Reachability and mortality problems for restricted hierarchical piecewise constant derivatives

Abstract

We show the NP-hardness of the reachability and mortality problems for a three dimensional variant of Piecewise Constant Derivative (PCD) systemcalled a bounded 3-dimensional Restricted Hierarchical PCD (3-RHPCD).Both problems are shown to be in PSPACE, even for ndimensional RHPCD. This is a restricted model with similarities to other models in the literature such as stopwatch automata, rectangular automata and PCDs.We also show that for an unbounded 3-RHPCD, both problems become undecidable via a simulation of a Minsky machine.