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## Synthesis of bounded integer parameters for parametric timed reachability games (2013)

Venue: | In ATVA, volume 8172 of Lecture Notes in Computer Science |

Citations: | 2 - 1 self |

### Citations

2650 | Timed Automata
- Alur
- 1999
(Show Context)
Citation Context ...ues. This approach, however, leads to the undecidability of the most important questions, such as reachability. Related work. Parametric timed automata [2], have been introduced as an extension of TA =-=[1]-=-, to overcome the limit of checking the correctness of the systems with respect to concrete timing constraints. The central problem for verification purposes, reachability-emptiness, which asks whethe... |

578 | Symbolic model checking for real-time systems.
- Henzinger
- 1994
(Show Context)
Citation Context ...ion that assigns a (parametric) invariant to each location. For any Q-valuation v on P , the structure v(A) obtained from A by replacing each constraint γ by v(γ) is a timed automaton with invariants =-=[1,10]-=-. The behavior of a PTA A is described by the behavior of all timed automata obtained by considering all possible valuations of parameters. Definition 2 (Semantics of a PTA). The concrete semantics of... |

243 | On the synthesis of discrete controllers for timed systems (an extended abstract).
- Maler, Pnueli, et al.
- 1995
(Show Context)
Citation Context ...aluations as symbolic constraints between parameters. We argue the relevance of this approach and demonstrate its practical usability with a small case-study. 1 Introduction Timed game automata (TGA) =-=[4,15]-=- have become a widely accepted formalism for modeling and analyzing control problems on timed systems. They are essentially timed automata (TA) with the set of actions divided into controllable (used ... |

157 | Contrloller synthesis for timed automata.
- Asarin, Maler, et al.
- 1998
(Show Context)
Citation Context ...aluations as symbolic constraints between parameters. We argue the relevance of this approach and demonstrate its practical usability with a small case-study. 1 Introduction Timed game automata (TGA) =-=[4,15]-=- have become a widely accepted formalism for modeling and analyzing control problems on timed systems. They are essentially timed automata (TA) with the set of actions divided into controllable (used ... |

146 | Parametric real-time reasoning,”
- Alur, Henzinger, et al.
- 1993
(Show Context)
Citation Context ... research program ImpRo (ANR2010-BLAN-0317). values. This approach, however, leads to the undecidability of the most important questions, such as reachability. Related work. Parametric timed automata =-=[2]-=-, have been introduced as an extension of TA [1], to overcome the limit of checking the correctness of the systems with respect to concrete timing constraints. The central problem for verification pur... |

92 | Linear parametric model checking of timed automata.
- Hune, Romijn, et al.
- 2002
(Show Context)
Citation Context ...ists a parameter valuation such that the automaton has an accepting run, is undecidable. This naturally lead to the search for a subclasses of the model for which some problems would be decidable. In =-=[11]-=-, L/U automata, which use each parameter as either a lower bound or an upper bound on clocks, is proposed. Reachability-emptiness problem is decidable for this model, but the state-space exploration s... |

90 | Efficient on-the-fly algorithms for the analysis of timed games.
- Cassez, David, et al.
- 2005
(Show Context)
Citation Context ...we first compute forward the whole reachable state-space, then propagate backwards the winning states, instead of interleaving the forward and backward computations as done in [12] as an extension of =-=[8]-=-. There would be no problem in restoring that interleaving in the setting proposed here. The computation consists of two fixed-points on the state-space of the PGA. To handle these sets of states, we ... |

72 |
Uppaal-tiga: Time for playing games!
- Behrmann, Cougnard, et al.
- 2007
(Show Context)
Citation Context ... matter what the environment does, the system ends up in the desired location. Such games are known to be decidable [15]. Introduction of this model is followed by the development of the tool support =-=[5]-=- successfully applied to numerous industrial case studies [9]. This model, however, requires complete knowledge of the systems. Thus, it is difficult to use it in the early design stages when the whol... |

45 | An inverse method for parametric timed automata,
- Andre, Chatain, et al.
- 2008
(Show Context)
Citation Context ...L), and they show that the model-checking problem is decidable, in discrete time over a PTA with one parametric clock, if the equality is not allowed in the formulae. A different approach is taken in =-=[3]-=- where the exploration starts from the initial set of parameter values, for which the system is correct, and enlarges the set ensuring that the behaviors of PTA are time-abstract equivalent. They give... |

17 |
S.L.: Decision problems for lower/upper bound parametric timed automata
- Bozzelli, Torre
- 2009
(Show Context)
Citation Context ...bound on clocks, is proposed. Reachability-emptiness problem is decidable for this model, but the state-space exploration still might not terminate. Decidability of L/U automata is further studied in =-=[6]-=-. The authors give the explicit representation of the set of parameters, when all parameters are integers and of the same type (L-automata and U-automata). In [7], the authors allow parameters both in... |

17 | P.A.: Automatic synthesis of robust and optimal controllers — an industrial case study
- Cassez, Jessen, et al.
- 2009
(Show Context)
Citation Context ...desired location. Such games are known to be decidable [15]. Introduction of this model is followed by the development of the tool support [5] successfully applied to numerous industrial case studies =-=[9]-=-. This model, however, requires complete knowledge of the systems. Thus, it is difficult to use it in the early design stages when the whole system is not fully characterized. Even when all timing con... |

16 | Integer parameter synthesis for timed automata.
- Jovanovic, Lime, et al.
- 2013
(Show Context)
Citation Context ... valuations Z. Then we define Succ(S, e) as Succ(Sl, e), with l being the source location of edge e. The reachable state-space of the PGA can be computed by the following fixed-point (when it exists) =-=[13]-=-: Sn+1 = Init(A)↗ ∪ ⋃ e∈E Succ(Sn, e), with S0 = ∅ The final fixed-point set is noted S∗. It follows from [11] that all Z are finite unions of convex polyhedra. In order to compute the winning states,... |

16 | Reachability-time games on timed automata
- Jurdziński, Trivedi
- 2007
(Show Context)
Citation Context ...n be enumerated in exponential time. Therefore, a problem that is EXPTIME for TGA, the corresponding bounded integer version for PGA is also EXPTIME. The reachability game is EXPTIME-complete for TGA =-=[14]-=-, and it is a special case of the reachability-emptiness game for PGA. We can thus conclude that the reachability-emptiness (synthesis) game for PGA is EXPTIME-complete for bounded integer parameters.... |

15 | Real-time model checking: Parameters everywhere,
- Raskin, Bruyere
- 2003
(Show Context)
Citation Context ...of L/U automata is further studied in [6]. The authors give the explicit representation of the set of parameters, when all parameters are integers and of the same type (L-automata and U-automata). In =-=[7]-=-, the authors allow parameters both in the model and the property (PTCTL), and they show that the model-checking problem is decidable, in discrete time over a PTA with one parametric clock, if the equ... |

4 | O.H.: Real-time control with parametric timed reachability games
- Jovanović, Faucou, et al.
(Show Context)
Citation Context ...uring that the behaviors of PTA are time-abstract equivalent. They give a conjecture for the termination of the algorithm, being true on the studied examples. Parametric Timed Game Automata (PGA): In =-=[12]-=-, we have introduced an extension of TGA, called parametric timed game automata (PGA) and its subclass for which the reachability-emptiness game, which asks whether there exist a parameter valuation s... |