Olga Tveretina (Karlsruhe Institute of Technology) |
Daniel Funke (Karlsruhe Institute of Technology) |
This paper deals with the problem of point-to-point reachability in multi-linear systems. These systems consist of a partition of the Euclidean space into a finite number of regions and a constant derivative assigned to each region in the partition, which governs the dynamical behavior of the system within it. The reachability problem for multi-linear systems has been proven to be decidable for the two-dimensional case and undecidable for the dimension three and higher.
Multi-linear systems however exhibit certain properties that make them very suitable for topological analysis. We prove that reachability can be decided exactly in the 3-dimensional case when systems satisfy certain conditions. We show with experiments that our approach can be orders of magnitude more efficient than simulation. |
ArXived at: https://dx.doi.org/10.4204/EPTCS.54.18 | bibtex | |
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