Related papers: Formalization of Transform Methods using HOL Light
High-order finite element methods (HO-FEM) are gaining popularity in the simulation community due to their success in solving complex flow dynamics. There is an increasing need to analyze the data produced as output by these simulations.…
We study relationships between different formulations of the local principle. Also we establish a connection among the local principle and the non-commutative Fourier transform approach to the investigation of convolution operator algebras.…
Robotic cell injection is used for automatically delivering substances into a cell and is an integral component of drug development, genetic engineering and many other areas of cell biology. Traditionally, the correctness of functionality…
We present a formalization of modern SAT solvers and their properties in a form of abstract state transition systems. SAT solving procedures are described as transition relations over states that represent the values of the solver's global…
This paper explores the idea of using defunctionalization as a proof technique for higher-order programs. Defunctionalization builds on substituting functional values by a first-order representation. Thus, its interest is that one can use…
The increasing penetration of renewable energy sources, characterised by low inertia and intermittent disturbances, presents substantial challenges to power system stability. As critical indicators of system stability, frequency dynamics…
A new method of quantum state tomography for quantum information processing is described. The method based on two-dimensional Fourier transform technique involves detection of all the off-diagonal elements of the density matrix in a…
We introduce a frequency-domain framework for convergence analysis of hyperparameters in game optimization, leveraging High-Resolution Differential Equations (HRDEs) and Laplace transforms. Focusing on the Lookahead algorithm--characterized…
Formal methods are mathematically-based techniques for the rigorous development of software-intensive systems. The railway signaling domain is a field in which formal methods have traditionally been applied, with several success stories.…
Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of…
Transformer language models are state of the art in a multitude of NLP tasks. Despite these successes, their opaqueness remains problematic. Recent methods aiming to provide interpretability and explainability to black-box models primarily…
The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$.…
The workshop aims at reviewing the state of the art and the state of the practice in which formal methods and analysis approaches are currently applied in SPLE. This leads to a discussion of a research agenda for the extension of existing…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
Cloud solutions are increasingly used for a plethora of purposes, including solving memory-intensive and computation-intensive problems. Ensuring the reliability, availability, scalability, and security of cloud solutions, as networked…
An introductory overview on Light-Front quantization, with some emphasis on recent achievements, is given. Light-Front quantization is the most promising and physical tool to study deep inelastic scattering on the basis of quark gluon…
We present the Colorization Transformer, a novel approach for diverse high fidelity image colorization based on self-attention. Given a grayscale image, the colorization proceeds in three steps. We first use a conditional autoregressive…
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 paper presents an explicit state-based modeling approach aimed at modeling Systems of Systems behavior. The approach allows to specify and verify incrementally safety and liveness rules without using model checking techniques. The…
The Common HOL project aims to facilitate porting source code and proofs between members of the HOL family of theorem provers. At the heart of the project is the Common HOL Platform, which defines a standard HOL theory and API that aims to…