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Decidability and Complexity Results for Timed Automata and Semi-linear Hybrid Automata

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Hybrid Systems: Computation and Control (HSCC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1790))

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Abstract

We define a new class of hybrid automata for which reach-ability is decidable—a proper superclass of the initialized rectangular hybrid automata—by taking parallel compositions of simple components. Attempting to generalize, we encounter timed automata with algebraic constants. We show that reachability is undecidable for these algebraic timed automata by simulating two-counter Minsky machines. Modifying the construction to apply to parametric timed automata, we reprove the undecidability of the emptiness problem, and then distinguish the dense and discrete-time cases with a new result. The algorithmic complexity—both classical and parametric—of one-clock parametric timed automata is also examined. We finish with a table of computability-theoretic complexity results, including that the existence of a Zeno run is Σ 11 -complete for semi-linear hybrid automata; it is too complex to be expressed in first-order arithmetic.

Research supported by the ARO under the MURI program “Integrated Approach to Intelligent Systems”, grant no. DAA H04-96-1-0341.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, NY, 14853

    Joseph S. Miller

Authors
  1. Joseph S. Miller
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Editor information

Editors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Nancy Lynch

  2. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15235, USA

    Bruce H. Krogh

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© 2000 Springer-Verlag Berlin Heidelberg

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Miller, J.S. (2000). Decidability and Complexity Results for Timed Automata and Semi-linear Hybrid Automata. In: Lynch, N., Krogh, B.H. (eds) Hybrid Systems: Computation and Control. HSCC 2000. Lecture Notes in Computer Science, vol 1790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46430-1_26

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  • DOI: https://doi.org/10.1007/3-540-46430-1_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67259-3

  • Online ISBN: 978-3-540-46430-3

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