## Expressiveness of updatable timed automata (2000)

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Venue: | Theoretical Computer Science |

Citations: | 28 - 9 self |

### BibTeX

@INPROCEEDINGS{Bouyer00expressivenessof,

author = {Patricia Bouyer and Catherine Dufourd and Emmanuel Fleury and Antoine Petit},

title = {Expressiveness of updatable timed automata},

booktitle = {Theoretical Computer Science},

year = {2000},

pages = {232--242},

publisher = {Springer}

}

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### Abstract

Abstract. We investigate extensions of Alur and Dill’s timed automata, based on the possibility to update the clocks in a more elaborate way than simply reset them to zero. We call these automata updatable timed automata. They form an undecidable class of models, in the sense that emptiness checking is not decidable. However, using an extension of the region graph construction, we exhibit interesting decidable subclasses. In a surprising way, decidability depends on the nature of the clock constraints which are used, diagonal-free or not, whereas these constraints play identical roles in timed automata. We thus describe in a quite precise way the thin frontier between decidable and undecidable classes of updatable timed automata. We also study the expressive power of updatable timed automata. It turns out that any updatable automaton belonging to some decidable subclass can be effectively transformed into an equivalent timed automaton without updates but with silent transitions. The transformation suffers from an enormous combinatorics blow-up which seems unavoidable. Therefore, updatable timed automata appear to be a concise model for representing and analyzing large classes of timed systems. 1

### Citations

3430 |
Communication and Concurrency
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- 1989
(Show Context)
Citation Context ...e of the families is equivalent to one automaton of the other. We write ` in both cases. For instance, Aut " (C df (X); U 0 (X)) ` Aut " (C(X); U 0 (X)), (see e.g. [7]). Bisimilarity Bisim=-=ilarity [15, 14-=-] is stronger than language equivalence. It denes a step by step correspondence between two transition systems. Two labelled transition systemssT = (S; S 0 ; E; ( e !) e2E ) and T 0 = (S 0 ; S 0 0 ; E... |

2176 | A theory of timed automata
- Alur, Dill
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(Show Context)
Citation Context ...mata (among them, see [ACD + 92], [AHV93], [AFH94], [ACH94], [Wil94], [HKWT95]). However the major property of timed automata is probably that emptiness checking is a decidable problem for this model =-=[AD94]-=-. Based on this nice theoretical result, several model-checkers have been developed (for instance CMC 1 [LL98], HYTECH 2 [HHWT95,HHWT97], KRONOS 3 [Yov97] and UPPAAL 4 [LPY97,BLL + 98]) and a lot of c... |

558 | UPPAAL in a nutshell
- Larsen, Pettersson, et al.
- 1997
(Show Context)
Citation Context ...ity between updatable and classical timed automata. 1 Introduction Since their introduction by Alur and Dill [2, 3], timed automata have been one of the most studied models for real-time systems (see =-=[4, 1, 16, 8, 12, 17, 13]-=-). In particular numerous works proposed extensions of timed automata [7, 10, 11]. This paper focuses on one of this extension, the so-called updatable timed automata, introduced in order to model the... |

438 | Automata for Modelling Real-Time Systems - Alur, Dill - 1994 |

392 | Hytech: a model checker for hybrid systems. Software Tools for Technology Transfer
- Henzinger, Ho, et al.
- 1997
(Show Context)
Citation Context ...ity between updatable and classical timed automata. 1 Introduction Since their introduction by Alur and Dill [2, 3], timed automata have been one of the most studied models for real-time systems (see =-=[4, 1, 16, 8, 12, 17, 13]-=-). In particular numerous works proposed extensions of timed automata [7, 10, 11]. This paper focuses on one of this extension, the so-called updatable timed automata, introduced in order to model the... |

109 | Parametric real-time reasoning
- Alur, Henzinger, et al.
- 1993
(Show Context)
Citation Context ...omata are one of the most-studied and most-established models for real-time systems. Numerous works have been devoted to the “theoretical” comprehension of timed automata (among them, see [ACD + 92], =-=[AHV93]-=-, [AFH94], [ACH94], [Wil94], [HKWT95]). However the major property of timed automata is probably that emptiness checking is a decidable problem for this model [AD94]. Based on this nice theoretical re... |

59 | H.W.Toi. An implementation of three algorithms for timing verification based on automata emptiness - Alur, Courcoubetis, et al. - 1992 |

57 | Characterization of the expressive power of silent transitions in timed automata
- Bérard, Petit, et al.
- 1998
(Show Context)
Citation Context ...e not allowed but coincides with the original model otherwise. Note that, contrary to the untimed setting, silent transitions strictly increase the expressive power of the model (see [BGP96,DGP97] or =-=[BDGP98]-=- for a survey). Several other exotic extensions have been proposed among which we can mention [DZ98] where subsets of clocks can be “freezed”. The aim of the present paper is to investigate an other w... |

