Abstract
This paper investigates the time-bounded version of the reachability problem for hybrid automata. This problem asks whether a given hybrid automaton can reach a given target location within T time units, where T is a constant rational value. We show that, in contrast to the classical (unbounded) reachability problem, the timed-bounded version is decidable for rectangular hybrid automata provided only non-negative rates are allowed. This class of systems is of practical interest and subsumes, among others, the class of stopwatch automata. We also show that the problem becomes undecidable if either diagonal constraints or both negative and positive rates are allowed.
Work supported by the projects: (i) QUASIMODO (FP7- ICT-STREP-214755), Quasimodo: “Quantitative System Properties in Model-Driven-Design of Embedded”, http://www.quasimodo.aau.dk/ , (ii) GASICS (ESF-EUROCORES LogiCCC), Gasics: “Games for Analysis and Synthesis of Interactive Computational Systems”, http://www.ulb.ac.be/di/gasics/ , (iii) Moves: “Fundamental Issues in Modelling, Verification and Evolution of Software”, http://moves.ulb.ac.be , a PAI program funded by the Federal Belgian Government, (iv) the ARC project AUWB-2010–10/15-UMONS-3, (v) the FRFC project 2.4515.11 and (vi) a grant from the National Bank of Belgium.
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Brihaye, T., Doyen, L., Geeraerts, G., Ouaknine, J., Raskin, JF., Worrell, J. (2011). On Reachability for Hybrid Automata over Bounded Time. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22012-8_33
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DOI: https://doi.org/10.1007/978-3-642-22012-8_33
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