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arXiv · 1106.1245

Deciding Reachability for 3-Dimensional Multi-Linear Systems

Olga Tveretina·Daniel Funke
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Abstract

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.

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Olga Tveretina, Daniel Funke. 2011-06-07. Deciding Reachability for 3-Dimensional Multi-Linear Systems. https://doi.org/10.4204/eptcs.54.18

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