Related papers: Some notes on the abstraction operation for Multi-…

A certain analysis of all possible associative binary operations on N is presented. This is equivalent with an analysis of all possible monoid structures on N. Several results and a conjecture in this regard are given.

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…

We introduce the notion of BMT independence, allowing us to take arbitrary mixtures of boolean, monotone, and tensor independence and generalizing the notion of BM independence of Wysoczanski. Pair-wise independence relations are encoded…

In this work, we consider the problem of autonomously discovering behavioral abstractions, or options, for reinforcement learning agents. We propose an algorithm that focuses on the termination condition, as opposed to -- as is common --…

This paper is concerned with a compositional approach for constructing both infinite (reduced-order models) and finite abstractions (a.k.a. finite Markov decision processes (MDPs)) of large-scale interconnected discrete-time stochastic…

Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…

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…

In this paper, we provide a compositional approach for constructing finite abstractions (a.k.a. finite Markov decision processes (MDPs)) of interconnected discrete-time stochastic switched systems. The proposed framework is based on a…

We study the asymptotic optimality of abstraction-based control synthesis algorithms. Specifically, we consider uncertain MDP (UMDP) abstraction, and investigate whether refinement leads to optimal results, i.e., an optimal controller and…

Reasoning about functions that operate over algebraic data types is an important problem for a large variety of applications. One application of particular interest is network applications that manipulate or reason about complex message…

Mixed monotone systems form an important class of nonlinear systems that have recently received attention in the abstraction-based control design area. Slightly different definitions exist in the literature, and it remains a challenge to…

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…

Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…

A common technique for checking properties of complex state machines is to build a finite abstraction then check the property on the abstract system -- where a passing check on the abstract system is only transferred to the original system…

Many methods for Model-based Reinforcement learning (MBRL) in Markov decision processes (MDPs) provide guarantees for both the accuracy of the model they can deliver and the learning efficiency. At the same time, state abstraction…

In this semi-tutorial paper, we first review the information-theoretic approach to account for the computational costs incurred during the search for optimal actions in a sequential decision-making problem. The traditional (MDP) framework…

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…

Approximations during program analysis are a necessary evil, as they ensure essential properties, such as soundness and termination of the analysis, but they also imply not always producing useful results. Automatic techniques have been…

In this paper, we propose a compositional approach for the construction of finite abstractions (a.k.a. finite Markov decision processes (MDPs)) for networks of discrete-time stochastic control subsystems that are not necessarily…

We propose a multi-scale approach for computing abstractions of dynamical systems, that incorporates both local and global optimal control to construct a goal-specific abstraction. For a local optimal control problem, we not only design the…