Related papers: On second-order cone positive systems
Local certification is a topic originating from distributed computing, where a prover tries to convince the vertices of a graph $G$ that $G$ satisfies some property $\mathcal{P}$. To convince the vertices, the prover gives a small piece of…
Entanglement certification is crucial in physical experiments, particularly when only partial knowledge of the quantum state is available. In this context, we present an entanglement criterion based on positive but not completely positive…
A robustness certificate is the minimum distance of a given input to the decision boundary of the classifier (or its lower bound). For {\it any} input perturbations with a magnitude smaller than the certificate value, the classification…
We investigate the problem of verifying different properties of discrete time dynamical systems, namely, reachability, safety and reach-while-avoid. To achieve this, we adopt a data driven perspective and, using past system trajectories as…
The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one…
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…
A barrier certificate is an inductive invariant function which can be used for the safety verification of a hybrid system. Safety verification based on barrier certificate has the benefit of avoiding explicit computation of the exact…
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…
Positivity is one of the three conditions for causal inference from observational data. The standard way to validate positivity is to analyze the distribution of propensity. However, to democratize the ability to do causal inference by…
In recent years, techniques based on convex optimization and real algebra that produce converging hierarchies of lower bounds for polynomial minimization problems have gained much popularity. At their heart, these hierarchies rely crucially…
In a first contribution, we revisit two certificates of positivity on (possibly non-compact) basic semialgebraic sets due to Putinar and Vasilescu [Comptes Rendus de l'Acad\'emie des Sciences-Series I-Mathematics, 328(6) (1999) pp.…
Certified randomness can be generated with untrusted remote quantum computers using multiple known protocols, one of which has been recently realized experimentally. Unlike the randomness sources accessible on today's classical computers,…
We provide out-of-sample certificates on the controlled invariance property of a given set with respect to a class of black-box linear systems. Specifically, we consider linear time-invariant models whose state space matrices are known only…
This paper introduces the notion of control closure certificates to synthesize controllers for discrete-time control systems against $\omega$-regular specifications. Typical functional approaches to synthesize controllers against…
Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees…
Certificates to a linear algebra computation are additional data structures for each output, which can be used by a---possibly randomized---verification algorithm that proves the correctness of each output. The certificates are essentially…
Probabilistic pushdown automata (pPDA) are a standard model for discrete probabilistic programs with procedures and recursion. In pPDA, many quantitative properties are characterized as least fixpoints of polynomial equation systems. In…
Many systems contain latent variables that make their dynamics partially unidentifiable or cause distribution shifts in the observed statistics between offline and online data. However, existing control techniques often assume access to…
Quantum correlations and non-projective measurements underlie a plethora of information-theoretic tasks, otherwise impossible in the classical world. Existing schemes to certify such non-classical resources in a device-independent manner…
Numerical optimization (solving optimization problems using digital computers) currently dominates but has three major drawbacks: high energy consumption, poor scalability, and lack of an execution time certificate. To address these…