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Formal methods have been applied widely to verifying the safety requirements of Communication-Based Train Control (CBTC) systems, while the problem situations could be much simplified. In industrial practices of CBTC systems, however, huge complexity arises, which renders those methods nearly impossible to apply. In this paper, we aim to reduce the state space of formal verification problems in Zone Controller, a sub-system of a typical CBTC. We achieve the simplification goal by reducing the total number of device variables. To do this, two projection methods are proposed based on Problem Frames and constraints, respectively. The Problem Frames based method decomposes the system according to sub-properties through functional decomposition, whilst the constraints based projection method removes redundant variables. Our industrial case study demonstrates the feasibility though an evaluation, confirming that these two methods are effective in reducing the state spaces of complex verification problems in this application domain.

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In component-based architecture, a component is a unit of computation or a data store. Connectors are architectural building blocks used to model interactions among components. However, in some particular complex real-time systems, it is non-determinate and confused to distinguish some modules functioning as components as well as connectors. Therefore, a unified model method is demanded to describe those modules. In this paper, we propose a method to divide components into reactive and active component based on providing or requiring services when they interact with each other. A reactive component provides services and could call services of other reactive components. Active components call reactive components and are used to coordinate reactive components. Active and reactive timed automata are unified defined by extending timed automata to denote them. Then, we redefine the component composition language and present the semantics of composition of timed automata. A case study of Train Integrity Detection System illustrates the usage of our unified models for active and reactive components.