breaking through the 3/2 ...
- research-articleFebruary 2024
Optimal Auctions through Deep Learning: Advances in Differentiable Economics
Journal of the ACM (JACM), Volume 71, Issue 1Article No.: 5, Pages 1–53https://doi.org/10.1145/3630749Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981, but more than 40 years later, a full analytical understanding of the optimal ...
- research-articleOctober 2023
Exponentially Faster Massively Parallel Maximal Matching
Journal of the ACM (JACM), Volume 70, Issue 5Article No.: 34, Pages 1–18https://doi.org/10.1145/3617360The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, we still have a limited understanding of maximal matching which is one of the central problems of ...
- research-articleOctober 2023
Proximity Gaps for Reed–Solomon Codes
Journal of the ACM (JACM), Volume 70, Issue 5Article No.: 31, Pages 1–57https://doi.org/10.1145/3614423A collection of sets displays a proximity gap with respect to some property if for every set in the collection, either (i) all members are δ-close to the property in relative Hamming distance or (ii) only a tiny fraction of members are δ-close to the ...
- research-articleOctober 2023
On Strongest Algebraic Program Invariants
Journal of the ACM (JACM), Volume 70, Issue 5Article No.: 29, Pages 1–22https://doi.org/10.1145/3614319A polynomial program is one in which all assignments are given by polynomial expressions and in which all branching is nondeterministic (as opposed to conditional). Given such a program, an algebraic invariant is one that is defined by polynomial ...
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- research-articleOctober 2023
Near-optimal Lower Bounds on Quantifier Depth and Weisfeiler–Leman Refinement Steps
Journal of the ACM (JACM), Volume 70, Issue 5Article No.: 32, Pages 1–32https://doi.org/10.1145/3195257We prove near-optimal tradeoffs for quantifier depth (also called quantifier rank) versus number of variables in first-order logic by exhibiting pairs of n-element structures that can be distinguished by a k-variable first-order sentence but where every ...
- research-articleAugust 2023
On the Zeros of Exponential Polynomials
Journal of the ACM (JACM), Volume 70, Issue 4Article No.: 26, Pages 1–26https://doi.org/10.1145/3603543We consider the problem of deciding the existence of real roots of real-valued exponential polynomials with algebraic coefficients. Such functions arise as solutions of linear differential equations with real algebraic coefficients. We focus on two ...
- research-articleApril 2023
Intermediate Value Linearizability: A Quantitative Correctness Criterion
Journal of the ACM (JACM), Volume 70, Issue 2Article No.: 17, Pages 1–21https://doi.org/10.1145/3584699Big data processing systems often employ batched updates and data sketches to estimate certain properties of large data. For example, a CountMin sketch approximates the frequencies at which elements occur in a data stream, and a batched counter counts ...
- research-articleMarch 2023
A Universal Law of Robustness via Isoperimetry
Journal of the ACM (JACM), Volume 70, Issue 2Article No.: 10, Pages 1–18https://doi.org/10.1145/3578580Classically, data interpolation with a parametrized model class is possible as long as the number of parameters is larger than the number of equations to be satisfied. A puzzling phenomenon in deep learning is that models are trained with many more ...
- research-articleNovember 2022
- research-articleOctober 2022
Decentralized Asynchronous Crash-resilient Runtime Verification
Journal of the ACM (JACM), Volume 69, Issue 5Article No.: 34, Pages 1–31https://doi.org/10.1145/3550483Runtime verification is a lightweight method for monitoring the formal specification of a system during its execution. It has recently been shown that a given state predicate can be monitored consistently by a set of crash-prone asynchronous distributed ...
- research-articleJune 2022
- research-articleJune 2022
- research-articleMarch 2022
Polynomial Multiplication over Finite Fields in Time \( O(n \log n \)
Journal of the ACM (JACM), Volume 69, Issue 2Article No.: 12, Pages 1–40https://doi.org/10.1145/3505584 - research-articleOctober 2021
Stable Model Semantics for Guarded Existential Rules and Description Logics: Decidability and Complexity
Journal of the ACM (JACM), Volume 68, Issue 5Article No.: 35, Pages 1–87https://doi.org/10.1145/3447508This work investigates the decidability and complexity of database query answering under guarded existential rules with nonmonotonic negation according to the classical stable model semantics. In this setting, existential quantification is interpreted ...
- research-articleSeptember 2021
Distribution-free, Risk-controlling Prediction Sets
Journal of the ACM (JACM), Volume 68, Issue 6Article No.: 43, Pages 1–34https://doi.org/10.1145/3478535While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the ...
- research-articleMay 2021
- research-articleMay 2020
Scene Grammars, Factor Graphs, and Belief Propagation
Journal of the ACM (JACM), Volume 67, Issue 4Article No.: 19, Pages 1–41https://doi.org/10.1145/3396886We describe a general framework for probabilistic modeling of complex scenes and for inference from ambiguous observations. The approach is motivated by applications in image analysis and is based on the use of priors defined by stochastic grammars. We ...
- research-articleJanuary 2020
Silence
Journal of the ACM (JACM), Volume 67, Issue 1Article No.: 3, Pages 1–26https://doi.org/10.1145/3377883The cost of communication is a substantial factor affecting the scalability of many distributed applications. Every message sent can incur a cost in storage, computation, energy, and bandwidth. Consequently, reducing the communication costs of ...
- research-articleJanuary 2020
Matrix Multiplication, a Little Faster
Journal of the ACM (JACM), Volume 67, Issue 1Article No.: 1, Pages 1–31https://doi.org/10.1145/3364504Strassen’s algorithm (1969) was the first sub-cubic matrix multiplication algorithm. Winograd (1971) improved the leading coefficient of its complexity from 6 to 7. There have been many subsequent asymptotic improvements. Unfortunately, most of these ...