2011/06/07 by Olga Tveretina, Daniel Funke
Computer Science · #cs.LO
paper · pdf · doi:10.4204/eptcs.54.18
published as EPTCS 54, 2011, pp. 250-262 · In Proceedings GandALF 2011, arXiv:1106.0814
arxiv created 2011/06/07 · arxiv updated 2011/06/08
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.