@inproceedings{4434,
  abstract     = {The algorithmic approach to the analysis of timed and hybrid systems is fundamentally limited by undecidability, of universality in the timed case (where all continuous variables are clocks), and of emptiness in the rectangular case (which includes drifting clocks). Traditional proofs of undecidability encode a single Turing computation by a single timed trajectory. These proofs have nurtured the hope that the introduction of “fuzziness” into timed and hybrid models (in the sense that a system cannot distinguish between trajectories that are sufficiently similar) may lead to decidability. We show that this is not the case, by sharpening both fundamental undecidability results. Besides the obvious blow our results deal to the algorithmic method, they also prove that the standard model of timed and hybrid systems, while not “robust” in its definition of trajectory acceptance (which is affected by tiny perturbations in the timing of events), is quite robust in its mathematical properties: the undecidability barriers are not affected by reasonable perturbations of the model.},
  author       = {Henzinger, Thomas A and Raskin, Jean},
  booktitle    = {Proceedings of the 3rd International Workshop on Hybrid Systems},
  isbn         = {9783540672593},
  location     = {Pittsburgh, PA, USA},
  pages        = {145 -- 159},
  publisher    = {Springer},
  title        = {{Robust undecidability of timed and hybrid systems}},
  doi          = {10.1007/3-540-46430-1_15},
  volume       = {1790},
  year         = {2000},
}

@inproceedings{4481,
  abstract     = {Since hybrid embedded systems are pervasive and often safety-critical, guarantees about their correct performance are desirable. The hybrid systems model checker HyTech provides such guarantees and has successfully verified some systems. However, HyTech severely restricts the continuous dynamics of the system being analyzed and, therefore, often forces the use of prohibitively expensive discrete and polyhedral abstractions. We have designed a new algorithm, which is capable of directly verifying hybrid systems with general continuous dynamics, such as linear and nonlinear differential equations. The new algorithm conservatively overapproximates the reachable states of a hybrid automaton by using interval numerical methods. Interval numerical methods return sets of points that enclose the true result of numerical computation and, thus, avoid distortions due to the accumulation of round-off errors. We have implemented the new algorithm in a successor tool to HyTech called HyperTech. We consider three examples: a thermostat with delay, a two-tank water system, and an air-traffic collision avoidance protocol. HyperTech enables the direct, fully automatic analysis of these systems, which is also more accurate than the use of polyhedral abstractions.},
  author       = {Henzinger, Thomas A and Horowitz, Benjamin and Majumdar, Ritankar and Wong Toi, Howard},
  booktitle    = {Proceedings of the 3rd International Workshop on Hybrid Systems},
  isbn         = {9783540672593},
  location     = {Pittsburgh, PA, USA},
  pages        = {130 -- 144},
  publisher    = {Springer},
  title        = {{Beyond HyTech: Hybrid systems analysis using interval numerical methods}},
  doi          = {10.1007/3-540-46430-1_14},
  volume       = {1790},
  year         = {2000},
}