Symbolic-numeric problems in the automatic analysis and verification of cyber-physical systems

Abstract

Cyber-Physical Systems (CPS) are integrations of computation and physical processes. Already now, more or less no new consumer device or industrial machinery does not have some form of integrated computation. Since such systems not only interact with each other, but also with humans, their malfunction can endanger human life, and hence it is essential for them to work correctly. Important examples of properties that are used for specifying system correctness are: " Safety: The system state always stays in a certain set considered to be safe. " Progress: The system state will eventually reach some set considered to be desirable. It is important to notice that here we deal with nondeterministic systems: They do not possess a single initial state, but an uncountable set of initial states, and for a given state, further evolution of a system is not fixed but, in general, there are uncountably many further evolutions. So, when we want to automatically verify the correctness of such systems, due to this non-determinism, we need some form of global reasoning and a form of representing the above uncountable sets. Or, in other words, we need symbolic computation. Considering the two aspects of CPS, computation and physical processes, the first aspect is based on computer programs, which are fixed abstract objects. Hence, for analyzing pure software systems, classical symbolic computation is the natural candidate. However, the second aspect, physical processes, is prone to perturbations, whose analysis is one of the main tasks of numerical analysis. As a consequence, for analyzing cyber-physical systems, we need global reasoning in the presence of perturbations, or in other words, symbolic-numeric computation. In the talk we will discuss the problem of computing with the resulting symbolic objects, and their usage in algorithms for the automatic analysis and verification of cyber-physical systems. The talk will draw on joint work with Zhikun She, Tomáš Dzetkulič and many others.