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Algorithmic Analysis of Polygonal Hybrid Systems, Part I: Reachability
, 2007
"... In this work we are concerned with the formal verification of twodimensional nondeterministic hybrid systems, namely polygonal differential inclusion systems (SPDIs). SPDIs are a class of nondeterministic systems that correspond to piecewise constant differential inclusions on the plane, for which ..."
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Cited by 14 (6 self)
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In this work we are concerned with the formal verification of twodimensional nondeterministic hybrid systems, namely polygonal differential inclusion systems (SPDIs). SPDIs are a class of nondeterministic systems that correspond to piecewise constant differential inclusions on the plane, for which we study the reachability problem. Our contribution is the development of an algorithm for solving exactly the reachability problem of SPDIs. We extend the geometric approach due to Maler and Pnueli [MP93] to nondeterministic systems, based on the combination of three techniques: the representation of the twodimensional continuoustime dynamics as a onedimensional discretetime system (using Poincaré maps), the characterization of the set of qualitative behaviors of the latter as a finite set of types of signatures, and acceleration used to explore reachability according to each of these types.
Computing Invariance Kernels of Polygonal Hybrid Systems
 NORDIC JOURNAL OF COMPUTING
, 2004
"... Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. One way of analysing such systems (and hybrid systems in general) is through the study of their phase portrait, which characterise the systems’ qualitative behav ..."
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Cited by 7 (5 self)
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Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions. One way of analysing such systems (and hybrid systems in general) is through the study of their phase portrait, which characterise the systems’ qualitative behaviour. In this paper we identify and compute an important object of polygonal hybrid systems’ phase portrait, namely invariance kernels. An invariant set is a set of points such that any trajectory starting in such point keep necessarily rotating in the set forever and the invariance kernel is the largest of such sets. We show that this kernel is a nonconvex polygon and we give a noniterative algorithm for computing the coordinates of its vertexes and edges. Moreover, we show some properties of such systems’ simple cycles.
Compositional algorithm for parallel model checking of polygonal hybrid systems
 In 3rd International Colloquium on Theoretical Aspects of Computing (ICTAC’06), volume 4281 of LNCS
, 2006
"... 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 ..."
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Cited by 6 (6 self)
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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. 1
A New BreadthFirst Search Algorithm for Deciding SPDI Reachability
, 2003
"... Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions (SPDIs). Using an important object of SPDIs' phase portrait, the invariance kernels, which can be computed noniteratively, we present a breadthfirst sea ..."
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Cited by 2 (1 self)
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Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant differential inclusions (SPDIs). Using an important object of SPDIs' phase portrait, the invariance kernels, which can be computed noniteratively, we present a breadthfirst search algorithm for solving the reachability problem for SPDIs. Invariance kernels play an important role in the termination of the algorithm.
General Terms Verification of hybrid systems
"... Analysis of systems containing both discrete and continuous dynamics, hybrid systems, is a difficult issue. Most problems have been shown to be undecidable in general, and decidability holds only for few classes where the dynamics are restricted and/or the dimension is low. In this paper we present ..."
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Analysis of systems containing both discrete and continuous dynamics, hybrid systems, is a difficult issue. Most problems have been shown to be undecidable in general, and decidability holds only for few classes where the dynamics are restricted and/or the dimension is low. In this paper we present some theoretical results concerning the decidability of the reachability problem for a class of planar hybrid systems called Generalized Polygonal Hybrid Systems (GSPDI). These new results provide means to optimize a previous reachability algorithm, making the implementation feasible. We also discuss the implementation of the algorithm into the tool GSPeeDI.
Fig.1. GSPDI.
"... Abstract. 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 socalled SPDIs. Unlike SPeeDI (a tool for re ..."
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Abstract. 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 socalled SPDIs. Unlike SPeeDI (a tool for reachability analysis of SPDIs) the underlying analysis of GSPeeDI is based on a breadthfirst search algorithm, and it can handle more general systems.
Improving Polygonal Hybrid Systems Reachability Analysis through the use of the Phase Portrait Abstract
"... In this paper we deal with a subclass of planar hybrid automata, denoted by SPDI, which can be represented by piecewise constant differential inclusions. The computation of certain objects of the phase portrait of an SPDI, namely the viability, controllability, invariance kernels and semiseparatrix ..."
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In this paper we deal with a subclass of planar hybrid automata, denoted by SPDI, which can be represented by piecewise constant differential inclusions. The computation of certain objects of the phase portrait of an SPDI, namely the viability, controllability, invariance kernels and semiseparatrix curves have been shown to be efficiently decidable. On the other hand, although the reachability problem for SPDIs is known to be decidable, its complexity makes it unfeasible on large systems. We present and combine recent results on the use of the SPDI phase portraits for improving reachability analysis by (i) statespace reduction and (ii) decomposition techniques of the state space, enabling compositional parallelization of the analysis. Both techniques contribute to increase the feasibility of reachability analysis on large SPDI systems. Key words: hybrid systems, polygonal differential inclusions; compositional reachability algorithm 1
ABSTRACT Improving Polygonal Hybrid Systems Reachability Analysis through the use of the Phase Portrait
"... Polygonal hybrid systems (SPDI) are a subclass of planar hybrid automata which can be represented by piecewise constant dierential inclusions. The computation of certain objects of the phase portrait of an SPDI, namely the viability, controllability, invariance kernels and semiseparatrix curves hav ..."
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Polygonal hybrid systems (SPDI) are a subclass of planar hybrid automata which can be represented by piecewise constant dierential inclusions. The computation of certain objects of the phase portrait of an SPDI, namely the viability, controllability, invariance kernels and semiseparatrix curves have been shown to be eciently decidable. On the other hand, although the reachability problem for SPDIs is known to be decidable, its complexity makes it unfeasible on large systems. We summarise our recent results on the use of the SPDI phase portraits for improving reachability analysis by (i) statespace reduction and (ii) decomposition techniques of the state space, enabling compositional parallelisation of the analysis. Both techniques contribute to increasing the feasability of reachability analysis on large SPDI systems. 1.
Computation and Visualisation of Phase Portraits for Model Checking SPDIs
"... Hybrid systems combining discrete and continuous dynamics arise as mathematical models of various artificial and natural systems, and as an approximation to complex continuous systems. Reachability analysis has been the principal research question in the verification of hybrid systems, even though i ..."
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Hybrid systems combining discrete and continuous dynamics arise as mathematical models of various artificial and natural systems, and as an approximation to complex continuous systems. Reachability analysis has been the principal research question in the verification of hybrid systems, even though it is a wellknown