On the decidability and complexity of problems for restricted hierarchical hybrid systems

Bell

doi:10.1016/j.tcs.2016.09.003

On the decidability and complexity of problems for restricted hierarchical hybrid systems

Bell

Authors

Paul Bell p.c.bell@keele.ac.uk

Abstract

We study variants of a recently introduced hybrid system model, called a Hierarchical Piecewise Constant Derivative (HPCD). These variants (loosely called Restricted HPCDs) form a class of natural models with similarities to many other well known hybrid system models in the literature such as Stopwatch Automata, Rectangular Automata and PCDs. We study the complexity of reachability and mortality problems for variants of RHPCDs and show a variety of results, depending upon the allowed powers. These models form a useful tool for the study of the complexity of such problems for hybrid systems, due to their connections with existing models. We show that the reachability problem and the mortality problem are co-NP-hard for bounded 3-dimensional RHPCDs (3-RHPCDs). Reachability is shown to be in PSPACE, even for n-dimensional RHPCDs. We show that for an unbounded 3-RHPCD, the reachability and mortality problems become undecidable. For a nondeterministic variant of 2-RHPCDs, the reachability problem is shown to be PSPACE-complete.

Acceptance Date	Sep 6, 2016
Publication Date	Nov 1, 2016
Journal	Theoretical Computer Science
Print ISSN	0304-3975
Publisher	Elsevier
Pages	47 - 63
DOI	https://doi.org/10.1016/j.tcs.2016.09.003
Publisher URL	https://www.sciencedirect.com/science/article/pii/S0304397516304674?via%3Dihub