Related papers: Essentially optimal interactive certificates in li…
We present proof labeling schemes for graphs with bounded pathwidth that can decide any graph property expressible in monadic second-order (MSO) logic using $O(\log n)$-bit vertex labels. Examples of such properties include planarity,…
Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic…
Several signal recovery tasks can be relaxed into semidefinite programs with rank-one minimizers. A common technique for proving these programs succeed is to construct a dual certificate. Unfortunately, dual certificates may not exist under…
In the context of fine-grained complexity, we investigate the notion of certificate enabling faster polynomial-time algorithms. We specifically target radius (minimum eccentricity), diameter (maximum eccentricity), and all-eccentricity…
We study the problem of {\sl certification}: given queries to a function $f : \{0,1\}^n \to \{0,1\}$ with certificate complexity $\le k$ and an input $x^\star$, output a size-$k$ certificate for $f$'s value on $x^\star$. This abstractly…
A wide range of learning tasks require human input in labeling massive data. The collected data though are usually low quality and contain inaccuracies and errors. As a result, modern science and business face the problem of learning from…
We study certificates in static data structures. In the cell-probe model, certificates are the cell probes which can uniquely identify the answer to the query. As a natural notion of nondeterministic cell probes, lower bounds for…
Let $A(x)=A\_0+x\_1A\_1+...+x\_nA\_n$ be a linear matrix, or pencil, generated by given symmetric matrices $A\_0,A\_1,...,A\_n$ of size $m$ with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a…
Local certification is a distributed mechanism enabling the nodes of a network to check the correctness of the current configuration, thanks to small pieces of information called certificates. For many classic global properties, like…
The problem of solving linear systems is one of the most fundamental problems in computer science, where given a satisfiable linear system $(A,b)$, for $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$, we wish to find a vector $x…
We introduce I/O-optimal certifying algorithms for bipartite graphs, as well as for the classes of split, threshold, bipartite chain, and trivially perfect graphs. When the input graph is a class member, the certifying algorithm returns a…
We study the problem of efficiently certifying upper bounds on the independence number of $\ell$-uniform hypergraphs. This is a notoriously hard problem, with efficient algorithms failing to approximate the independence number within…
We deploy numerical semidefinite programming and conversion to exact rational inequalities to certify that for a positive semidefinite input polynomial or rational function, any representation as a fraction of sums-of-squares of polynomials…
A cofactor representation of an ideal element, that is, a representation in terms of the generators, can be considered as a certificate for ideal membership. Such a representation is typically not unique, and some can be a lot more…
In this note, we present a simple algorithm for computing a \emph{$k$-connectivity certificate} in dynamic graph streams. Our algorithm uses $O(n \log^2 n \cdot \max\{k, \log n \log k\})$ bits of space which improves upon the $O(kn \log^3…
Algorithmic verification of realistic systems to satisfy safety and other temporal requirements has suffered from poor scalability of the employed formal approaches. To design systems with rigorous guarantees, many approaches still rely on…
We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite…
For a graph G=(V,E), finding a set of disjoint edges that do not share any vertices is called a matching problem, and finding the maximum matching is a fundamental problem in the theory of distributed graph algorithms. Although local…
Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness…
As state-of-the-art neural networks are deployed on reasoning and algorithmic tasks, exactness guarantees become increasingly important. However, high average-case accuracy can still mask inconsistent behaviors. This motivates exact…