Related papers: FORM version 4.0
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
The rise of automated code generation tools, such as large language models (LLMs), has introduced new challenges in ensuring the correctness and efficiency of scientific software, particularly in complex kernels, where numerical stability,…
Context: Formal methods (FMs) have been around for a while, still being unclear how to leverage their benefits, overcome their challenges, and set new directions for their improvement towards a more successful transfer into practice.…
The goal of this paper is to help mainstream programmers routinely use formal verification on their smart contracts by 1) proposing a new YAML-format for writing general-purpose formal specifications, 2) demonstrating how a formal…
The FormCalc package automates the computation of FeynArts amplitudes up to one loop including the generation of a Fortran code for the numerical evaluation of the squared matrix element. Major new or enhanced features in Version 5 are:…
Guarded normal form requires occurrences of fixpoint variables in a {\mu}-calculus-formula to occur under the scope of a modal operator. The literature contains guarded transformations that effectively bring a {\mu}-calculus-formula into…
Formal Methods are mathematically-based techniques for software design and engineering, which enable the unambiguous description of and reasoning about a system's behaviour. Autonomous systems use software to make decisions without human…
This paper presents Fossil 2.0, a new major release of a software tool for the synthesis of certificates (e.g., Lyapunov and barrier functions) for dynamical systems modelled as ordinary differential and difference equations. Fossil 2.0 is…
We examine several currently used techniques for visualizing complex-valued functions applied to modular forms. We plot several examples and study the benefits and limitations of each technique. We then introduce a method of visualization…
When studying families in the moduli space of dynamical systems, choosing an appropriate representative function for a conjugacy class can be a delicate task. The most delicate questions surround rationality of the conjugacy class compared…
Recent strides in interpretable machine learning (ML) research reveal that models exploit undesirable patterns in the data to make predictions, which potentially causes harms in deployment. However, it is unclear how we can fix these…
We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.
Recognizing and understanding conversational groups, or F-formations, is a critical task for situated agents designed to interact with humans. F-formations contain complex structures and dynamics, yet are used intuitively by people in…
Capture calculus has recently been proposed as a solution to effect checking, achieved by tracking the captured references of terms in the types. Boxes, along with the box and unbox operations, are a crucial construct in capture calculus,…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
We present a generic and executable formalization of signature-based algorithms (such as Faug\`ere's $F_5$) for computing Gr\"obner bases, as well as their mathematical background, in the Isabelle/HOL proof assistant. Said algorithms are…
The ergm package supports the statistical analysis and simulation of network data. It anchors the statnet suite of packages for network analysis in R introduced in a special issue in Journal of Statistical Software in 2008. This article…
Recent advances in foundation models, particularly Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs), have facilitated the development of intelligent agents capable of performing complex tasks. By leveraging the…
A major update of the program FeynGame is introduced. One of its main new functionalities is to visualize Feynman graphs generated by QGRAF. The QGRAF output can be either pasted into the FeynGame canvas for individual graphs, or the whole…
Signature-based algorithms is a popular kind of algorithms for computing Gr\"obner bases, and many related papers have been published recently. In this paper, no new signature-based algorithms and no new proofs are presented. Instead, a…