Abstract
Event-B is a formal modeling language that is very suitable for software engineering, but it lacks the ability of modeling time. Researchers have proposed some methods for modeling time constraints in Event-B. The limitations with existing methods are that, first of all, the existing research work lacks a systematic time refinement framework based on Event-B; secondly, the existing methods only model time in the Event-B framework and cannot be smoothly converted to automata-based models such as timed automata that facilitate the verification of time properties. These limitations make it more difficult to model and verify real-time systems with Event-B because it is very time-consuming to prove time properties in the Event-B framework. In this paper, we firstly proposed a systematic time refinement framework to express and refine time constraints in Event-B. Secondly, we also proposed various vertical refinement patterns and horizontal extension patterns to guide modelers to refine the Event-B real-time model step by step. Finally, we use a real-time system case to demonstrate the practicality of our method. The experimental results show that the proposed method can make the real-time system modeling in Event-B more convenient and the models are easier to convert to the timed automata model, thereby facilitating the verification of various time properties.
Highlights
In order to model and verify real-time systems using Event-B, the work done by the researchers includes the following: the first direction is to use the capabilities of the
According to the viewpoint of Dominique Cansell et al [2], it is very difficult and time-consuming to verify the time properties in the Event-B model. ird, there are some problems to translate the Event-B model to UPPAAL timed automata directly, because many syntactic elements in Event-B modeling language which are based on first-order predicate logic cannot be directly converted into timed automata
We proposed “vertical refinement pattern” and “horizontal refinement pattern” based on timed automata patterns proposed by Dong. ese patterns can help the modeler to construct a real-time EventB model quickly. ird, we proposed the concept of the iUML-B functional state machine and iUML-B clock state machine to model the untimed part and timed part of the system, respectively
Summary
Joris Rehm [6,7,8] proposed a “duration pattern” to express the time interval between two events, which enable people to model and reason about real-time properties in Event-B. E other direction of modeling and verifying real-time system using Event-B is to translate the Event-B model into a UPPAAL timed automata. Alexei Iliasov [13] proposed a method to translate the Event-B model to a timed automata model which used the process view as the intermediate representation language between the Event-B model and the UPPAAL model. After the refinement of Event-B model and the proof of consistency, the Event-B model is translated into a corresponding timed automata model, and verification of time properties is performed in the UPPAAL environment. After the refinement of Event-B model and the proof of consistency, the Event-B model is translated into a corresponding timed automata model, and verification of time properties is performed in the UPPAAL environment. e final model (including Event-B model and timed automata model) of the system is got gradually by adopting this iterative process. e advantage of this method is that it does not require any modifications to the Event-B model and timed automata model, nor does it need to learn new formal systems. e shortcoming of this method is that many elements in Event-B modeling language are based on first-order predicate logic which cannot be directly converted into timed automata
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