Formal Verification of Cyber-Physical Systems Using Theorem Proving

Abstract

Due to major breakthroughs in software and engineering technologies, embedded systems are increasingly being utilized in areas ranging from aerospace and next-generation transportation systems, to smart grid and smart cities, to health care systems, and broadly speaking to what is known as Cyber-Physical Systems (CPS). A CPS is primarily composed of several electronic, communication and controller modules and some actuators and sensors. The mix of heterogeneous underlying smart technologies poses a number of technical challenges to the design and more severely to the verification of such complex infrastructure. In fact, a CPS shall adhere to strict safety, reliability, performance and security requirements, where one needs to capture both physical and random aspects of the various CPS modules and then analyze their interrelationship across interlinked continuous and discrete dynamics. Oftentimes however, system bugs remain uncaught during the analysis and in turn cause unwanted scenarios that may have serious consequences in safety-critical applications. In this paper, we introduce some of the challenges surrounding the design and verification of contemporary CPS with the advent of smart technologies. In particular, we survey recent developments in the use of theorem proving, a formal method, for the modeling, analysis and verification of CPS, and overview some real world CPS case studies from the automotive, avionics and healthtech domains from system level to physical components.

Formalizing chemical physics using the Lean theorem prover

“…In particular, we ask "How can we formally represent a collection of proofs/derivations using an interactive theorem prover?" Theorem provers have previously been used to formalize derivations in physics: theorems from Newton's Principia, 26,27 versions of relativity theory, 28,29 electromagnetic optics, 30 and geometrical optics 31 have been described and proved using proof assistants. Articial intelligence tools for scientic discovery have also used theorem provers in designing optical quantum experiments, 32 as well as for rediscovering and deriving scientic equations from data and background theory.…”

Formalization of Bond Graph using Higher-order-logic Theorem Proving

“…However, none of these contributions provide the BG based analysis of systems, which is the scope of the current paper. A more detailed account of the formal analysis of the engineering and physical systems can be found at [41].…”

Formal Verification of Control Modules in Cyber-Physical Systems

“…Existing theorem provers have to consider various aspects of CPS. The survey on developed tools is provided in [ 55 ] with the conclusion that only one dedicated theorem prover (KeYMaera) has been developed for analyzing hybrid systems. Theorem proving is also used in [ 56 ], with a conceptual framework for the development of complex systems based on higher-order logic specification.…”