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
Computation and visualisation of phase portraits for model checking SPDIs
Gordon J. Pace,Gerardo Schneider +1 more
- 29 Mar 2008
TL;DR: This work states that polygonal hybrid systems (SPDIs) can be used, for instance, in the analysis of approximations of non-linear differential equations in two-dimensions.
ParaPlan: A Tool for Parallel Reachability Analysis of Planar Polygonal Differential Inclusion Systems
Andrei Sandler,Olga Tveretina +1 more
- 06 Sep 2017
TL;DR: Andrei Sandler, and Olga Tveretina, ‘ParaPlan: A Tool for Parallel Reachability Analysis of Planar Polygonal Differential Inclusion Systems’, in Patricia Bouyer, Andrea Orlandini and Pierluigi San Pietro, eds.
ParaPlan: A Tool for Parallel Reachability Analysis of Planar Polygonal Differential Inclusion Systems
Andrei Sandler,Olga Tveretina +1 more
TL;DR: The ParaPlan tool as mentioned in this paper provides the reachability analysis of planar hybrid systems defined by differential inclusions (SPDI) using the parallelized and optimized version of the algorithm underlying the SPeeDI tool.
Improving Polygonal Hybrid Systems Reachability Analysis through the use of the Phase Portrait
Gordon J. Pace,Gerardo Schneider +1 more
- 01 Jan 2008
TL;DR: This paper presents and combines recent results on the use of the SPDI phase portraits for improving reachability analysis by (i) state-space reduction and (ii) decomposition techniques of the state space, enabling compositional parallelization of the analysis.
Reachability analysis of complex planar hybrid systems
Hallstein Asheim Hansen,Gerardo Schneider,Gerardo Schneider,Martin Steffen +3 more
- 01 Dec 2013
TL;DR: An optimized algorithm that answers reachability questions for GSPDIs, where all cycles in the reachability graph are accelerated, and an algorithm by which more complex planar hybrid automata are over-approximated by G SPDIs subject to two measures of precision.
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.