## Deciding reachability for planar multi-polynomial systems (1996)

Venue: | In Hybrid Systems III, LNCS 1066 |

Citations: | 14 - 0 self |

### BibTeX

@INPROCEEDINGS{Cerans96decidingreachability,

author = {Karlis Cerans and Juris V Ksna},

title = {Deciding reachability for planar multi-polynomial systems},

booktitle = {In Hybrid Systems III, LNCS 1066},

year = {1996},

pages = {389--400},

publisher = {Springer Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. In this paper we investigate the decidability of the reachability problem for planar non-linear hybrid systems. A planar hybrid system has the property that its state space corresponds to the standard Euclidean plane, which is partitioned into a nite number of (polyhedral) regions. To each of these regions is assigned some vector eld which governs the dynamical behaviour of the system within this region. We prove the decidability of point to point and region to region reachability problems for planar hybrid systems for the case when trajectories within the regions can be described by polynomials of arbitrary degree. 1

### Citations

2176 | A theory of timed automata
- Alur, Dill
- 1994
(Show Context)
Citation Context ...uous variables), this usually makes the system state space (wildly) in nite. However, there has already been much progress in the area, starting from the region graph based methods for Timed Automata =-=[2, 3, 6]-=-, and leading to recent more general results and systematic investigations on what is decidable about hybrid systems (see, for instance, [1, 9, 8]). Still, most of these results are concerned with the... |

658 | The algorithmic analysis of hybrid systems
- Alur
- 1995
(Show Context)
Citation Context ...rom the region graph based methods for Timed Automata [2, 3, 6], and leading to recent more general results and systematic investigations on what is decidable about hybrid systems (see, for instance, =-=[1, 9, 8]-=-). Still, most of these results are concerned with the analysis automation for linear hybrid systems, where the continuous variables are allowed to change the value during the course of time at some x... |

296 | What’s decidable about hybrid automata
- Henzinger, Kopke, et al.
- 1995
(Show Context)
Citation Context ...rom the region graph based methods for Timed Automata [2, 3, 6], and leading to recent more general results and systematic investigations on what is decidable about hybrid systems (see, for instance, =-=[1, 9, 8]-=-). Still, most of these results are concerned with the analysis automation for linear hybrid systems, where the continuous variables are allowed to change the value during the course of time at some x... |

113 | Algorithmic analysis of nonlinear hybrid systems
- Henzinger, Ho
- 1995
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Citation Context ...verned by some non-linear laws. Therefore it is natural to ask, whether there are natural classes of non-linear HS, which do admit automated veri cation. An important study of this problem is already =-=[7]-=-, where the possibilityofveri cation on nonlinear hybrid systems via the reduction to linear clock and rate hybrid automata is discussed, and corresponding at least sound veri cation methods are prese... |

91 | Effective polynomial computation - Zippel |

66 |
Decidability of bisimulation equivalences for parallel timer processes
- Ĉerāns
- 1992
(Show Context)
Citation Context ...uous variables), this usually makes the system state space (wildly) in nite. However, there has already been much progress in the area, starting from the region graph based methods for Timed Automata =-=[2, 3, 6]-=-, and leading to recent more general results and systematic investigations on what is decidable about hybrid systems (see, for instance, [1, 9, 8]). Still, most of these results are concerned with the... |

62 | Hybrid automata with finite bisimulations’’, in ICIALP 95: Automata, Languages, and programming - Henzinger - 1995 |

30 | On some Relations between Dynamical Systems and Transition Systems
- Asarin, Maler
- 1994
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Citation Context ...ts of appropriate polynomials. Our results can be viewed as showing the non-essentiality ofthelinearity requirement for the decidability results in the setting of [10]. However,asit has been shown in =-=[4]-=-, the 2-dimensionality requirement isessential for the decidability of the reachability even for the case of multi-linear systems (in [4] a construction modeling Turing machines by 3-dimensional multi... |

27 |
Reachability analysis of planar multilinear systems
- Maler, Pnueli
- 1993
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Citation Context ...ion reachability problems for planar hybrid systems for the case when trajectories within the regions can be described by polynomials of arbitrary degree. Our results are a generalization of those of =-=[10]-=-, where the subcase of our problem with the vector elds within the regions being constant (the so-called multi-linear model) was considered. We are able to reuse also a part of the proof from [10] tos... |

12 |
Automata for modeling real time systems
- Alur, Dill
- 1990
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Citation Context ...uous variables), this usually makes the system state space (wildly) in nite. However, there has already been much progress in the area, starting from the region graph based methods for Timed Automata =-=[2, 3, 6]-=-, and leading to recent more general results and systematic investigations on what is decidable about hybrid systems (see, for instance, [1, 9, 8]). Still, most of these results are concerned with the... |

12 |
Algorithmic problems in analysis of real time system specifications
- Cerans
- 1992
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Citation Context ...on-deterministic, with any rate from a certain xed interval). It can be noted, however, that for the full class of linear HS even the simpliest veri cation problems are undecidable (see, for instance =-=[6, 5,1]-=-),soany decidability result in this area is bound to indentify a certain subclass of systems to which itdoesapply. ? This work has been partially supported by Grant No.93-596 from Latvian Council of S... |

10 |
Hybrid automata with nite bisimulations
- Henzinger
- 1995
(Show Context)
Citation Context ...rom the region graph based methods for Timed Automata [2, 3, 6], and leading to recent more general results and systematic investigations on what is decidable about hybrid systems (see, for instance, =-=[1, 9, 8]-=-). Still, most of these results are concerned with the analysis automation for linear hybrid systems, where the continuous variables are allowed to change the value during the course of time at some x... |