Acceleration of Affine Hybrid Transformations

  • Bernard Boigelot
  • Frédéric Herbreteau
  • Isabelle Mainz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8837)


This work addresses the computation of the set of reachable configurations of linear hybrid automata. The approach relies on symbolic state-space exploration, using acceleration in order to speed up the computation and to make it terminate for a broad class of systems. Our contribution is an original method for accelerating the control cycles of linear hybrid automata, i.e., to compute their unbounded repeated effect. The idea consists in analyzing the data transformations that label these cycles, by reasoning about the geometrical features of the corresponding system of linear constraints. This approach is complete over Multiple Counters Systems (MCS), and is able to accelerate hybrid transformations that are out of scope of existing techniques.


Linear Constraint Convex Polyhedron Periodic Behavior Simple Cycle 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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  1. 1.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Boigelot, B.: Symbolic Methods for Exploring Infinite State Spaces. Ph.D. thesis, Université de Liège (1998)Google Scholar
  3. 3.
    Boigelot, B.: On iterating linear transformations over recognizable sets of integers. Theoretical Computer Science 309(1-3), 413–468 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Boigelot, B., Brusten, J., Degbomont, J.F.: Automata-based symbolic representations of polyhedra. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 3–20. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  5. 5.
    Boigelot, B., Herbreteau, F.: The power of hybrid acceleration. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 438–451. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Boigelot, B., Herbreteau, F., Jodogne, S.: Hybrid acceleration using real vector automata. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 193–205. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Boigelot, B., Jodogne, S., Wolper, P.: An effective decision procedure for linear arithmetic over the integers and reals. ACM Transactions on Computational Logic 6(3), 614–633 (2005)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bozga, M., Gîrlea, C., Iosif, R.: Iterating octagons. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 337–351. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Bozga, M., Iosif, R., Konečný, F.: Fast acceleration of ultimately periodic relations. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 227–242. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Bozga, M., Iosif, R., Konečný, F.: Safety problems are NP-complete for flat integer programs with octagonal loops. In: McMillan, K.L., Rival, X. (eds.) VMCAI 2014. LNCS, vol. 8318, pp. 242–261. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  11. 11.
    Comon, H., Jurski, Y.: Multiple counters automata, safety analysis and Presburger arithmetic. In: Vardi, M.Y. (ed.) CAV 1998. LNCS, vol. 1427, pp. 268–279. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  12. 12.
    Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proc. POPL 1977, pp. 238–252. ACM Press (1977)Google Scholar
  13. 13.
    Degbomont, J.F.: Implicit Real-Vector Automata. Ph.D. thesis, Université de Liège (2013)Google Scholar
  14. 14.
    Henzinger, T.A.: The theory of hybrid automata. In: Proc. LICS 1996, pp. 278–292. IEEE Computer Society Press (1996)Google Scholar
  15. 15.
    Zhou, C., Hoare, C.A.R., Ravn, A.P.: A calculus of durations. Information Processing Letters 40(5), 269–276 (1991)MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Bernard Boigelot
    • 1
  • Frédéric Herbreteau
    • 2
  • Isabelle Mainz
    • 1
  1. 1.Institut Montefiore, B28Univ. LiègeBelgium
  2. 2.Univ. Bordeaux & CNRSTalenceFrance

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