Related papers: Supermartingale Certificates for Quantitative Omeg…
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 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…
We propose new supermartingale-based certificates for verifying almost sure satisfaction of $\omega$-regular properties: (1) generalised Streett supermartingales (GSSMs) and their lexicographic extension (LexGSSMs), (2) distribution-valued…
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 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…
This paper addresses the quantitative verification of finite-time constrained occupation time for stochastic continuous-time systems governed by stochastic differential equations (SDEs). Unlike classical reachability analysis, which focuses…
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…
Multi-objective probabilistic model checking is a powerful technique for verifying stochastic systems against multiple (potentially conflicting) properties. To enhance the trustworthiness and explainability of model checking tools, we…
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 present a data-driven approach to the quantitative verification of probabilistic programs and stochastic dynamical models. Our approach leverages neural networks to compute tight and sound bounds for the probability that a stochastic…
We study the problem of co-designing control barrier functions and linear state feedback controllers for discrete-time linear systems affected by additive disturbances. For disturbances of bounded magnitude, we provide a semi-definite…
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…
This paper focuses on synthesizing control policies for discrete-time stochastic control systems together with a lower bound on the probability that the systems satisfy the complex temporal properties. The desired properties of the system…
This paper provides a discretization-free solution to the synthesis of approx-imation-free closed-form controllers for unknown nonlinear systems to enforce complex properties expressed by $\omega$-regular languages, as recognized by…
The paper presents a methodology for temporal logic verification of continuous-time switched stochastic systems. Our goal is to find the lower bound on the probability that a complex temporal property is satisfied over a finite time…
This paper is concerned with a compositional scheme for the construction of control barrier certificates for interconnected discrete-time stochastic systems. The main objective is to synthesize switching control policies against…
This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite time horizon. We use stochastic barrier functions as a means to quantify the probability that a system exits a given safe region of the state…
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…
Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…
We study an optimal control problem on infinite time horizon with semimartingale strategies, random coefficients and regime switching. The value function and the optimal strategy can be characterized in terms of three systems of backward…