Related papers: First-Order Tests for Toricity
Statistical significance testing is widely accepted as a means to assess how well a difference in effectiveness reflects an actual difference between systems, as opposed to random noise because of the selection of topics. According to…
The first-order (FO) model checking problem asks, given an FO sentence $\phi$ and a graph $G$, whether $G$ is a model of $\phi$. This problem is known to be $\mathsf{AW[*]}$-hard when parameterized by the quantifier rank of the formula. A…
We tackle the problem of quantifying the number of objects by a generative text-to-image model. Rather than retraining such a model for each new image domain of interest, which leads to high computational costs and limited scalability, we…
We consider the polynomial ring in finitely many variables over an algebraically closed field of positive characteristic, and initiate the systematic study of ideals preserved by the action of the general linear group by changes of…
Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate…
A CM-order is a reduced order equipped with an involution that mimics complex conjugation. The Witt-Picard group of such an order is a certain group of ideal classes that is closely related to the "minus part" of the class group. We present…
New algorithms for prime factorization that outperform the existing ones or take advantage of particular properties of the prime factors can have a practical impact on present implementations of cryptographic algorithms that rely on the…
We present a probabilistic algorithm to test if a homogeneous polynomial ideal $I$ defining a scheme $X$ in $\mathbb{P}^n$ is radical using Segre classes and other geometric notions from intersection theory. Its worst case complexity…
We discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete. We then…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
The large size and complex decision mechanisms of state-of-the-art text classifiers make it difficult for humans to understand their predictions, leading to a potential lack of trust by the users. These issues have led to the adoption of…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
We introduce a method for the detection of Statistically Validated Simplices in higher-order networks. Statistically validated simplices represent the maximal sets of nodes of any size that consistently interact collectively and do not…
We apply the homomorphism complex construction to partially ordered sets, introducing a new topological construction based on the set of maximal chains in a graded poset. Our primary objects of study are distributive lattices, with special…
We extend the theory and the algorithms of Border Bases to systems of Laurent polynomial equations, defining "toric" roots. Instead of introducing new variables and new relations to saturate by the variable inverses, we propose a more…
Similarity measures based purely on word embeddings are comfortably competing with much more sophisticated deep learning and expert-engineered systems on unsupervised semantic textual similarity (STS) tasks. In contrast to commonly used…
Many natural computational problems in computer science, mathematics, physics, and other sciences amount to deciding if two objects are equivalent. Often this equivalence is defined in terms of group actions. A natural question is to ask…
Replication studies are increasingly conducted to assess the credibility of scientific findings. Most of these replication attempts target studies with a superiority design, but there is a lack of methodology regarding the analysis of…