相关论文: A Hierarchy of Supermartingales for $\omega$-Regul…

We present for the first time a supermartingale certificate for $\omega$-regular specifications. We leverage the Robbins & Siegmund convergence theorem to characterize supermartingale certificates for the almost-sure acceptance of Streett…

We present the first supermartingale certificate for quantitative $\omega$-regular properties of discrete-time infinite-state stochastic systems. Our certificate is defined on the product of the stochastic system and a limit-deterministic…

We introduce a general methodology for quantitative model checking and control synthesis with supermartingale certificates. We show that every specification that is invariant to time shifts admits a stochastic invariant that bounds its…

Lexicographic Ranking SuperMartingale (LexRSM) is a probabilistic extension of Lexicographic Ranking Function (LexRF), which is a widely accepted technique for verifying program termination. In this paper, we are the first to propose sound…

We introduce for the first time a neural-certificate framework for continuous-time stochastic dynamical systems. Autonomous learning systems in the physical world demand continuous-time reasoning, yet existing learnable certificates for…

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…

We consider the verification of neural network policies for discrete-time stochastic systems with respect to reach-avoid specifications. We use a learner-verifier procedure that learns a certificate for the specification, represented as a…

We introduce a general methodology for the construction of sound and complete proof rules for the almost-sure and quantitative acceptance of reactivity properties on time-homogeneous Markov chains with general state spaces. Reactivity…

Due to their expressive power, neural networks (NNs) are promising templates for functional optimization problems, particularly for reach-avoid certificate generation for systems governed by stochastic differential equations (SDEs).…

The possibility of errors in human-engineered formal verification software, such as model checkers, poses a serious threat to the purpose of these tools. An established approach to mitigate this problem are certificates -- lightweight,…

The problem of stopping stochastic gradient descent (SGD) in an online manner, based solely on the observed trajectory, is a challenging theoretical problem with significant consequences for applications. While SGD is routinely monitored as…

In this paper, we investigate the probabilistic formal verification of stochastic dynamical systems over continuous state spaces. Motivated by problems in state estimation and information-flow security, we introduce the notion of…

We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of…

A classical approach to studying Markov decision processes (MDPs) is to view them as state transformers. However, MDPs can also be viewed as distribution transformers, where an MDP under a strategy generates a sequence of probability…

This paper introduces Farkas certificates for lower and upper bounds on minimal and maximal reachability probabilities in Markov decision processes (MDP), which we derive using an MDP-variant of Farkas' Lemma. The set of all such…

A barrier certificate, defined over the states of a dynamical system, is a real-valued function whose zero level set characterizes an inductively verifiable state invariant separating reachable states from unsafe ones. When combined with…

We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in…

Probabilistic programs extend classical imperative programs with real-valued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almost-sure)…

We describe a new algorithm, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially, `beyond worst-case guarantees') for data in indexed search trees. Our first contribution is…

We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and…