55 | Specifying timed state sequences in powerful decidable logics and timed automata. Formal Techniques
- Wilke
- 1994
(Show Context)
Citation Context ...ity between updatable and classical timed automata. 1 Introduction Since their introduction by Alur and Dill [2, 3], timed automata have been one of the most studied models for real-time systems (see =-=[4, 1, 16, 8, 12, 17, 13]-=-). In particular numerous works proposed extensions of timed automata [7, 10, 11]. This paper focuses on one of this extension, the so-called updatable timed automata, introduced in order to model the... |

51 | New Generation of UPPAAL - Bengtsson, Larsen, et al. |

45 | A determinizable class of timed automata - Alur, Fix, et al. - 1994 |

42 | Are timed automata updatable - Bouyer, Dufourd, et al. - 2000 |

40 | The observational power of clocks
- Alur, Courcoubetis, et al.
- 1994
(Show Context)
Citation Context ...he most-studied and most-established models for real-time systems. Numerous works have been devoted to the “theoretical” comprehension of timed automata (among them, see [ACD + 92], [AHV93], [AFH94], =-=[ACH94]-=-, [Wil94], [HKWT95]). However the major property of timed automata is probably that emptiness checking is a decidable problem for this model [AD94]. Based on this nice theoretical result, several mode... |

32 | Shrinking timed automata
- Sankur, Bouyer, et al.
- 2011
(Show Context)
Citation Context ...oint of view, the main interest of this work is to provide a sound theoretical framework for the use of updatable timed automata as a model in real case studies (if that was necessary, a recent paper =-=[Bou03]-=- has recalled how much these theoretical frameworks were necessary to tools). Indeed, updatable timed automata allow to represent in a concise way systems which can not be modelled in a natural way by... |

20 | Timed automata with periodic clock constraints
- Choffrut, Goldwurm
(Show Context)
Citation Context ...ks with a constant leads to an undecidable class of automata (see [AD94] but also [Duf97,BD00] where more precise results on the number of clocks are given). Periodic clock constraints, as defined in =-=[CG00]-=-, allow to express properties like "the value of a clock is even" or "the value of a clock is of the form 0.5+3n where n is some integer. The corresponding class of automata is strictly more powerful ... |

18 | On the power of non observable actions in timed automata - Bérard, Gastin, et al. - 1996 |

17 | Static guard analysis in timed automata verification - Behrmann, Bouyer, et al. - 2003 |

16 | Automated verification of a parametric real-time program: the ABR conformance protocol - Bérard, Fribourg - 1999 |

15 |
Controlled timed automata
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(Show Context)
Citation Context ...Alur and Dill [2, 3], timed automata have been one of the most studied models for real-time systems (see [4, 1, 16, 8, 12, 17, 13]). In particular numerous works proposed extensions of timed automata =-=[7, 10, 11]-=-. This paper focuses on one of this extension, the so-called updatable timed automata, introduced in order to model the ATM protocol ABR [9]. Updatable timed automata are constructed with updates of t... |

12 | Analysing the pgm protocol with uppaal - Berard, Bouyer, et al. - 2002 |

12 |
Concurrency and automata on in¯nite sequences
- Park
- 1981
(Show Context)
Citation Context ...e of the families is equivalent to one automaton of the other. We write ` in both cases. For instance, Aut " (C df (X); U 0 (X)) ` Aut " (C(X); U 0 (X)), (see e.g. [7]). Bisimilarity Bisim=-=ilarity [15, 14-=-] is stronger than language equivalence. It denes a step by step correspondence between two transition systems. Two labelled transition systemssT = (S; S 0 ; E; ( e !) e2E ) and T 0 = (S 0 ; S 0 0 ; E... |

11 | Timed automata and additive clock constraints
- Bérard, Dufourd
(Show Context)
Citation Context |

9 |
Kronos: A verication tool for real-time systems
- Yovine
- 1997
(Show Context)
Citation Context |

4 |
Automatic verication of a parametric real-time program : the ABR conformance protocol
- Brard, Fribourg
- 1999
(Show Context)
Citation Context ...umerous works proposed extensions of timed automata [7, 10, 11]. This paper focuses on one of this extension, the so-called updatable timed automata, introduced in order to model the ATM protocol ABR [9]. Updatable timed automata are constructed with updates of the following forms: x : c j x : y + c where x; y are clocks; c 2 Q + and 2 f ; =; 6=; ; >g In [5], the (un)decidability of emptiness of... |

4 | Analysing the PGM protocol with UPPAAL - Brard, Bouyer, et al. - 2002 |

3 | Jean-François Monin. A compared study of two correctness proofs for the standardized algorithm of abr conformance - Bérard, Fribourg, et al. |

3 | Removing ε-transitions in timed automata - Diekert, Gastin, et al. |

1 |
Expressiveness of updatable timed automata. Research report, ENS de Cachan
- Bouyer, Dufourd, et al.
- 2000
(Show Context)
Citation Context ...ata are introduced in Section 3. The bisimulation algorithms are presented in Section 4. For lack of space, this paper contains only some sketchs of proofs. They are available on the technical report [6]. 2 Updatable Timed Automata Timed Words and Clocks If Z is any set, let Z (respectively Z ! ) be the set of nite (resp. innite) sequences of elements in Z and let Z 1 = Z [Z ! . We consider as ... |

1 | Removing #-transitions in timed automata - Diekert, Gastin, et al. |