The Polyhedron-Hitting Problem
Ventsislav Chonev, Joël Ouaknine, James Worrell · 2014
We consider polyhedral versions of Kannan and Lipton’s Orbit Problem—determining whether a target polyhedron V may be reached from a starting point x under repeated applications of a linear transformation A in an ambient vector space Qm. We present what amounts to a com-plete characterisation of the decidability landscape for this problem, expressed as a function of the dimension m of the ambient space, together with the dimension of the polyhedral target V: more precisely, for each pair of dimensions, we either establish decidability, or show hardness for longstanding open problems. 1