Related papers: Unbounded-Thread Reachability via Symbolic Executi…
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
We study timed systems in which some timing features are unknown parameters. Parametric timed automata (PTAs) are a classical formalism for such systems but for which most interesting problems are undecidable. Notably, the parametric…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical…
In this work, we present a numerical optimal control framework for reachable set computation using \emph{normotopes}, a new set representation as a norm ball with a shaping matrix. In reachable set computations, we expect to continuously…
Reachability analysis is a powerful tool for computing the set of states or outputs reachable for a system. While previous work has focused on systems described by state-space models, we present the first methods to compute reachable sets…
Timed pushdown automata (TPDA) are an expressive formalism combining recursion with a rich logic of timing constraints. We prove that reachability relations of TPDA are expressible in linear arithmetic, a rich logic generalising Presburger…
This article presents the complexity of reachability decision problems for parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a…
Learning-enabled planning and control algorithms are increasingly popular, but they often lack rigorous guarantees of performance or safety. We introduce an algorithm for computing underapproximate backward reachable sets of nonlinear…
This paper shows how to harness existing theorem provers for first-order logic to automatically verify safety properties of imperative programs that perform dynamic storage allocation and destructive updating of pointer-valued structure…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
We study the computation of lower and upper probabilities of hitting a target set of states for imprecise Markov chains, where transition uncertainty is modelled by a convex set of transition matrices. In the precise case, hitting…
We investigate the problem of parameter synthesis for time Petri nets with a cost variable that evolves both continuously with time, and discretely when firing transitions. More precisely, parameters are rational symbolic constants used for…
As neural networks (NNs) become more prevalent in safety-critical applications such as control of vehicles, there is a growing need to certify that systems with NN components are safe. This paper presents a set of backward reachability…
We approach the 3-SAT satisfiability problem with the quantum-inspired method of imaginary time propagation (ITP) applied to matrix product states (MPS) on a classical computer. This ansatz is fundamentally limited by a quantum entanglement…
Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm…
Ensuring the correctness of critical real-time systems, involving concurrent behaviours and timing requirements, is crucial. Timed automata extend finite-state automata with clocks, compared in guards and invariants with integer constants.…
Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear…
We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free…