Related papers: A General Theory of Additive State Space Abstracti…
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…
We consider generalizations of the familiar fifteen-piece sliding puzzle on the 4 by 4 square grid. On larger grids with more pieces and more holes, asymptotically how fast can we move the puzzle into the solved state? We also give a…
In this work, we derive conditions under which compositional abstractions of networks of stochastic hybrid systems can be constructed using the interconnection topology and joint dissipativity-type properties of subsystems and their…
Systems of fixpoint equations over complete lattices, consisting of (mixed) least and greatest fixpoint equations, allow one to express a number of verification tasks such as model-checking of various kinds of specification logics or the…
Abstraction plays an important role in the generalisation of knowledge and skills and is key to sample efficient learning. In this work, we study joint temporal and state abstraction in reinforcement learning, where temporally-extended…
Generalized planning is about finding plans that solve collections of planning instances, often infinite collections, rather than single instances. Recently it has been shown how to reduce the planning problem for generalized planning to…
Abstraction of a continuous-space model into a finite state and input dynamical model is a key step in formal controller synthesis tools. To date, these software tools have been limited to systems of modest size (typically $\leq$ 6…
Despite significant advancements in post-hoc explainability techniques for neural networks, many current methods rely on heuristics and do not provide formally provable guarantees over the explanations provided. Recent work has shown that…
At its core, abstraction is the process of generalizing from specific instances to broader concepts or models, with the primary objective of reducing complexity while preserving properties essential to the intended purpose. It is…
The modelling of discrete regulatory networks combines a graph specifying the pairwise influences between the variables of the system, and a parametrisation from which can be derived a discrete transition system. Given the influence graph…
Regular transition systems (RTS) are a popular formalism for modeling infinite-state systems in general, and parameterised systems in particular. In a CONCUR 22 paper, Esparza et al. introduce a novel approach to the verification of RTS,…
The behavior and architecture of large scale discrete state systems found in computer software and hardware can be specified and analyzed using a particular class of primitive recursive functions. This paper begins with an illustration of…
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…
Discrete abstractions have become a standard approach to assist control synthesis under complex specifications. Most techniques for the construction of discrete abstractions are based on sampling of both the state and time spaces, which may…
Multi-robot path planning is difficult due to the combinatorial explosion of the search space with every new robot added. Complete search of the combined state-space soon becomes intractable. In this paper we present a novel form of…
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…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
While humans readily generalize abstract concepts to more complex or larger tasks, building Reinforcement Learning (RL) systems with this ability remains elusive. Here, we present the first theoretical model of how such Out-of-Distribution…
Learning abstractions directly from data is a core challenge in robotics. Humans naturally operate at an abstract level, reasoning over high-level subgoals while delegating execution to low-level motor skills -- an ability that enables…
Infinite-state games are a commonly used model for the synthesis of reactive systems with unbounded data domains. Symbolic methods for solving such games need to be able to construct intricate arguments to establish the existence of winning…