Hybrid Communicating Sequential Processes (HCSP) is a powerful formal modeling language for hybrid systems, which is an extension of CSP by introducing differential equations for modeling continuous evolution and interrupts for modeling interaction between continuous and discrete dynamics. In this paper, we investigate the semantic foundation for HCSP from an operational point of view by proposing the notion of approximate bisimulation, which provides an appropriate criterion to characterize the equivalence between HCSP processes with continuous and discrete behaviour. We give an algorithm to determine whether two HCSP processes are approximately bisimilar. In addition, based on which, we propose an approach on how to discretize HCSP, i.e., given an HCSP process A, we construct another HCSP process B which does not contain any continuous dynamics such that A and B are approximately bisimilar with given precisions. This provides a rigorous way to transform a verified control model to a correct program model, which fills the gap in the design of embedded systems.

In model-driven design of embedded systems, how to generate code from high-level control models seamlessly and correctly is challenging. This is because hybrid systems are involved with continuous evolution, discrete jumps, and the complicated entanglement between them, while code only contains discrete actions. In this article, we investigate the code generation from Hybrid Communicating Sequential Processes (HCSP), a formal hybrid control model, to SystemC. We first introduce the notion of approximate bisimulation as a criterion to check the consistency between two different systems, especially between the original control model and the final generated code. We prove that it is decidable whether two HCSPs are approximately bisimilar in bounded time and unbounded time with some conditions, respectively. For both the cases, we present two sets of rules correspondingly for discretizing HCSPs and prove that the original HCSP model and the corresponding discretization are approximately bisimilar. Furthermore, based on the discretization, we define a transformation function to map a discretized HCSP model to SystemC code such that they are also approximately bisimilar. We finally implement a tool to automatically realize the translation from HCSP to SystemC code and illustrate our approach through some case studies.

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