Related papers: Reductions in local certification
We continue the investigation of locally testable codes, i.e., error-correcting codes for whom membership of a given word in the code can be tested probabilistically by examining it in very few locations. We give two general results on…
Increasing the automaticity of proofs in deductive verification of C programs is a challenging task. When applied to industrial C programs known heuristics to generate simpler verification conditions are not efficient enough. This is mainly…
Let F = F_p for any fixed prime p >= 2. An affine-invariant property is a property of functions on F^n that is closed under taking affine transformations of the domain. We prove that all affine-invariant property having local…
A property of finite graphs is called nondeterministically testable if it has a "certificate" such that once the certificate is specified, its correctness can be verified by random local testing. In this paper we study certificates that…
In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…
The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured…
Let $\mathbb{Q}$ (resp. $\mathbb{R}$) be the field of rational (resp. real) numbers and $X = (X_1, \ldots, X_n)$ be variables. Deciding the non-negativity of polynomials in $\mathbb{Q}[X]$ over $\mathbb{R}^n$ or over semi-algebraic domains…
We study data-driven least squares (LS) problems with semidefinite (SD) constraints and derive finite-sample guarantees on the spectrum of their optimal solutions when these constraints are relaxed. In particular, we provide a high…
Computational problem certificates are additional data structures for each output, which can be used by a-possibly randomized-verification algorithm that proves the correctness of each output. In this paper, we give an algorithm that…
Browsers can detect malicious websites that are provisioned with forged or fake TLS/SSL certificates. However, they are not so good at detecting malicious websites if they are provisioned with mistakenly issued certificates or certificates…
Polyhedra form an established abstract domain for inferring runtime properties of programs using abstract interpretation. Computations on them need to be certified for the whole static analysis results to be trusted. In this work, we look…
Let $G$ be a graph and $S\subseteq V(G)$. If every two adjacent vertices of $G$ have different metric $S$-representations, then $S$ is a local metric generator for $G$. A local metric generator of smallest order is a local metric basis for…
There has been a rapid development and interest in adversarial training and defenses in the machine learning community in the recent years. One line of research focuses on improving the performance and efficiency of adversarial robustness…
Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…
The Minimum Vertex Cover (MinVC) problem is a well-known NP-hard problem. Recently there has been great interest in solving this problem on real-world massive graphs. For such graphs, local search is a promising approach to finding optimal…
Fair representation learning provides an effective way of enforcing fairness constraints without compromising utility for downstream users. A desirable family of such fairness constraints, each requiring similar treatment for similar…
The Fewest Clues Problem (FCP) framework has been introduced to study the complexity of determining whether a solution to an \NP~problem can be uniquely identified by specifying a subset of the certificate. For a given problem $P \in \NP$,…
Attribute and size reductions are key issues in formal concept analysis. In this paper, we consider a special kind of equivalence relation to reduce concept lattices, which will be called local congruence. This equivalence relation is based…
We propose the first general and practical framework to design certifiable algorithms for robust geometric perception in the presence of a large amount of outliers. We investigate the use of a truncated least squares (TLS) cost function,…
A parameterised Boolean equation system (PBES) is a set of equations that defines sets as the least and/or greatest fixed-points that satisfy the equations. This system is regarded as a declarative program defining functions that take a…