Related papers: A Foundational Theory of Quantitative Abstraction:…
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…
A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. Typically, abstractions…
Like with most large-scale systems, the evaluation of quantitative properties of collective adaptive systems is an important issue that crosscuts all its development stages, from design (in the case of engineered systems) to runtime…
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…
We present a categorical framework for relating causal models that represent the same system at different levels of abstraction. We define a causal abstraction as natural transformations between appropriate Markov functors, which concisely…
At the intersection of dynamical systems, control theory, and formal methods lies the construction of symbolic abstractions: these typically represent simpler, finite-state models whose behavior mimics that of an underlying concrete system…
We propose a compositional approach for constructing abstractions of general Markov decision processes using approximate probabilistic relations. The abstraction framework is based on the notion of $\delta$-lifted relations, using which one…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
While the utility of well-chosen abstractions for understanding and predicting the behaviour of complex systems is well appreciated, precisely what an abstraction $\textit{is}$ has so far has largely eluded mathematical formalization. In…
In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines…
The abstraction of dynamical systems is a powerful tool that enables the design of feedback controllers using a correct-by-design framework. We investigate a novel scheme to obtain data-driven abstractions of discrete-time stochastic…
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…
An abstraction can be used to relate two structural causal models representing the same system at different levels of resolution. Learning abstractions which guarantee consistency with respect to interventional distributions would allow one…
Symbolic control techniques aim to satisfy complex logic specifications. A critical step in these techniques is the construction of a symbolic (discrete) abstraction, a finite-state system whose behaviour mimics that of a given…
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI.…
We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much…
This paper is concerned with a compositional approach for constructing abstractions of interconnected discrete-time stochastic control systems. The abstraction framework is based on new notions of so-called stochastic simulation functions,…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
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…