Abstract
We consider a method for the bounded safety analysis of hybrid systems, whose continuous behaviour is intertwined with discrete execution steps. The method computes a tree of state sets, which together over-approximate reachability by bounded-length executions. If none of the state sets intersects with a given set of unsafe states then we have proven bounded safety. Otherwise, we iteratively repeat parts of the computations with locally refined search parameters, in order to reduce the over-approximation error.
In this paper we present a parallelization technique for the above method. We identify independent computations that can be carried out by different threads/processes concurrently, and examine how to achieve work-balance between the threads at low communication cost. Furthermore, we discuss how to assure mutually exclusive node access during refinement computations, without high synchronization costs. We evaluate our proposed solutions experimentally on some benchmarks.
This work was supported by the German research council (DFG) in the context of the HyPro project and the DFG Research Training Group 2236 UnRAVeL.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Althoff, M., Dolan, J.M.: Online verification of automated road vehicles using reachability analysis. IEEE Trans. Robot. 30(4), 903–918 (2014)
Frehse, G., et al.: SpaceEx: scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_30
Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258–263. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_18
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). https://doi.org/10.1007/978-3-540-31954-2_19
Frehse, G., Kateja, R., Le Guernic, C.: Flowpipe approximation and clustering in space-time. In: Proceedings of HSCC 2013, pp. 203–212. ACM (2013)
Le Guernic, C., Girard, A.: Reachability analysis of linear systems using support functions. Nonlinear Anal. Hybrid Syst. 4(2), 250–262 (2010)
Bogomolov, S., Donzé, A., Frehse, G., Grosu, R., Johnson, T.T., Ladan, H., Podelski, A., Wehrle, M.: Guided search for hybrid systems based on coarse-grained space abstractions. STTT 18(4), 449–467 (2016)
Schupp, S., Ábrahám, E.: Efficient dynamic error reduction for hybrid systems reachability analysis. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10806, pp. 287–302. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89963-3_17. Accessible for reviewers under https://ths.rwth-aachen.de/research/publications/
Bak, S., Duggirala, P.S.: Simulation-equivalent reachability of large linear systems with inputs. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 401–420. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_20
Schupp, S., Nellen, J., Ábrahám, E.: Divide and conquer: variable set separation in hybrid systems reachability analysis. In: Proceedings of QAPL 2017. EPTCS, vol. 250, pp. 1–14. Open Publishing Association (2017)
Bogomolov, S., Forets, M., Frehse, G., Podelski, A., Schilling, C., Viry, F.: Reach set approximation through decomposition with low-dimensional sets and high-dimensional matrices. CoRR abs/1801.09526 (2018)
Chen, X., Sankaranarayanan, S.: Decomposed reachability analysis for nonlinear systems. In: Proceedings of RTSS 2016, pp. 13–24. IEEE Computer Society Press (2016)
Ray, R., Gurung, A.: Parallel state space exploration of linear systems with inputs using XSpeed. In: Proceedings of HSCC 2015, pp. 285–286. ACM (2015)
Henzinger, T.A.: The theory of hybrid automata. In: Proceedings of LICS 1996, pp. 278–292. IEEE Computer Society Press (1996)
Schupp, S., Ábrahám, E., Makhlouf, I.B., Kowalewski, S.: HyPro: A C++ library of state set representations for hybrid systems reachability analysis. In: Barrett, C., Davies, M., Kahsai, T. (eds.) NFM 2017. LNCS, vol. 10227, pp. 288–294. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57288-8_20
Schupp, S., Ábrahám, E., Chen, X., Ben Makhlouf, I., Frehse, G., Sankaranarayanan, S., Kowalewski, S.: Current challenges in the verification of hybrid systems. In: Berger, C., Mousavi, M.R. (eds.) CyPhy 2015. LNCS, vol. 9361, pp. 8–24. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25141-7_2
Frehse, G., Ray, R.: Design principles for an extendable verification tool for hybrid systems. In: Proceedings of ADHS 2009, pp. 244–249. IFAC-PapersOnLine (2009)
Fehnker, A., Ivančić, F.: Benchmarks for hybrid systems verification. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 326–341. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24743-2_22
Bu, L., Ray, R., Schupp, S.: ARCH-COMP17 category report: bounded model checking of hybrid systems with piecewise constant dynamics. In: Proceedings of ARCH 2017. EPiC Series in Computing, vol. 48, pp. 134–142. EasyChair (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Schupp, S., Ábrahám, E. (2018). Spread the Work: Multi-threaded Safety Analysis for Hybrid Systems. In: Johnsen, E., Schaefer, I. (eds) Software Engineering and Formal Methods. SEFM 2018. Lecture Notes in Computer Science(), vol 10886. Springer, Cham. https://doi.org/10.1007/978-3-319-92970-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-92970-5_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92969-9
Online ISBN: 978-3-319-92970-5
eBook Packages: Computer ScienceComputer Science (R0)