## On the Verification by Approximation of Duration Systems (2003)

### BibTeX

@MISC{Berregeb03onthe,

author = {Narjes Berregeb and Riadh Robbana},

title = {On the Verification by Approximation of Duration Systems},

year = {2003}

}

### OpenURL

### Abstract

Abstract: We consider the problem of verifying invariance properties for duration systems. Such systems are (extended) timed graphs with duration variables. They are especially suitable for describing real time schedulers. However, for this kind of systems, the verification problem of invariance properties is in general undecidable. We propose an over approximation method based on a particular extension of a given duration system, and we show that our over approximation includes all the digitization of all the real computations of the duration system. The over-approximated system can then be used to perform an interesting close analysis of invariance properties of the initial system, while other existing approaches fail.

### Citations

1965 | A theory of timed automata
- Alur, Dill
- 1994
(Show Context)
Citation Context ...tion of a finite region graph obtained by partitioning the (noncountable) set of states into a finite set of regions such that all the states in a same region satisfy the same reachability properties =-=[1, 2]-=-. However, such a finite region graph does not exist in general when integrators are considered. Actually, it has been shown that the reachability problem is undecidable for timed graphs extended by o... |

596 | The algorithmic analysis of hybrid systems
- Alur, Courcoubetis, et al.
- 1995
(Show Context)
Citation Context ...oposed in [4, 6, 10, 18, 19]. Duration variables are called integrators or stopwatch in [4, 18]. It is proved in [13] that stopwatch automata [18] have the same expressivity as linear hybrid automata =-=[5]-=-. The problem we consider in this paper is the verification of invariance properties for timed systems modelled by DVTG's. Invariance properties correspond to safety requirements on the behavior of th... |

360 |
Model-checking for realtime systems
- Alur, Courcoubetis, et al.
- 1990
(Show Context)
Citation Context ...formal verification, real-time scheduler. Received March 1, 2003; accepted October 30, 2003 1. Introduction Timed graphs constitute a powerful formalism widely adopted for modelling real-time systems =-=[3, 7, 16, 18, 21]-=-. A timed graph is a finite control locations graph, supplied with a set of clocks that can be tested and reset at each transition between locations. Each clock counts the elapsed time since its last ... |

359 | Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems - Alur, Courcoubetis, et al. - 1993 |

266 | What’s decidable about hybrid automata
- Henzinger, Kopke, et al.
- 1998
(Show Context)
Citation Context ...s one to reason about the durations of some particular locations instead of the whole elapsed time in some computation. DVTG's are particular cases of the general models of hybrid systems proposed in =-=[4, 9, 14, 18, 19]-=-. We give hereafter their formal definition and their operational semantics. 2.1. Definition First of all, let us introduce the notion of guard. Given a set of variables X, a guard on X is a boolean c... |

109 | What good are digital clocks
- Henzinger, Manna, et al.
- 1992
(Show Context)
Citation Context ...on 4 presents an example of the use of DVTG's to model timed systems and invariance formulas to express safety requirements on these systems. Then, in section 5, we present the notion of digitization =-=[15]-=- that we use and we define our approximation method. In section 6, we present the verification results. Concluding remarks are presented in section 7. 2. Duration Variables Timed Graphs We introduce i... |

77 | An approach to the description and analysis of hybrid systems - Nicollin, Olivero, et al. - 1993 |

64 |
Decidability of Bisimulation Equivalences for Parallel Timer Processes
- ˘Cerāns
- 1992
(Show Context)
Citation Context ...h a finite region graph does not exist in general when integrators are considered. Actually, it has been shown that the reachability problem is undecidable for timed graphs extended by one integrator =-=[11]-=-. This paper presents a technique extending a given DVTG system into another one containing the initial148 The International Arab Journal of Information Technology, Vol. 1, No. 2, July 2004 computati... |

23 | Decidable integration graphs - Kesten, Pnueli, et al. - 1999 |

22 |
On the automatic verification of systems with continuous variables and unbounded discrete data structures
- Bouajjani, Echahed, et al.
- 1994
(Show Context)
Citation Context ...formal verification, real-time scheduler. Received March 1, 2003; accepted October 30, 2003 1. Introduction Timed graphs constitute a powerful formalism widely adopted for modelling real-time systems =-=[3, 7, 16, 18, 21]-=-. A timed graph is a finite control locations graph, supplied with a set of clocks that can be tested and reset at each transition between locations. Each clock counts the elapsed time since its last ... |

21 | Liveness and acceleration in parameterized verification
- Pnueli, Shahar
- 2000
(Show Context)
Citation Context ...erties for timed systems modelled by DVTG's. Invariance properties correspond to safety requirements on the behavior of these systems, and thus, they constitute the major part of their specifications =-=[20]-=-. Invariance properties are the duals of reachability properties. Hence, the verification of invariance properties is equivalent to solving reachability problems. It is well known that the reachabilit... |

