  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.
