Linear Parametric Model Checking of Timed Automata
We present an extension of the model checker Uppaal capable of synthesize linear parameter constraints for the correctness of parametric timed automata. The symbolic representation of the (parametric) state-space is shown to be correct. A second contribution of this paper is the identification of a subclass of parametric timed automata (L/U automata), for which the emptiness problem is decidable, contrary to the full class where it is know to be undecidable. Also we present a number of lemmas enabling the verification effort to be reduced for L/U automata in some cases. We illustrate our approach by deriving linear parameter constraints for a number of well-known case studies from the literature (exhibiting a flaw in a published paper).
- 2.R. Alur, T.A. Henzinger, and M.Y. Vardi. Parametric real-time reasoning. In Proc. 25th Annual Symp. on Theory of Computing, pages 592–601. ACM Press, 1993.Google Scholar
- 4.G. Bandini, R. Lutje Spelberg, and H. Toetenel. Parametric verification of the IEEE 1394a root contention protocol using LPMC. http://tvs.twi.tudelft.nl/, July 2000. Submitted.
- 6.T.H. Cormen, C.E. Leiserson, and R.L. Rivest. Introduction to Algorithms. McGraw-Hill, Inc., 1991.Google Scholar
- 8.D. Dill. Timing assumptions and verification of finite-state concurrent systems. In Proc. Int. Workshop on Automatic Verification Methods for Finite State Systems, LNCS 407, pages 197–212. Springer-Verlag, 1990.Google Scholar
- 9.T. A. Henzinger, P.-H. Ho, and H. Wong-Toi. HyTech: A Model Checker for Hybrid Systems. In Proc. 9th Int. Conference on Computer Aided Verification, LNCS 1254, pages 460–463. Springer-Verlag, 1997.Google Scholar
- 10.T.S. Hune, J.M.T. Romijn, M.I.A. Stoelinga, and F.W. Vaandrager. Linear parametric model checking of timed automata. Report CSI-R0102, CSI, University of Nijmegen, January 2001.Google Scholar
- 12.R.F. Lutje Spelberg, W.J. Toetenel, and M. Ammerlaan. Partition refinement in real-time model checking. In Proc. FTRTFT’98, LNCS 1486, pages 143–157. Springer-Verlag, 1998.Google Scholar
- 13.D.P.L. Simons and M.I.A. Stoelinga. Mechanical verification of the IEEE 1394a root contention protocol using Uppaal2k. Technical Report CSI-R0009, CSI, University of Nijmegen, May 2000. Conditionally accepted for STTT.Google Scholar
- 15.S. Yovine. Model checking timed automata. In Lectures on Embedded Systems, LNCS 1494, pages 114–152. Springer-Verlag, October 1998.Google Scholar