17 |
Verifying invariance properties of timed systems with duration variables
- Bouajjani, Echahed, et al.
- 1994
(Show Context)
Citation Context ...umulated times, we must use a clock that can be stopped (frozen) when the task is interrupted, and resumed when the task is active. This is typically the case of real-time schedulers with pre-emption =-=[8]-=-. Thus, a natural and interesting extension of timed graphs remains consistent considering duration variables that count accumulated times spent at some particular control locations. Actually, duratio... |

11 |
D.L.: Automata for modeling real time systems
- Alur, Dill
- 1990
(Show Context)
Citation Context ...tion of a finite region graph obtained by partitioning the (noncountable) set of states into a finite set of regions such that all the states in a same region satisfy the same reachability properties =-=[1, 2]-=-. However, such a finite region graph does not exist in general when integrators are considered. Actually, it has been shown that the reachability problem is undecidable for timed graphs extended by o... |

8 |
Symbolic model checking for real time systems
- Henzinger, Nicollin, et al.
- 1994
(Show Context)
Citation Context ...formal verification, real-time scheduler. Received March 1, 2003; accepted October 30, 2003 1. Introduction Timed graphs constitute a powerful formalism widely adopted for modelling real-time systems =-=[3, 7, 16, 18, 21]-=-. A timed graph is a finite control locations graph, supplied with a set of clocks that can be tested and reset at each transition between locations. Each clock counts the elapsed time since its last ... |

3 |
Verification of context-free timed systems using linear hybrid observers
- Bouajjani, Echahed, et al.
(Show Context)
Citation Context ...s one to reason about the durations of some particular locations instead of the whole elapsed time in some computation. DVTG's are particular cases of the general models of hybrid systems proposed in =-=[4, 9, 14, 18, 19]-=-. We give hereafter their formal definition and their operational semantics. 2.1. Definition First of all, let us introduce the notion of guard. Given a set of variables X, a guard on X is a boolean c... |

2 |
Verification of Duration Systems Using an Approximation Approach
- Robbana
(Show Context)
Citation Context ...used to verify duration systems represented by DVTG's with a finite number of integrators while all the known models for which reachability is decidable [6, 8, 18] or can be verified by approximation =-=[22, 23]-=- have strong constraints and have at most one integrator. The paper is organized as follows. In the next section, we introduce our computational models, namely the duration variables timed graphs and ... |

1 |
Verifying ωRegular Properties for Subclasses of Linear Hybrid Systems
- Bouajjani, Robbana
- 1995
(Show Context)
Citation Context ...ntroduced in [8] which are defined exactly as timed graphs except that they involve duration variables instead of clocks. DVTG are particular cases of the general models of hybrid systems proposed in =-=[4, 6, 10, 18, 19]-=-. Duration variables are called integrators or stopwatch in [4, 18]. It is proved in [13] that stopwatch automata [18] have the same expressivity as linear hybrid automata [5]. The problem we consider... |

1 |
From Duration Calculus to Linear Hybrid Systems
- Bouajjani, Lakhnech, et al.
- 1995
(Show Context)
Citation Context ...ntroduced in [8] which are defined exactly as timed graphs except that they involve duration variables instead of clocks. DVTG are particular cases of the general models of hybrid systems proposed in =-=[4, 6, 10, 18, 19]-=-. Duration variables are called integrators or stopwatch in [4, 18]. It is proved in [13] that stopwatch automata [18] have the same expressivity as linear hybrid automata [5]. The problem we consider... |

1 |
The Impressive Power of Stopwatches
- Frank, Kim
- 2000
(Show Context)
Citation Context ...instead of clocks. DVTG are particular cases of the general models of hybrid systems proposed in [4, 6, 10, 18, 19]. Duration variables are called integrators or stopwatch in [4, 18]. It is proved in =-=[13]-=- that stopwatch automata [18] have the same expressivity as linear hybrid automata [5]. The problem we consider in this paper is the verification of invariance properties for timed systems modelled by... |

1 |
Integration Graphs: A Class of Durable Hybrid Systems
- Kesten, Pnueli, et al.
- 1993
(Show Context)
Citation Context |

1 |
Réduction et Vérification de Systèmes Temps-Réel Distribués,” in Colloque Francophone de l'Ingénierie des Protocoles (CFIP'99
- Robbana
- 1999
(Show Context)
Citation Context |

1 |
Verification of Integrated Timed Systems
- Robbana
- 1998
(Show Context)
Citation Context ...used to verify duration systems represented by DVTG's with a finite number of integrators while all the known models for which reachability is decidable [6, 8, 18] or can be verified by approximation =-=[22, 23]-=- have strong constraints and have at most one integrator. The paper is organized as follows. In the next section, we introduce our computational models, namely the duration variables timed graphs and ... |