相关论文: Lower bound for constant-size local certification

The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error…

Given a boolean predicate $\Pi$ on labeled networks (e.g., proper coloring, leader election, etc.), a self-stabilizing algorithm for $\Pi$ is a distributed algorithm that can start from any initial configuration of the network (i.e., every…

An ancestry labeling scheme assigns labels (bit strings) to the nodes of rooted trees such that ancestry queries between any two nodes in a tree can be answered merely by looking at their corresponding labels. The quality of an ancestry…

Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…

Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the…

Estimating spectral gaps of quantum many-body Hamiltonians is a highly challenging computational task, even under assumptions of locality and translation-invariance. Yet, the quest for rigorous gap certificates is motivated by their broad…

We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…

Self-stabilizing protocols enable distributed systems to recover correct behavior starting from any arbitrary configuration. In particular, when processors communicate by message passing, fake messages may be placed in communication links…

Proof-labeling schemes are known mechanisms providing nodes of networks with certificates that can be verified locally by distributed algorithms. Given a boolean predicate on network states, such schemes enable to check whether the…

We study the problem of efficiently refuting the k-colorability of a graph, or equivalently certifying a lower bound on its chromatic number. We give formal evidence of average-case computational hardness for this problem in sparse random…

A central task in quantum information science is state certification: testing whether an unknown state is $\epsilon_1$-close to a fixed target state, or $\epsilon_2$-far. Recent work has shown that surprisingly simple measurement…

For a given computational problem, a certificate is a piece of data that one (the prover) attaches to the output with the aim of allowing efficient verification (by the verifier) that this output is correct. Here, we consider the minimal…

In this paper we address the question of robustness of critical bit rates for the stabilization of networked control systems over digital communication channels. For a deterministic nonlinear system, the smallest bit rate above which…

Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…

Given $n$ copies of an unknown quantum state $\rho\in\mathbb{C}^{d\times d}$, quantum state certification is the task of determining whether $\rho=\rho_0$ or $\|\rho-\rho_0\|_1>\varepsilon$, where $\rho_0$ is a known reference state. We…

Local clustering aims at extracting a local structure inside a graph without the necessity of knowing the entire graph structure. As the local structure is usually small in size compared to the entire graph, one can think of it as a…

Local SGD is a popular optimization method in distributed learning, often outperforming other algorithms in practice, including mini-batch SGD. Despite this success, theoretically proving the dominance of local SGD in settings with…

In this paper, we study learning in probabilistic domains where the learner may receive incorrect labels but can improve the reliability of labels by repeatedly sampling them. In such a setting, one faces the problem of whether the fixed…

We propose a general framework to build certified proofs of distributed self-stabilizing algorithms with the proof assistant Coq. We first define in Coq the locally shared memory model with composite atomicity, the most commonly used model…

Formal verification is only as good as the specification of a system, which is also true for neural network verification. Existing specifications follow the paradigm of data as specification, where the local neighborhood around a reference…