Formalization of Lerch's Theorem using HOL Light

06/08/2018
by   Adnan Rashid, et al.
0

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 are firstly modeled using differential equations and then Laplace transform is applied to convert these differential equations to their equivalent algebraic equations. These equations can further be simplified to either obtain the transfer function of the system or to find out the solution of the differential equations in frequency domain. Next, the uniqueness of the Laplace transform provides the solution of these differential equations in the time domain. The traditional Laplace transform based analysis techniques, i.e., paper-and-pencil proofs and computer simulation methods are error-prone due to their inherent limitations and thus are not suitable for the analysis of the systems. Higher-order-logic theorem proving can overcome these limitations of these techniques and can ascertain accurate analysis of the systems. In this paper, we extend our higher-order logic formalization of the Laplace transform, which includes the formal definition of the Laplace transform and verification of its various classical properties. One of the main contributions of the paper is the formalization of Lerch's theorem, which describes the uniqueness of the Laplace transform and thus plays a vital role in solving linear differential equations in the frequency domain. For illustration, we present the formal analysis of a 4-π soft error crosstalk model, which is widely used in nanometer technologies, such as, Integrated Circuits (ICs).

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/16/2019

Formal Analysis of the Biological Circuits using Higher-order-logic Theorem Proving

Synthetic Biology is an interdisciplinary field that utilizes well-estab...
research
01/18/2020

FASiM: A Framework for Automatic Formal Analysis of Simulink Models of Linear Analog Circuits

Simulink is a graphical environment that is widely adapted for the model...
research
11/19/2021

Formalization of Transform Methods in Higher-order Logic: A Survey

Most of the engineering and physical systems are generally characterized...
research
08/13/2022

On the Formalization of the Heat Conduction Problem in HOL

Partial Differential Equations (PDEs) are widely used for modeling the p...
research
06/10/2022

Neural Laplace: Learning diverse classes of differential equations in the Laplace domain

Neural Ordinary Differential Equations model dynamical systems with ODEs...
research
07/18/2018

Formal Modeling of Robotic Cell Injection Systems in Higher-order Logic

Robotic cell injection is used for automatically delivering substances i...
research
04/09/2018

Simulation-Based Reachability Analysis for High-Index Large Linear Differential Algebraic Equations

Reachability analysis is a fundamental problem for safety verification a...

Please sign up or login with your details

Forgot password? Click here to reset