Robust undecidability of timed and hybrid systems.

*(English)*Zbl 0944.93018
Lynch, Nancy (ed.) et al., Hybrid systems: computation and control. 3rd international workshop, HSCC 2000, Pittsburgh, PA, USA, March 23-25, 2000. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1790, 145-159 (2000).

Authors’ 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 distinguished 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.

For the entire collection see [Zbl 0934.00029].

For the entire collection see [Zbl 0934.00029].

Reviewer: D.Franke (Hamburg)

##### MSC:

93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |

93C65 | Discrete event control/observation systems |

68Q45 | Formal languages and automata |

93C73 | Perturbations in control/observation systems |