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Deciding Concurrent Planar Monotonic Linear Hybrid Systems

  • Pavithra Prabhakar
  • Nima Roohi
  • Mahesh Viswanathan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9268)

Abstract

Decidability results for hybrid automata often exploit subtle properties about dimensionality (number of continuous variables), and interaction between discrete transitions and continuous trajectories of variables. Thus, the decidability results often do not carry over to parallel compositions of hybrid automata, even when there is no communication other than the implicit synchronization of time. In this paper, we show that the reachability problem for concurrently running planar, monotonic hybrid automata is decidable. Planar, monotonic hybrid automata are a special class of linear hybrid automata with only two variables, whose flows in all states are simultaneously monotonic along some direction in the plane. The reachability problem is known to be decidable for this class. Our concurrently running automata synchronize with respect to a global clock, and through labeled discrete transitions. The proof of decidability hinges on a new observation that the timed trace language of a planar monotonic automaton can be recognized by a timed automaton, and the decidability result follows from the decidability of composition of timed automata. Our results identify a new decidable subclass of multi-rate hybrid automata.

Keywords

Hybrid System Decidability Result Parallel Composition Discrete Transition Hybrid Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. TCS 138(1), 3–34 (1995)CrossRefzbMATHGoogle Scholar
  2. 2.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Asarin, E., Maler, O., Pnueli, A.: Reachability analysis of dynamical systems having piecewise-constant derivatives. Theoretical Computer Science 138(1), 35–65 (1995)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Asarin, E., Schneider, G., Yovine, S.: Algorithmic analysis of polygonal hybrid systems. Part I: Reachability. TCS 379(1–2), 231–265 (2007)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Casagrande, A., Corvaja, P., Piazza, C., Mishra, B.: Decidable compositions of o-minimal automata. In: Cha, S.S., Choi, J.-Y., Kim, M., Lee, I., Viswanathan, M. (eds.) ATVA 2008. LNCS, vol. 5311, pp. 274–288. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  6. 6.
    Henzinger, T.A.: The theory of hybrid automata. In: Proceeding of IEEE Symposium on Logic in Computer Science, pp. 278–292 (1996)Google Scholar
  7. 7.
    Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? Journal of Computer and System Sciences 57(1), 373–382 (1995)MathSciNetGoogle Scholar
  8. 8.
    Lafferriere, G., Pappas, G., Sastry, S.: o-minimal hybrid systems. MCSS 13, 1–21 (2000)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Miller, J.S.: Decidability and complexity results for timed automata and semi-linear hybrid automata. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 296–309. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  10. 10.
    Mysore, V., Pnueli, A.: Refining the undecidability frontier of hybrid automata. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 261–272. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  11. 11.
    Prabhakar, P., Vladimerou, V., Viswanathan, M., Dullerud, G.: A decidable class of planar linear hybrid systems. Theoretical Computer Science 574, 1–17 (2015)CrossRefMathSciNetGoogle Scholar
  12. 12.
    L. van den Dries: Tame Topology and O-minimal Structures. Cambridge UnivesityPress (1998)Google Scholar
  13. 13.
    Vladimerou, V., Prabhakar, P., Viswanathan, M., Dullerud, G.E.: STORMED Hybrid Systems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 136–147. Springer, Heidelberg (2008) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Pavithra Prabhakar
    • 1
  • Nima Roohi
    • 2
  • Mahesh Viswanathan
    • 2
  1. 1.IMDEA Software InstituteMadridSpain
  2. 2.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignChampaignUSA

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