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 PCD\(_{2m}\)) 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 PCD\(_{2m}\) if we slightly limit their dynamics, and thus we partially answer the open question of Asarin, Mysore, Pnueli and Schneider posed in [9].
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Notes
- 1.
A PCD can be seen as a special case of Polygonal Differential Inclusion Systems (SPDIs).
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Acknowledgements
The authors thank Vincent Delecroix, Alexey Kanel-Belov, Alexey Klimenko, Alexandra Skripchenko and Eugene Asarin for their kind help and consultations.
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Sandler, A., Tveretina, O. (2019). Deciding Reachability for Piecewise Constant Derivative Systems on Orientable Manifolds. In: Filiot, E., Jungers, R., Potapov, I. (eds) Reachability Problems. RP 2019. Lecture Notes in Computer Science(), vol 11674. Springer, Cham. https://doi.org/10.1007/978-3-030-30806-3_14
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