Abstract
We show the NP-hardness of the reachability and mortality problems for a three dimensional variant of Piecewise Constant Derivative (PCD) system called a bounded 3-dimensional Restricted Hierarchical PCD (3-RHPCD). Both problems are shown to be in PSPACE, even for n-dimensional 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.
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Bell, P.C., Chen, S., Jackson, L. (2014). Reachability and Mortality Problems for Restricted Hierarchical Piecewise Constant Derivatives. In: Ouaknine, J., Potapov, I., Worrell, J. (eds) Reachability Problems. RP 2014. Lecture Notes in Computer Science, vol 8762. Springer, Cham. https://doi.org/10.1007/978-3-319-11439-2_3
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DOI: https://doi.org/10.1007/978-3-319-11439-2_3
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