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

Abstract: 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 transform methods to prove various properties of these systems, such as, transfer function, frequency response and stability, and to find out solutions of the differential/difference equations. The conventional techniques for performing the transform methods based analysis have been unable to provide an accurate analysis of these systems. Therefore, higher-order-logic theorem proving, a formal method, has been used for accurately analyzing systems based on transform methods. In this paper, we survey developments for transform methods based analysis in various higher-order-logic theorem provers and overview the corresponding real world case studies from the avionics, medicine and transportation domains that have been analyzed based on these developments.