Template polyhedra generalize intervals and octagons to polyhedra whose facets are orthogonal to a given set of arbitrary directions. They have been employed in the abstract interpretation of programs and, with particular success, in the reachability analysis of hybrid automata. While previously, the choice of directions has been left to the user or a heuristic, we present a method for the automatic discovery of directions that generalize and eliminate spurious counterexamples. We show that for the class of convex hybrid automata, i.e., hybrid automata with (possibly nonlinear) convex constraints on derivatives, such directions always exist and can be found using convex optimization. We embed our method inside a CEGAR loop, thus enabling the time-unbounded reachability analysis of an important and richer class of hybrid automata than was previously possible. We evaluate our method on several benchmarks, demonstrating also its superior efficiency for the special case of linear hybrid automata.
This research was supported in part by the Austrian Science Fund (FWF) under grants S11402-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award), by the European Commission under grant 643921 (UnCoVerCPS), and by the ARC project DP140104219 (Robust AI Planning for Hybrid Systems).
589 - 606
TACAS: Tools and Algorithms for the Construction and Analysis of Systems
2017-04-22 – 2017-04-29
Bogomolov S, Frehse G, Giacobbe M, Henzinger TA. Counterexample guided refinement of template polyhedra. In: Vol 10205. Springer; 2017:589-606. doi:10.1007/978-3-662-54577-5_34
Bogomolov, S., Frehse, G., Giacobbe, M., & Henzinger, T. A. (2017). Counterexample guided refinement of template polyhedra (Vol. 10205, pp. 589–606). Presented at the TACAS: Tools and Algorithms for the Construction and Analysis of Systems, Uppsala, Sweden: Springer. https://doi.org/10.1007/978-3-662-54577-5_34
Bogomolov, Sergiy, Goran Frehse, Mirco Giacobbe, and Thomas A Henzinger. “Counterexample Guided Refinement of Template Polyhedra,” 10205:589–606. Springer, 2017. https://doi.org/10.1007/978-3-662-54577-5_34.
S. Bogomolov, G. Frehse, M. Giacobbe, and T. A. Henzinger, “Counterexample guided refinement of template polyhedra,” presented at the TACAS: Tools and Algorithms for the Construction and Analysis of Systems, Uppsala, Sweden, 2017, vol. 10205, pp. 589–606.
Bogomolov S, Frehse G, Giacobbe M, Henzinger TA. 2017. Counterexample guided refinement of template polyhedra. TACAS: Tools and Algorithms for the Construction and Analysis of Systems, LNCS, vol. 10205. 589–606.
Bogomolov, Sergiy, et al. Counterexample Guided Refinement of Template Polyhedra. Vol. 10205, Springer, 2017, pp. 589–606, doi:10.1007/978-3-662-54577-5_34.
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