相关论文: A simpler strong refutation of random $k$-XOR
Concurrent Constraint Programming (CCP) is a simple and powerful model for concurrency where agents interact by telling and asking constraints. Since their inception, CCP-languages have been designed for having a strong connection to logic.…
We study the problem of strongly refuting semirandom $k$-LIN$(\mathbb{F})$ instances: systems of $k$-sparse inhomogeneous linear equations over a finite field $\mathbb{F}$. For the case of $\mathbb{F} = \mathbb{F}_2$, this is the…
We initiate a study of the streaming complexity of constraint satisfaction problems (CSPs) when the constraints arrive in a random order. We show that there exists a CSP, namely $\textsf{Max-DICUT}$, for which random ordering makes a…
Around the turn of the century, Shor formulated his well-known and still-open conjecture stating that the accessible information of any quantum dichotomy, that is the maximum amount of classical information that can be decoded from a binary…
In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…
For a constraint satisfaction problem (CSP), a robust satisfaction algorithm is one that outputs an assignment satisfying most of the constraints on instances that are near-satisfiable. It is known that the CSPs that admit efficient robust…
Computational pseudorandomness studies the extent to which a random variable $\bf{Z}$ looks like the uniform distribution according to a class of tests $\cal{F}$. Computational entropy generalizes computational pseudorandomness by studying…
In 2013 Bei, Chen and Zhang introduced a trial and error model of computing, and applied to some constraint satisfaction problems. In this model the input is hidden by an oracle which, for a candidate assignment, reveals some information…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
We prove several results giving new and stronger connections between learning, circuit lower bounds and pseudorandomness. Among other results, we show a generic learning speedup lemma, equivalences between various learning models in the…
Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
In a streaming constraint satisfaction problem (streaming CSP), a $p$-pass algorithm receives the constraints of an instance sequentially, making $p$ passes over the input in a fixed order, with the goal of approximating the maximum…
Examples of small contingency tables on binary random variables with large integer programming gaps on the lower bounds of cell entries were constructed by Sullivant. We argue here that the margins for which these constructed large gaps…
We investigate the existence of a statistical-computational gap in multiple Gaussian graph alignment. We first generalize a previously established informational threshold from Vassaux and Massouli\'e (2025) to regimes where the number of…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
A Constraint Satisfaction Problem (CSP) is a computational problem where we are given variables and constraints about them; the question is whether the variables can be assigned values such that all constraints are satisfied. We give an…
A CSP with n variables ranging over a domain of d values can be solved by brute-force in d^n steps (omitting a polynomial factor). With a more careful approach, this trivial upper bound can be improved for certain natural restrictions of…
We survey the current state of affairs in the study of thresholds and sharp thresholds in random structures on the occasion of the recent proof of the Kahn--Kalai Conjecture by Park and Pham and the fairly recent proof of the satisfiability…
We consider the problem of approximately solving constraint satisfaction problems with arity $k > 2$ ($k$-CSPs) on instances satisfying certain expansion properties, when viewed as hypergraphs. Random instances of $k$-CSPs, which are also…