Related papers: Backwards Reachability for Probabilistic Timed Aut…
This paper presents optimizations to improve the scalability of reachability analysis on a subclass of hybrid automata extended with stochasticity. The optimizations target different components of the analysis, such as quantifier…
This paper proposes an algorithm to maximize reachability probabilities for rectangular automata with random clocks via a history-dependent prophetic scheduler. This model class incorporates time-induced nondeterminism on discrete behavior…
We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a…
Forward reachability analysis is the predominant approach for verifying reach-avoid properties in neural feedback systems (dynamical systems controlled by neural networks). This dominance stems from the limited scalability of existing…
This paper is about reachability analysis in a restricted subclass of multi-pushdown automata. We assume that the control states of an automaton are partially ordered, and all transitions of an automaton go downwards with respect to the…
Control applications for cyber-physical systems must make reliably safe control decisions in the presence of continuous dynamics as well as stochastic uncertainty. Providing safety guarantees for such systems requires formal modeling and…
Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition…
Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that…
Updatable timed automata (UTA) are extensions of classic timed automata that allow special updates to clock variables, like x:= x - 1, x := y + 2, etc., on transitions. Reachability for UTA is undecidable in general. Various subclasses with…
Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This paper is concerned with developing scalable algorithms that under-approximate the backward reachable sets, for…
This paper investigates reachability analysis for max-plus linear systems (MPLS), an important class of dynamical systems that model synchronization and delay phenomena in timed discrete-event systems. We specifically focus on backward…
The "backward simulation" of a stochastic process is defined as the stochastic dynamics that trace a time-reversed path from the target region to the initial configuration. If the probabilities calculated by the original simulation are…
The increasing prevalence of neural networks (NNs) in safety-critical applications calls for methods to certify their behavior and guarantee safety. This paper presents a backward reachability approach for safety verification of neural…
Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…
We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique,…
The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem.…
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…
Safety assurance is a critical yet challenging aspect when developing self-driving technologies. Hamilton-Jacobi backward-reachability analysis is a formal verification tool for verifying the safety of dynamic systems in the presence of…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
Backward reachability (also termed controllability) has been extensively studied in control theory, and tools for a wide class of systems have been developed. Nevertheless, assessing a backward reachability analysis or synthesis remains…