Metamathematics for Systems Design Comprehensive Transfer of Formal Methods Techniques to Cyber-Physical Systems

摘要

This position paper describes the context, the goal, the strategy and the tactics of the ERATO MMSD project (2016-2022). The project aims at enhanced quality assurance measures for industry products like cars. In doing so, we follow a recent trend and exploit formal methods, a body of mathematical techniques originally developed for computer systems. However, there are fundamental gaps in application of formal methods to industry products: additional concerns in industry products such as continuous dynamics of physical components and quantitative measures such as probability, time, and cost make problems fundamentally different from those about software. Formal methods that accommodate these concerns is an active research area, which shows that it is a hard problem. There are several successful theoretical developments in this direction. They typically combine one individual technique with one specific concern, such as hybrid automata that extend automata with continuous dynamics. Our project aims to contribute to this hard problem in a unique way. In our project we will take a unique metamathematical strategy to bridging the gaps: instead of creating one technique for each concern, we want to find a meta-level theory that describes how to develop such techniques for many potential concerns in general. Through this strategy, together with our emphasis on real-world applications in industry, we expect a new prototype of applied mathematics will emerge. In this prototype, abstraction and genericity-characteristics of modern mathematics that are not often associated with application-are turned into crucial advantages in applications.