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        Deciding Reachability for Piecewise Constant Derivative Systems on Orientable Manifolds

        Author
        Sandler, Andrei
        Tveretina, Olga
        Attention
        2299/22466
        Abstract
        A hybrid automaton is a finite state machine combined with some k real-valued continuous variables, where k determines the number of the automaton dimensions. This formalism is widely used for modelling safety-critical systems, and verification tasks for such systems can often be expressed as the reachability problem for hybrid automata. Asarin, Mysore, Pnueli and Schneider defined classes of hybrid automata lying on the boundary between decidability and undecidability in their seminal paper ‘Low dimensional hybrid systems - decidable, undecidable, don’t know’ [9]. They proved that certain decidable classes become undecidable when given a little additional computational power, and showed that the reachability question remains unsolved for some 2-dimensional systems. Piecewise Constant Derivative Systems on 2-dimensional manifolds (or PCD2m) constitute a class of hybrid automata for which decidability of the reachability problem is unknown. In this paper we show that the reachability problem becomes decidable for PCD2m if we slightly limit their dynamics, and thus we partially answer the open question of Asarin, Mysore, Pnueli and Schneider posed in [9].
        Publication date
        2019-09-06
        Published in
        Reachability Problems - 13th International Conference, RP 2019, Proceedings
        Published version
        https://doi.org/10.1007/978-3-030-30806-3_14
        License
        Other
        Other links
        http://hdl.handle.net/2299/22466
        Relations
        School of Engineering and Computer Science
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