Book Chapter10.1007/11921240_12
A compositional algorithm for parallel model checking of polygonal hybrid systems
Gordon J. Pace,Gerardo Schneider +1 more
- 20 Nov 2006
- pp 168-182
TL;DR: In this article, a compositional parallel algorithm for reachability analysis of planar hybrid systems defined by constant differential inclusions (SPDI) has been presented, based on the qualitative information obtained from the phase portrait of an SPDI, in particular the controllability kernel.
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Abstract: The reachability problem as well as the computation of the phase portrait for the class of planar hybrid systems defined by constant differential inclusions (SPDI), has been shown to be decidable. The existing reachability algorithm is based on the exploitation of topological properties of the plane which are used to accelerate certain kind of cycles. The complexity of the algorithm makes the analysis of large systems generally unfeasible. In this paper we present a compositional parallel algorithm for reachability analysis of SPDIs. The parallelization is based on the qualitative information obtained from the phase portrait of an SPDI, in particular the controllability kernel.
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Citations
Algorithmic analysis of polygonal hybrid systems, part I: Reachability
TL;DR: The development of an algorithm for solving exactly the reachability problem of SPDIs, a class of non-deterministic systems that correspond to piecewise constant differential inclusions on the plane, is developed.
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Algorithmic analysis of polygonal hybrid systems, Part II: Phase portrait and tools
TL;DR: This paper shows how to compute the viability, controllability and invariance kernels, as well as semi-separatrix curves for SPDIs, and presents the tool SPeeDI^+, which implements a reachability algorithm and computes phase portraits of SPDIs.
13
Relaxing Goodness Is Still Good
Gordon J. Pace,Gerardo Schneider +1 more
- 01 Sep 2008
TL;DR: The decidability result is extended to generalised SPDIs (GSPDI), SPDIs not satisfying the goodness assumption, and an algorithmic solution to decide reachability of such systems is given.
GSPeeDI --- A Verification Tool for Generalized Polygonal Hybrid Systems
Hallstein Asheim Hansen,Gerardo Schneider +1 more
- 12 Aug 2009
TL;DR: The GSPeeDI tool implements a decision procedure for the reachability analysis of GSPDIs, planar hybrid systems whose dynamics is given by differential inclusions, and that are not restricted by the goodness assumption from previous work on the so-called SPDIs.
4
Proceedings of CSAW'06
John Abela,Angelo Dalli,Kristian Guillaumier +2 more
- 01 Jan 2006
TL;DR: The proceedings of the fourth Computer Science Annual Workshop (CSAW’06) were published in this paper, which was held at the University of Malta, Valletta, Malta.
References
A theory of timed automata
Rajeev Alur,David L. Dill +1 more
TL;DR: Alur et al. as discussed by the authors proposed timed automata to model the behavior of real-time systems over time, and showed that the universality problem and the language inclusion problem are solvable only for the deterministic automata: both problems are undecidable (II i-hard) in the non-deterministic case and PSPACE-complete in deterministic case.
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Widening the Boundary between Decidable and Undecidable Hybrid Systems
Eugene Asarin,Gerardo Schneider +1 more
- 20 Aug 2002
TL;DR: It is shown that the reachable question for some two dimensional hybrid systems are undecidable and that for other 2-dim systems this question remains unanswered, showing that it is as hard as the reachability problem for Piecewise Affine Maps, that is a well known open problem.