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We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an…
Automated synthesis of reactive control protocols from temporal logic specifications has recently attracted considerable attention in various applications in, for example, robotic motion planning, network management, and hardware design. An…
Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space,…
Abstraction (in its various forms) is a powerful established technique in model-checking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an…
Neural abstractions have been recently introduced as formal approximations of complex, nonlinear dynamical models. They comprise a neural ODE and a certified upper bound on the error between the abstract neural network and the concrete…
Accuracy and generalization of dynamics models is key to the success of model-based reinforcement learning (MBRL). As the complexity of tasks increases, so does the sample inefficiency of learning accurate dynamics models. However, many…
We develop a pseudo-metric analogue of bisimulation for generalized semi-Markov processes. The kernel of this pseudo-metric corresponds to bisimulation; thus we have extended bisimulation for continuous-time probabilistic processes to a…
The concept of abstraction has been independently developed both in the context of AI Planning and discounted Markov Decision Processes (MDPs). However, the way abstractions are built and used in the context of Planning and MDPs is…
Multi-valued networks provide a simple yet expressive qualitative state based modelling approach for biological systems. In this paper we develop an abstraction theory for asynchronous multi-valued network models that allows the state space…
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…
This article is concerned with a data-driven divide-and-conquer strategy to construct symbolic abstractions for interconnected control networks with unknown mathematical models. We employ a notion of alternating bisimulation functions (ABF)…
This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…
We present abstraction-refinement algorithms for model checking safety properties of timed automata. The abstraction domain we consider abstracts away zones by restricting the set of clock constraints that can be used to define them, while…
Bisimulation metrics are powerful tools for measuring similarities between stochastic processes, and specifically Markov chains. Recent advances have uncovered that bisimulation metrics are, in fact, optimal-transport distances, which has…
This paper is concerned with a compositional approach for constructing infinite abstractions of interconnected discrete-time stochastic control systems. The proposed approach uses the interconnection matrix and joint dissipativity-type…
This paper proposes a method for abstracting control systems by timed game automata, and is aimed at obtaining automatic controller synthesis. The proposed abstraction is based on partitioning the state space of a control system using…
State abstraction has been an essential tool for dramatically improving the sample efficiency of reinforcement-learning algorithms. Indeed, by exposing and accentuating various types of latent structure within the environment, different…
Abstractions of dynamical systems enable their verification and the design of feedback controllers using simpler, usually discrete, models. In this paper, we propose a data-driven abstraction mechanism based on a novel metric between Markov…
Neural networks are hypothesized to implement interpretable causal mechanisms, yet verifying this requires finding a causal abstraction -- a simpler, high-level Structural Causal Model (SCM) faithful to the network under interventions.…
We study the automated abstraction-based synthesis of correct-by-construction control policies for stochastic dynamical systems with unknown dynamics. Our approach is to learn an abstraction from sampled data, which is represented in the…