## Efficient on-the-fly algorithms for the analysis of timed games (2005)

### Cached

### Download Links

Venue: | IN CONCUR 05, LNCS 3653 |

Citations: | 60 - 18 self |

### BibTeX

@INPROCEEDINGS{Cassez05efficienton-the-fly,

author = {Franck Cassez and Alexandre David and Emmanuel Fleury and Kim G. Larsen and Didier Lime},

title = {Efficient on-the-fly algorithms for the analysis of timed games},

booktitle = {IN CONCUR 05, LNCS 3653},

year = {2005},

pages = {66--80},

publisher = {Springer}

}

### OpenURL

### Abstract

In this paper, we propose a first efficient on-the-fly algorithm for solving games based on timed game automata with respect to reachability and safety properties. The algorithm we propose is a symbolic extension of the on-the-fly algorithm suggested by Liu & Smolka [15] for linear-time model-checking of finite-state systems. Being on-the-fly, the symbolic algorithm may terminate long before having explored the entire state-space. Also the individual steps of the algorithm are carried out efficiently by the use of so-called zones as the underlying data structure. Various optimizations of the basic symbolic algorithm are proposed as well as methods for obtaining time-optimal winning strategies (for reachability games). Extensive evaluation of an experimental implementation of the algorithm yields very encouraging performance results.

### Citations

2203 | A theory of timed automata
- AND, DILL
- 1994
(Show Context)
Citation Context .... Also for timed systems, on-the-fly algorithms have been absolutely crucial to the success of model-checking tools such as Kronos [8] and Uppaal [13] in their analysis of timed automata based models =-=[2]-=-. Both reachability, safety as 1 Though timed games for long have been known to be decidable there has until now been a lack of efficient and truly on-the-fly algorithms for their analysis.swell as ge... |

566 | UPPAAL in a Nutshell
- Larsen, Pettersson, et al.
- 1997
(Show Context)
Citation Context ...h performs on-the-fly model-checking of LTL properties. Also for timed systems, on-the-fly algorithms have been absolutely crucial to the success of model-checking tools such as Kronos [8] and Uppaal =-=[13]-=- in their analysis of timed automata based models [2]. Both reachability, safety as 1 Though timed games for long have been known to be decidable there has until now been a lack of efficient and truly... |

416 |
The SPIN Model Checker
- Holzmann
- 2003
(Show Context)
Citation Context ...nce the end of the 80’s [12,4,15] and is one of the most important techniques applied in finite-state model-checkers using enumerative or explicit state-space representation, as is the case with SPIN =-=[10]-=-, which performs on-the-fly model-checking of LTL properties. Also for timed systems, on-the-fly algorithms have been absolutely crucial to the success of model-checking tools such as Kronos [8] and U... |

208 | On the synthesis of discrete controllers for timed systems - Maler, Pnueli, et al. - 1995 |

169 | On the synthesis of strategies in infinite games
- Thomas
- 1995
(Show Context)
Citation Context ... strategies over G. A strategy f is state-based whenever ∀ρ, ρ ′ ∈ Runs(G),last(ρ) = last(ρ ′ ) implies that f(ρ) = f(ρ ′ ). Statebased strategies are also called memoryless strategies in game theory =-=[9,19]-=-. The restricted behavior of a TGA G controlled with some strategy f is defined by the notion of outcome [9]. Definition 4 (Outcome). Let G = (L, ℓ0, Act, X, E, Inv) be a TGA and f a strategy over G. ... |

129 | Kronos: a Model-Checking Tool for Real-Time Systems
- Bozga, Daws, et al.
- 1998
(Show Context)
Citation Context ...SPIN [10], which performs on-the-fly model-checking of LTL properties. Also for timed systems, on-the-fly algorithms have been absolutely crucial to the success of model-checking tools such as Kronos =-=[8]-=- and Uppaal [13] in their analysis of timed automata based models [2]. Both reachability, safety as 1 Though timed games for long have been known to be decidable there has until now been a lack of eff... |

125 | Controller synthesis for timed automata
- Asarin, Maler, et al.
- 1998
(Show Context)
Citation Context ...ously, for all initial states of the form (ℓ1, x) with x ≤ 1 there is such a winning strategy2 . Fig.1. A Timed Game Automaton Though such timed game automata for long have been known to be decidable =-=[16,6,9]-=- there is still a lack of efficient and truly on-the-fly algorithms for their analysis. Most of the suggested algorithms are based on backwards fix-point computations of the set of winning states [16,... |

93 | Optimal paths in weighted timed automata
- Alur, Torre, et al.
- 2001
(Show Context)
Citation Context ...en successfully applied to optimal scheduling problems with guiding and pruning heuristics being added to yield on-the-fly algorithms which quickly lead to near-optimal (time- or cost-wise) schedules =-=[5,3,11,18]-=-. x < 1 u2 x := 0 x < 1 u3 c3 ℓ1 ℓ2 ℓ3 ℓ4 x > 1;u1 x ≤ 1;c1 x ≥ 2;c2 x ≤ 1;c4 ℓ5 Goal We consider timed game automata and how to decide the existence of a winning strategy w.r.t. reachability or safet... |

