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Bell, PC, Chen, S and Jackson, L (2016) On the decidability and complexity of problems for restricted hierarchical hybrid systems. Theoretical Computer Science, 652. pp. 47-63. ISSN 0304-3975
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On the decidability and complexity of problems for restricted hierarchical hybrid systems.pdf - Accepted Version Available under License Creative Commons Attribution Non-commercial No Derivatives. Download (579kB) | Preview |
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.
| Item Type: | Article |
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| Uncontrolled Keywords: | 08 Information And Computing Sciences, 01 Mathematical Sciences |
| Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
| Divisions: | Computer Science & Mathematics |
| Publisher: | Elsevier |
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| Date Deposited: | 27 Sep 2018 11:17 |
| Last Modified: | 04 Sep 2021 02:25 |
| DOI or ID number: | 10.1016/j.tcs.2016.09.003 |
| URI: | https://researchonline.ljmu.ac.uk/id/eprint/9331 |
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