FORMALIZATION OF LAPLACE TRANSFORM USING THE MULTIVARIABLE CALCULUS THEORY OF HOL-LIGHT By SYEDA HIRA TAQDEES

Algebraic techniques based on Laplace transform are widely used for solving differential equations and evaluating transfer of signals while analyzing physical aspects of many safety-critical systems. To facilitate formal analysis of these systems, we present the formalization of Laplace transform using the multivariable calculus theories of HOL-Light. In particular, we use integral, differential, transcendental and topological theories of multivariable calculus to formally define Laplace transform in higher-order logic and reason about the correctness of Laplace transform properties, such as existence, linearity, frequency shifting and differentiation and integration in time domain. In order to demonstrate the practical effectiveness of this formalization, we use it to develop a verification scheme of analog circuits. These days, analog circuits have become an integral part of almost all embedded systems. However, the unavailability of accurate analysis methods for analog circuits, which exhibit continuous behavior, jeopardizes the usage of embedded systems in many safety-critical applications. In order to overcome this limitation, we propose to use higher-order-logic theorem proving for verifying analog circuits. Towards this direction, this thesis presents an approach to formally verify the transfer functions of continuous models of analog circuits using the Laplace transform theory. In particular, we presents a higher-order-logic formalization of the Kirchhoffs voltage and current laws and basic analog components using the HOL-Light theorem prover. To illustrate the practical effectiveness and utilization of the proposed approach, we provide the formal analysis of first and second-order Sallen-Key low-pass filters and Linear Transfer Converter (LTC) circuit, which are commonly used electrical circuit.