Related papers: Some notes on the abstraction operation for Multi-…
Whether explicit or implicit, sets are a critical part of many pieces of software. As a result, it is necessary to develop abstractions of sets for the purposes of abstract interpretation, model checking, and deductive verification.…
Analysis of Markov Decision Processes (MDP) is often hindered by state space explosion. Abstraction is a well-established technique in model checking to mitigate this issue. This paper presents a novel lazy abstraction method for MDP…
This paper deals with the problem of simultaneously making many (M) binary decisions based on one realization of a random data matrix X. M is typically large and X will usually have M rows associated with each of the M decisions to make,…
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
We present a methodology for formulating simplifying abstractions in machine learning systems by identifying and harnessing the utility structure of decisions. Machine learning tasks commonly involve high-dimensional output spaces (e.g.,…
Abstraction of operation processes is a fundamental step for simulation modeling. To reliably abstract an operation process, modelers rely on text information to study and understand details of operations. Aiming at reducing modelers'…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
We present a semantics based framework for analysing the quantitative behaviour of programs with regard to resource usage. We start from an operational semantics equipped with costs. The dioid structure of the set of costs allows for…
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
Abstraction of Markov Decision Processes is a useful tool for solving complex problems, as it can ignore unimportant aspects of an environment, simplifying the process of learning an optimal policy. In this paper, we propose a new algorithm…
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…
Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of…
Matroids and semigraphoids are discrete structures abstracting and generalizing linear independence among vectors and conditional independence among random variables, respectively. Despite the different nature of conditional independence…
Iterative abstraction refinement techniques are one of the most prominent paradigms for the analysis and verification of systems with large or infinite state spaces. This paper investigates the changes of truth values of system properties…
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…
In this paper, we build double theories capturing the idea of nondeterministic behaviors and trajectories. Following Libkind and Myers' Double Operadic Theory of Systems, we construct monoidal semi double categories of interfaces, along…
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…
This paper describes the development of finite abstractions of Max-Plus-Linear (MPL) systems using tropical operations. The idea of tropical abstraction is inspired by the fact that an MPL system is a discrete-event model updating its state…
Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model…
General-purpose agents require fine-grained controls and rich sensory inputs to perform a wide range of tasks. However, this complexity often leads to intractable decision-making. Traditionally, agents are provided with task-specific action…