Related papers: Abstract Separation Systems
The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree depth. In this paper we survey results related to this concept…
Abstraction plays a key role in concept learning and knowledge discovery; this paper is concerned with computational abstraction. In particular, we study the nature of abstraction through a group-theoretic approach, formalizing it as…
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…
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 Abstraction and Reasoning Corpus (ARC) aims at benchmarking the performance of general artificial intelligence algorithms. The ARC's focus on broad generalization and few-shot learning has made it difficult to solve using pure machine…
Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…
We present two frameworks for structure-preserving model order reduction of interconnected subsystems, improving tractability of the reduction methods while ensuring stability and accuracy bounds of the reduced interconnected model. Instead…
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,…
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…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
Combinatorial topology is used in distributed computing to model concurrency and asynchrony. The basic structure in combinatorial topology is the simplicial complex, a collection of subsets called simplices of a set of vertices, closed…
In the present paper we formally define the notion of abstract program slicing, a general form of program slicing where properties of data are considered instead of their exact value. This approach is applied to a language with numeric and…
Probabilistic abstract interpretation is a theory used to extract particular properties of a computer program when it is infeasible to test every single inputs. In this paper we apply the theory on neural networks for the same purpose: to…
This technical report presents a general framework for parsing a variety of grammar formalisms. We develop a grammar formalism, called an Abstract Grammar, which is general enough to represent grammars at many levels of the hierarchy,…
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…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the…
Alternative set theory (AST) may be suitable for the ones who try to capture objects or phenomenons with some kind of indefiniteness of a border. While AST provides various notions for advanced mathematical studies, correspondence of them…