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Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with…
In this paper, we investigate the hybrid tractability of binary Quantified Constraint Satisfaction Problems (QCSPs). First, a basic tractable class of binary QCSPs is identified by using the broken-triangle property. In this class, the…
We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means…
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…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by…
Computing the reachability probability in infinite state probabilistic models has been the topic of numerous works. Here we introduce a new property called \emph{divergence} that when satisfied allows to compute reachability probabilities…
Inquiries such as whether a task A depends on a task B, whether an author A has been influenced by a paper B, whether a certain protein is associated with a specific biological process or molecular function, or whether class A inherits from…
This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition,…
We address the safety verification and synthesis problems for real-time systems. We introduce real-time programs that are made of instructions that can perform assignments to discrete and real-valued variables. They are general enough to…
Type-level programming is an increasingly popular way to obtain additional type safety. Unfortunately, it remains a second-class citizen in the majority of industrially-used programming languages. We propose a new dependently-typed system…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…
When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…
We examine the problem of maximizing the reachability of a given source in temporal graphs that are given as the union of k temporal paths, i.e., every given path is a sequence of edges with strictly increasing labels that denote…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property…
Path polymorphism is the ability to define functions that can operate uniformly over arbitrary recursively specified data structures. Its essence is captured by patterns of the form $x\,y$ which decompose a compound data structure into its…
Reachability analysis evaluates system safety, by identifying the set of states a system may evolve within over a finite time horizon. In contrast to model-based reachability analysis, data-driven reachability analysis estimates reachable…
We study the problem of parametric parallel complexity analysis of concurrent, message-passing programs. To make the analysis local and compositional, it is based on a conservative extension of binary session types, which structure the type…
Strictness analysis is critical to efficient implementation of languages with non-strict evaluation, mitigating much of the performance overhead of laziness. However, reasoning about strictness at the source level can be challenging and…