Related papers: A Formally Verified HOL Algebra for Dynamic Reliab…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
This paper presents differential-algebraic refinement logic (dARL) with which one can deductively verify both properties and relations of differential-algebraic programs (DAPs) that extend hybrid dynamical systems with…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
This paper proposes a novel maximum-likelihood (ML) soft-decision decoding framework for linear block codes, termed error-building decoding (EBD). The complete decoding process can be performed using only the parity-check matrix, without…
Achieving highly reliable networks is essential for network operators to ensure proper packet delivery in the event of software errors or hardware failures. Networks must ensure reachability and routing correctness, such as subnet isolation…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
In this paper, we introduce a hybrid zonotope-based approach for formally verifying the behavior of autonomous systems operating under Linear Temporal Logic (LTL) specifications. In particular, we formally verify the LTL formula by…
The block diagonal structure of an affinity matrix is a commonly desired property in cluster analysis because it represents clusters of feature vectors by non-zero coefficients that are concentrated in blocks. However, recovering a block…
We discuss a formal framework for using algebraic structures to model a meta-language that can write, compose, and provide interoperability between abstractions of DSLs. The purpose of this formal framework is to provide a verification of…
The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…
Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an…
This work presents a formalized proof of modal completeness for G\"odel-L\"ob provability logic (GL) in the HOL Light theorem prover. We describe the code we developed, and discuss some details of our implementation, focusing on our choices…
Network topology matrices are algebraic representations of graphs that are widely used in modeling and analysis of various applications including electrical circuits, communication networks and transportation systems. In this paper, we…
Many security- and performance-critical domains, such as cryptography, rely on low-level verification to minimize the trusted computing surface and allow code to be written directly in assembly. However, verifying assembly code against a…
In this paper we propose an algebraic formalization of connectors in the quantitative setting, in order to address their non-functional features in architectures of component-based systems. We firstly present a weighted Algebra of…
This paper presents a novel holistic deep learning framework that simultaneously addresses the challenges of vulnerability to input perturbations, overparametrization, and performance instability from different train-validation splits. The…
Deep neural networks (DNNs) are widely used in real-world applications, yet they remain vulnerable to errors and adversarial attacks. Formal verification offers a systematic approach to identify and mitigate these vulnerabilities, enhancing…
The aim of this work is to construct a cohomology theory controlling the deformations of a general Drinfel'd algebra. The task is accomplished in three steps. The first step is the construction of a modified cobar complex adapted to a…
Synchronous model is a type of formal models for modelling and specifying reactive systems. It has a great advantage over other real-time models that its modelling paradigm supports a deterministic concurrent behaviour of systems. Various…