Related papers: Decidability of multiset, set and numerically deci…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by…
Reliable uncertainty quantification is crucial for trustworthy decision-making and the deployment of AI models in medical imaging. While prior work has explored the ability of neural networks to quantify predictive, epistemic, and aleatoric…
We consider reachability decision problems for linear dynamical systems: Given a linear map on $\mathbb{R}^d$ , together with source and target sets, determine whether there is a point in the source set whose orbit, obtained by repeatedly…
In image classification tasks, deep learning models are vulnerable to image distortions i.e. their accuracy significantly drops if the input images are distorted. An image-classifier is considered "reliable" if its accuracy on distorted…
The determination of the computational complexity of multi-agent pathfinding on directed graphs has been an open problem for many years. For undirected graphs, solvability can be decided in polynomial time, as has been shown already in the…
Medical image segmentation is inherently uncertain. For a given image, there may be multiple plausible segmentation hypotheses, and physicians will often disagree on lesion and organ boundaries. To be suited to real-world application,…
This investigation studies the decidability problem of plane edge coloring with three symbols. In the edge coloring (or Wang tiles) of a plane, unit squares with colored edges that have one of $p$ colors are arranged side by side such that…
In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…
This paper addresses the task of set prediction using deep feed-forward neural networks. A set is a collection of elements which is invariant under permutation and the size of a set is not fixed in advance. Many real-world problems, such as…
We study the undirected divisibility graph in which the vertex set is a finite subset of consecutive natural numbers up to N.We derive analytical expressions for measures of the graph like degree, clustering, geodesic distance and…
Altenbernd, Thomas and W\"ohrle have considered in [ATW02] acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\"uchi and Muller ones,…
Declarative Distributed Systems (DDSs) are distributed systems grounded in logic programming. Although DDS model-checking is undecidable in general, we detect decidable cases by tweaking the data-source bounds, the message expressiveness,…
In 1934, Whitney raised the question of how to recognize whether a function f defined on a closed subset X of Euclidean space is the restriction of a function that is continuously differentiable to order p. A necessary and sufficient…
Image classification is a fundamental application in computer vision. Recently, deeper networks and highly connected networks have shown state of the art performance for image classification tasks. Most datasets these days consist of a…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…
The satisfiability problem for First-order Modal Logic (\FOML) is undecidable even for simple fragments like having only unary predicates, two variables etc. Recently a new way to identify decidable fragments of \FOML has been introduced…
In the past years, deep learning models have been successfully applied in several cognitive tasks. Originally inspired by neuroscience, these models are specific examples of differentiable programs. In this paper we define and motivate…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
Multivariate multiplicity codes (Kopparty, Saraf, and Yekhanin, J. ACM 2014) are linear codes where the codewords are described by evaluations of multivariate polynomials (with a degree bound) and their derivatives up to a fixed order, on a…