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SAT–LP–IIS joint-directed path-oriented bounded reachability analysis of linear hybrid automata

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Abstract

As discrete jumps and continuous flows tangle in the behavior of linear hybrid automata (LHA), the bounded model checking (BMC) for reachability of LHA is a challenging problem. Current works try to handle this problem by encoding all the discrete and continuous behaviors in the bound into a set of SMT formulas which can then be solved by SMT solvers. However, when the system size is large, the object SMT problem could be huge and difficult to solve. Instead of encoding everything into one constraint set, this paper proposes a SAT–LP–IIS joint-directed solution to conduct the BMC for reachability of LHA in a layered way. First, the bounded graph structure of LHA is encoded into a propositional formula set, and solved by SAT solvers to find potential paths which can reach the target location on the graph. Then, the feasibility of certain path is encoded into a set of linear constraints which can then be solved by linear programming (LP) efficiently. If the path is not feasible, irreducible infeasible set (IIS) technique is deployed to locate an infeasible path segment which will be fed to the SAT solver to accelerate the enumerating process. Experiments show that by this SAT–LP–IIS joint-directed solution, the memory usage of the BMC of LHA is well-controlled and the performance outperforms the state-of-the-art SMT-style competitors significantly.

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Notes

  1. The size of this model can be easily expanded by introducing more cars into the system, which will increase new locations and variables in the model. For example, we show the performance data on different automated highway examples with number of cars from 10 to 500 in Tables 7, 8, 9, and 10.

    Table 2 Performance data on the water-level monitor automaton
    Full size table
    Table 3 Performance data on the temperature control system
    Full size table
    Table 4 Performance data on the sample automaton
    Full size table
    Table 5 Performance data on the train control system
    Full size table
    Table 6 Performance data on the new sample automaton
    Full size table
    Table 7 Performance data on the highway system with 10 vehicles
    Full size table
    Table 8 Performance data on the highway system with 100 vehicles
    Full size table
    Table 9 Performance data on the highway system with 200 vehicles variables
    Full size table
    Table 10 Performance data on the highway system with 500 vehicles
    Full size table

  2. As BACH-SAT is implemented with JAVA, we can only give its maximum memory usage here.

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Acknowledgments

The authors want to thank the anonymous reviewers and editors for their valuable advices on improving this paper. This work is supported by the National Key Basic Research Program of China(2014CB340703), the National Natural Science Foundation of China (No.91318301, No.61321491, No.61100036), the National 863 High-Tech Program of China (No.2012AA011205), and by the Jiangsu Province Research Foundation (No.BK2011558).

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  1. State Key Laboratory of Novel Software Techniques, The Department of Computer Science and Technology, Nanjing University, Nanjing, Jiangsu, China

    Dingbao Xie, Lei Bu, Jianhua Zhao & Xuandong Li

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  1. Dingbao Xie
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Correspondence to Lei Bu.

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Xie, D., Bu, L., Zhao, J. et al. SAT–LP–IIS joint-directed path-oriented bounded reachability analysis of linear hybrid automata. Form Methods Syst Des 45, 42–62 (2014). https://doi.org/10.1007/s10703-014-0210-3

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