Related papers: Formalization of Transform Methods using HOL Light
To study the dynamical behaviour of the engineering and physical systems, we often need to capture their continuous behaviour, which is modeled using differential equations, and perform the frequency-domain analysis of these systems.…
The Laplace transform is an algebraic method that is widely used for analyzing physical systems by either solving the differential equations modeling their dynamics or by evaluating their transfer function. The dynamics of the given system…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation…
Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…
Recent developments in autonomous driving, vehicle-to-vehicle communication and smart traffic controllers have provided a hope to realize platoon formation of vehicles. The main benefits of vehicle platooning include improved safety,…
When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial…
In this work we present new methods for transforming and solving finite series by using the Laplace transform. In addition we introduce both an alternative method based on the Fourier transform and a simplified approach. The latter allows a…
We present an algorithm for converting proofs from the OpenTheory interchange format, which can be translated to and from any of the HOL family of proof languages (HOL4, HOL Light, ProofPower, and Isabelle), into the ZFC-based Metamath…
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…
We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present 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…
Bond graph is a unified graphical approach for describing the dynamics of complex engineering and physical systems and is widely adopted in a variety of domains, such as, electrical, mechanical, medical, thermal and fluid mechanics.…
In this preliminary work, we propose to use a polynomial approach in order to study the stability of switched systems. The proposed strategy is based on the Bernstein interpolation method that may transform a switched system into a…
Partial Differential Equations (PDEs) are widely used for modeling the physical phenomena and analyzing the dynamical behavior of many engineering and physical systems. The heat equation is one of the most well-known PDEs that captures the…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
The control of Biomedical Systems in Physical Human-Robot Interaction (pHRI) plays a pivotal role in achieving the desired behavior by ensuring the intended transfer function and stability of subsystems within the overall system.…