Related papers: Decidability of multiset, set and numerically deci…
We show that every convex code realizable by compact sets in the plane admits a realization consisting of polygons, and analogously every open convex code in the plane can be realized by interiors of polygons. We give factorial-type bounds…
The ordered structures of natural, integer, rational and real numbers are studied in this thesis. The theories of these numbers in the language of order are decidable and finitely axiomatizable. Also, their theories in the language of order…
We examine the notion of anticonfinement and the role it has to play in the singularity analysis of discrete systems. A singularity is said to be anticonfined if singular values continue to arise indefinitely for the forward and backward…
In this article, we compile the work done by various mathematicians on the topic of the fixed divisor of a polynomial. This article explains most of the results concisely and is intended to be an exhaustive survey. We present the results on…
Being able to interpret, or explain, the predictions made by a machine learning model is of fundamental importance. This is especially true when there is interest in deploying data-driven models to make high-stakes decisions, e.g. in…
We use a semantic interpretation to investigate the problem of defining an expressive but decidable type system with bounded quantification. Typechecking in the widely studied System Fsub is undecidable thanks to an undecidable subtyping…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
We study connections between linear equations over various semigroups and recursively enumerable sets of positive integers. We give variants of the universal Diophantine representation of recursively enumerable sets of positive integers…
Technological and computational advances continuously drive forward the broad field of deep learning. In recent years, the derivation of quantities describing theuncertainty in the prediction - which naturally accompanies the modeling…
We consider the problem whether termination of affine integer loops is decidable. Since Tiwari conjectured decidability in 2004, only special cases have been solved. We complement this work by proving decidability for the case that the…
We propose a generic framework for establishing the decidability of a wide range of logical entailment problems (briefly called querying), based on the existence of countermodels that are structurally simple, gauged by certain types of…
The image of a polynomial map is a constructible set. While computing its closure is standard in computer algebra systems, a procedure for computing the constructible set itself is not. We provide a new algorithm, based on algebro-geometric…
Determinant codes are a class of exact-repair regenerating codes for distributed storage systems with parameters (n, k = d, d). These codes cover the entire trade-off between per-node storage and repair-bandwidth. In an earlier work of the…
In the context of image classification, Concept Bottleneck Models (CBMs) first embed images into a set of human-understandable concepts, followed by an intrinsically interpretable classifier that predicts labels based on these intermediate…
We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
One of the most basic, longstanding open problems in the theory of dynamical systems is whether reachability is decidable for one-dimensional piecewise affine maps with two intervals. In this paper we prove that for injective maps, it is…
Model explanations such as saliency maps can improve user trust in AI by highlighting important features for a prediction. However, these become distorted and misleading when explaining predictions of images that are subject to systematic…
With unified model-generated images now widespread online, attributing their model of origin offers a path toward transparency and deeper insight into the characteristic behaviors of individual models. Prior work has explored provenance in…
Clinician-facing predictive models are increasingly present in the healthcare setting. Regardless of their success with respect to performance metrics, all models have uncertainty. We investigate how to visually communicate uncertainty in…