Related papers: Abstract Separation Systems
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
{\tt AbstractSimplicialComplexes.m2} is a computer algebra package written for the computer algebra system {\tt Macaulay2} \cite{M2}. It provides new infrastructure to work with abstract simplicial complexes and related homological…
Abstraction is a fundamental part when learning behavioral models of systems. Usually the process of abstraction is manually defined by domain experts. This paper presents a method to perform automatic abstraction for network protocols. In…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
In this paper we provide for parsing with respect to grammars expressed in a general TFS-based formalism, a restriction of ALE. Our motivation being the design of an abstract (WAM-like) machine for the formalism, we consider parsing as a…
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…
Model transformation tools assist system designers by reducing the labor--intensive task of creating and updating models of various aspects of systems, ensuring that modeling assumptions remain consistent across every model of a system, and…
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…
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…
A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems,…
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…
The Explainable Abstract Trains Dataset is an image dataset containing simplified representations of trains. It aims to provide a platform for the application and research of algorithms for justification and explanation extraction. The…
Abstraction is a key verification technique to improve scalability. However, its use for neural networks is so far extremely limited. Previous approaches for abstracting classification networks replace several neurons with one of them that…
Humans are capable of abstracting away irrelevant details when studying problems. This is especially noticeable for problems over grid-cells, as humans are able to disregard certain parts of the grid and focus on the key elements important…
We present infinite analogues of our splinter lemma from [Trees of tangles in abstract separation systems, arXiv:1909.09030]. From these we derive several tree-of-tangles-type theorems for infinite graphs and infinite abstract separation…
We carry out a proof theoretic analysis of the wellfoundedness of recursive path orders in an abstract setting. We outline a very general termination principle and extract from its wellfoundedness proof subrecursive bounds on the size of…
Characterizing hybrid ASP solving in a generic way is difficult since one needs to abstract from specific theories. Inspired by lazy SMT solving, this is usually addressed by treating theory atoms as opaque. Unlike this, we propose a…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
We describe a notion of (abstract) projective line over a field as a set equipped with a certain first order structure, and a projectivity between projective lines as a bijection preserving this structure. The structure in question is that…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…