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Efficient Bounded Reachability Computation for Rectangular Automata

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Reachability Problems (RP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6945))

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Abstract

We present a new approach to compute the reachable set with a bounded number of jumps for a rectangular automaton. The reachable set under a flow transition is computed as a polyhedron which is represented by a conjunction of finitely many linear constraints. If the bound is viewed as a constant, the computation time is polynomial in the number of variables.

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References

  1. Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? J. Comput. Syst. Sci. 57(1), 94–124 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Henzinger, T.A., Ho, P., Wong-Toi, H.: Algorithmic analysis of nonlinear hybrid systems. IEEE Transactions on Automatic Control 43(4), 540–554 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Preußig, J., Kowalewski, S., Wong-Toi, H., Henzinger, T.A.: An algorithm for the approximative analysis of rectangular automata. In: Ravn, A.P., Rischel, H. (eds.) FTRTFT 1998. LNCS, vol. 1486, pp. 228–240. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  4. Wong-Toi, H., Preußig, J.: A procedure for reachability analysis of rectangular automata. In: Proc. of American Control Conference, vol. 3, pp. 1674–1678 (2000)

    Google Scholar 

  5. Doyen, L., Henzinger, T.A., Raskin, J.: Automatic rectangular refinement of affine hybrid systems. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 144–161. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chutinan, A., Krogh, B.H.: Computing polyhedral approximations to flow pipes for dynamic systems. In: Proc. of CDC 1998. IEEE Press, Los Alamitos (1998)

    Google Scholar 

  8. Stursberg, O., Krogh, B.H.: Efficient representation and computation of reachable sets for hybrid systems. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 482–497. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Girard, A.: Reachability of uncertain linear systems using zonotopes. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 291–305. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: Hytech: A model checker for hybrid systems. Software Tools for Technology Transfer (1), 110–122 (1997)

    Google Scholar 

  11. Frehse, G.: Phaver: Algorithmic verification of hybrid systems past hytech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Ziegler, G.M.: Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. Springer, Heidelberg (1995)

    MATH  Google Scholar 

  13. Chen, X., Abraham, E., Frehse, G.: Efficient bounded reachability computation for rectangular automata. Technical report, RWTH Aachen University (2011), http://www-i2.informatik.rwth-aachen.de/i2/hybrid_research_pub0/

  14. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  15. Fukuda, K.: From the zonotope construction to the minkowski addition of convex polytopes. J. Symb. Comput. 38(4), 1261–1272 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Weibel, C., Fukuda, K.: Computing faces up to k dimensions of a minkowski sum of polytopes. In: Proc. of CCCG 2005, pp. 256–259 (2005)

    Google Scholar 

  17. Henzinger, T.A.: The theory of hybrid automata. In: Proc. of LICS 1996, pp. 278–292 (1996)

    Google Scholar 

  18. Fukuda, K.: cdd, cddplus and cddlib homepage, http://www.ifor.math.ethz.ch/~fukuda/cdd_home/

  19. Frehse, G., Le Guernic, C., Donzé, A., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: 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 

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Author information

Authors and Affiliations

  1. RWTH Aachen University, Germany

    Xin Chen & Erika Ábrahám

  2. Université Grenoble 1 Joseph Fourier, Verimag, France

    Goran Frehse

Authors
  1. Xin Chen
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  2. Erika Ábrahám
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  3. Goran Frehse
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica e Scienze dell’Informazione, Università di Genova, via Dodecaneso 35, 16146, Genoa, Italy

    Giorgio Delzanno

  2. Department of Computer Science, University of Liverpool, Ashton St, Ashton Building, L69 3BX, Liverpool, UK

    Igor Potapov

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Chen, X., Ábrahám, E., Frehse, G. (2011). Efficient Bounded Reachability Computation for Rectangular Automata. In: Delzanno, G., Potapov, I. (eds) Reachability Problems. RP 2011. Lecture Notes in Computer Science, vol 6945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24288-5_13

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  • DOI: https://doi.org/10.1007/978-3-642-24288-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24287-8

  • Online ISBN: 978-3-642-24288-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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