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Reachability problems for hierarchical piecewise constant derivative systems
conference contribution
posted on 2013-10-17, 11:15 authored by Paul Bell, Shang ChenIn this paper, we investigate the computability and complexity of reachability problems for two-dimensional hierarchical piecewise constant derivative (HPCD) systems. The main interest in HPCDs stems from the fact that their reachability problem is on the border between decidability and undecidability, since it is equivalent to that of reachability for one-dimensional piecewise affine maps (PAMs) which is a long standing open problem. Understanding the most expressive hybrid system models that retain decidability for reachability has generated a great deal of interest over the past few years. In this paper, we show a restriction of HPCDs (called RHPCDs) which leads to the reachability problem becoming decidable. We then study which additional powers we must add to the RHPCD model to render it 1D PAM-equivalent. Finally, we show NP-hardness of reachability for nondeterministic RHPCDs.
History
School
- Science
Department
- Computer Science
Citation
BELL, P.C. and CHEN, S., 2013. Reachability problems for hierarchical piecewise constant derivative systems. IN: Abdulla, P.Z. and Potapov, I. (eds.). Reachability Problems for Hierarchical Piecewise Constant Derivative Systems: 7th International Workshop, RP 2013, Uppsala, Sweden, September 24-26, 2013 Proceedings. Lecture Notes in Computer Science; 8169, pp. 46-58.Publisher
© Springer-Verlag Berlin HeidelbergVersion
- AM (Accepted Manuscript)
Publication date
2013Notes
The final publication is available at link.springer.com.ISBN
9783642410369;9783642410352ISSN
0302-9743Publisher version
Book series
Notes in Computer Science;8169Language
- en