Abstract
We present a new approach to compute the reachable set with a bounded number of jumps for a rectangular automaton. The reachable set under a flow transition is computed as a polyhedron which is represented by a conjunction of finitely many linear constraints. If the bound is viewed as a constant, the computation time is polynomial in the number of variables.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? J. Comput. Syst. Sci. 57(1), 94–124 (1998)
Henzinger, T.A., Ho, P., Wong-Toi, H.: Algorithmic analysis of nonlinear hybrid systems. IEEE Transactions on Automatic Control 43(4), 540–554 (1998)
Preußig, J., Kowalewski, S., Wong-Toi, H., Henzinger, T.A.: An algorithm for the approximative analysis of rectangular automata. In: Ravn, A.P., Rischel, H. (eds.) FTRTFT 1998. LNCS, vol. 1486, pp. 228��240. Springer, Heidelberg (1998)
Wong-Toi, H., Preußig, J.: A procedure for reachability analysis of rectangular automata. In: Proc. of American Control Conference, vol. 3, pp. 1674–1678 (2000)
Doyen, L., Henzinger, T.A., Raskin, J.: Automatic rectangular refinement of affine hybrid systems. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 144–161. Springer, Heidelberg (2005)
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Chutinan, A., Krogh, B.H.: Computing polyhedral approximations to flow pipes for dynamic systems. In: Proc. of CDC 1998. IEEE Press, Los Alamitos (1998)
Stursberg, O., Krogh, B.H.: Efficient representation and computation of reachable sets for hybrid systems. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 482–497. Springer, Heidelberg (2003)
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)
Henzinger, T.A., Ho, P.-H., Wong-Toi, H.: Hytech: A model checker for hybrid systems. Software Tools for Technology Transfer (1), 110–122 (1997)
Frehse, G.: Phaver: Algorithmic verification of hybrid systems past hytech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005)
Ziegler, G.M.: Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. Springer, Heidelberg (1995)
Chen, X., Abraham, E., Frehse, G.: Efficient bounded reachability computation for rectangular automata. Technical report, RWTH Aachen University (2011), http://www-i2.informatik.rwth-aachen.de/i2/hybrid_research_pub0/
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
Fukuda, K.: From the zonotope construction to the minkowski addition of convex polytopes. J. Symb. Comput. 38(4), 1261–1272 (2004)
Weibel, C., Fukuda, K.: Computing faces up to k dimensions of a minkowski sum of polytopes. In: Proc. of CCCG 2005, pp. 256–259 (2005)
Henzinger, T.A.: The theory of hybrid automata. In: Proc. of LICS 1996, pp. 278–292 (1996)
Fukuda, K.: cdd, cddplus and cddlib homepage, http://www.ifor.math.ethz.ch/~fukuda/cdd_home/
Frehse, G., Le Guernic, C., Donzé, A., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: Spaceex: Scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, X., Ábrahám, E., Frehse, G. (2011). Efficient Bounded Reachability Computation for Rectangular Automata. In: Delzanno, G., Potapov, I. (eds) Reachability Problems. RP 2011. Lecture Notes in Computer Science, vol 6945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24288-5_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-24288-5_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24287-8
Online ISBN: 978-3-642-24288-5
eBook Packages: Computer ScienceComputer Science (R0)