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Verifying Nonpolynomial Hybrid Systems by Qualitative Abstraction and Automated Theorem Proving

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8430))

Abstract

Few methods can automatically verify nonlinear hybrid systems that are modelled by nonpolynomial functions. Qualitative abstraction is a potential alternative to numerical reachability methods for formally verifying these systems. The QUANTUM abstracter is shown to be competitive at verifying several benchmark nonpolynomial hybrid systems.

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References

  1. Frehse, G., et al.: SpaceEx: Scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  2. Tiwari, A.: Abstractions for hybrid systems. Form. Methods Syst. Des. 32(1), 57–83 (2008)

    Article  MATH  Google Scholar 

  3. Tiwari, A.: HybridSAL relational abstracter. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 725–731. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Eggers, A., Ramdani, N., Nedialkov, N., Fränzle, M.: Improving SAT modulo ODE for hybrid systems analysis by combining different enclosure methods. In: Barthe, G., Pardo, A., Schneider, G. (eds.) SEFM 2011. LNCS, vol. 7041, pp. 172–187. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Dang, T., Maler, O., Testylier, R.: Accurate hybridization of nonlinear systems. In: Hybrid Systems: Computation and Control, pp. 11–20. ACM (2010)

    Google Scholar 

  6. Akbarpour, B., Paulson, L.C.: MetiTarski: An automatic theorem prover for real-valued special functions. Journal of Automated Reasoning 44, 175–205 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  7. Tiwari, A., Khanna, G.: Series of abstractions for hybrid automata. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, pp. 465–478. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Denman, W.: QUANTUM: Qualitative abstractions of non-polynomial models. In: Qualitative Reasoning (August 2013)

    Google Scholar 

  9. Ishii, D., Ueda, K., Hosobe, H.: An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systems. Int. J. Softw. Tools Technol. Transf. 13(5), 449–461 (2011)

    Article  Google Scholar 

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Denman, W. (2014). Verifying Nonpolynomial Hybrid Systems by Qualitative Abstraction and Automated Theorem Proving. In: Badger, J.M., Rozier, K.Y. (eds) NASA Formal Methods. NFM 2014. Lecture Notes in Computer Science, vol 8430. Springer, Cham. https://doi.org/10.1007/978-3-319-06200-6_15

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  • DOI: https://doi.org/10.1007/978-3-319-06200-6_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06199-3

  • Online ISBN: 978-3-319-06200-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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