Deciding reachability for planar multi-polynomial systems

  • Kārlis Čerāns
  • Juris Vīksna
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1066)


In this paper we investigate the decidability of the reachability problem for planar non-linear hybrid systems. A planar hybrid system has the property that its state space corresponds to the standard Euclidean plane, which is partitioned into a finite number of (polyhedral) regions. To each of these regions is assigned some vector field which governs the dynamical behaviour of the system within this region. We prove the decidability of point to point and region to region reachability problems for planar hybrid systems for the case when trajectories within the regions can be described by polynomials of arbitrary degree.


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  1. 1.
    R. Alur, C. Courcoubetis, N. Halbwachs, T.A. Henzinger, P.H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and Y. Yovine. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3–34, 1995.CrossRefGoogle Scholar
  2. 2.
    R. Alur and D. Dill. Automata for modeling real time systems. In Proceedings of ICALP'90, volume 443 of Lecture Notes in Computer Science, pages 322–335, 1990.Google Scholar
  3. 3.
    R. Alur and D. Dill. A theory of timed automata. Theoretical Computer Science, 126:183–235, 1994.CrossRefGoogle Scholar
  4. 4.
    E. Asarin and O. Maler. On some relations between dynamical systems and transition systems. In Proceedings of the 21st International Colloquium ICALP94, volume 820 of Lecture Notes in Computer Science, pages 59–72, 1994.Google Scholar
  5. 5.
    K. Čerāns. Algorithmic problems in analysis of real time system specifications. PhD thesis, University of Latvia, 1992.Google Scholar
  6. 6.
    K. Čerāns. Decidability of bisimulation equivalences for parallel timer processes. In Proceedings of CAV'92, volume 663 of Lecture Notes in Computer Science, pages 302–315, 1992.Google Scholar
  7. 7.
    P.A. Henzinger and P.H. Ho. Algorithmic analysis of nonlinear hybrid systems. In Proceedings of CAV'95, Lecture Notes in Computer Science, 1995.Google Scholar
  8. 8.
    T.A. Henzinger. Hybrid automata with finite bisimulations. In Proceedings of ICALP'95, volume 944 of Lecture Notes in Computer Science, pages 324–335, 1995.Google Scholar
  9. 9.
    T.A. Henzinger, P. Kopke, A. Puri, and P. Varaiya. What's decidable about hybrid automata? In Proceedings of the 27th ACM Symposium on Theory of Computing, 1995.Google Scholar
  10. 10.
    O. Maler and A. Pnueli. Reachability analysis of planar multi-linear systems. In Proceedings of the 5th International Conference of Computer Aided Verification, volume 697 of Lecture Notes in Computer Science, pages 194–209, 1993.Google Scholar
  11. 11.
    R. Zippel. Effective polynomial computation. Kluwer Academic Publishers, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Kārlis Čerāns
    • 1
  • Juris Vīksna
    • 1
  1. 1.Institute of Mathematics and Computer ScienceThe University of LatviaRīgaLatvia

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