89 |
Model checking and boolean graphs
- Andersen
- 1994
(Show Context)
Citation Context ...ntire state-space of the given model. For finite-state (untimed) systems the search for optimal (linear) on-the-fly or local algorithms has been a very active research topic since the end of the 80’s =-=[12,4,15]-=- and is one of the most important techniques applied in finite-state model-checkers using enumerative or explicit state-space representation, as is the case with SPIN [10], which performs on-the-fly m... |

69 | As soon as possible: Time optimal control for timed automata
- Asarin, Maler
- 1999
(Show Context)
Citation Context ...en successfully applied to optimal scheduling problems with guiding and pruning heuristics being added to yield on-the-fly algorithms which quickly lead to near-optimal (time- or cost-wise) schedules =-=[5,3,11,18]-=-. x < 1 u2 x := 0 x < 1 u3 c3 ℓ1 ℓ2 ℓ3 ℓ4 x > 1;u1 x ≤ 1;c1 x ≥ 2;c2 x ≤ 1;c4 ℓ5 Goal We consider timed game automata and how to decide the existence of a winning strategy w.r.t. reachability or safet... |

48 |
Resource-optimal scheduling using priced timed automata
- Rasmussen, Larsen, et al.
- 2004
(Show Context)
Citation Context ...en successfully applied to optimal scheduling problems with guiding and pruning heuristics being added to yield on-the-fly algorithms which quickly lead to near-optimal (time- or cost-wise) schedules =-=[5,3,11,18]-=-. x < 1 u2 x := 0 x < 1 u3 c3 ℓ1 ℓ2 ℓ3 ℓ4 x > 1;u1 x ≤ 1;c1 x ≥ 2;c2 x ≤ 1;c4 ℓ5 Goal We consider timed game automata and how to decide the existence of a winning strategy w.r.t. reachability or safet... |

44 | Symbolic algorithms for infinite-state games
- Alfaro, Henzinger, et al.
- 2001
(Show Context)
Citation Context ...ously, for all initial states of the form (ℓ1, x) with x ≤ 1 there is such a winning strategy2 . Fig.1. A Timed Game Automaton Though such timed game automata for long have been known to be decidable =-=[16,6,9]-=- there is still a lack of efficient and truly on-the-fly algorithms for their analysis. Most of the suggested algorithms are based on backwards fix-point computations of the set of winning states [16,... |

36 |
Efficient Local Correctness Checking
- Larsen
- 1992
(Show Context)
Citation Context ...ntire state-space of the given model. For finite-state (untimed) systems the search for optimal (linear) on-the-fly or local algorithms has been a very active research topic since the end of the 80’s =-=[12,4,15]-=- and is one of the most important techniques applied in finite-state model-checkers using enumerative or explicit state-space representation, as is the case with SPIN [10], which performs on-the-fly m... |

32 | On-the-Fly Controller Synthesis for Discrete and Dense-Time Systems
- Tripakis, Altisen
- 1999
(Show Context)
Citation Context ...tion graph of the timed game automata of Fig. 1, which incorrectly classifies the initial state as being uncontrollable when viewed as a finite-state game. As a remedy to this problem, the authors of =-=[20,1]-=- propose a partially onthe-fly method for solving reachability games for a timed game automaton A. However, this method involves an extremely expensive preprocessing step in which the quotient graph o... |

24 | Optimal-reachability and control for acyclic weighted timed automata
- Torre, Mukhopadhyay, et al.
- 2002
(Show Context)
Citation Context |

23 | Simple linear-time algorithms for minimal fixed points (extended abstract
- Liu, Smolka
- 1998
(Show Context)
Citation Context ...olving games based on timed game automata with respect to reachability and safety properties 1 . The algorithm we propose is a symbolic extension of the on-the-fly algorithm suggested by Liu & Smolka =-=[15]-=- for linear-time model-checking of finite-state systems. Being on-the-fly, the symbolic algorithm may terminate long before having explored the entire state-space. Also the individual steps of the alg... |

15 | Tools for controller synthesis of timed systems
- Altisen, Tripakis
(Show Context)
Citation Context ...tion graph of the timed game automata of Fig. 1, which incorrectly classifies the initial state as being uncontrollable when viewed as a finite-state game. As a remedy to this problem, the authors of =-=[20,1]-=- propose a partially onthe-fly method for solving reachability games for a timed game automaton A. However, this method involves an extremely expensive preprocessing step in which the quotient graph o... |

9 |
Distributed reachability analysis in timed automata. Software Tool For Technology Transfer (STTT), 2004. Currently available in the Online First edition of STTT
- Behrmann
(Show Context)
Citation Context ...ular for optimal strategies. Our algorithm is well suited for distributed implementation by its use of unordered waiting-list and there are plans to pursue this directions as has been done for Uppaal =-=[7]-=-. We are also investigating how to extract strategies and represent them compactly with CDDs (Clock Decision Diagrams). Acknowledgments. The authors want to thank Patricia Bouyer and Gerd Behrmann for... |

6 |
Controller Synthesis for the “Production Cell” Case Study
- Melcher, Winkelmann
- 1998
(Show Context)
Citation Context ...ted: with or without inclusion checking between zones, with or without back-propagation of the losing states, and with or without pruning. To benchmark the implementations we used the Production Cell =-=[14,17]-=- case study (Fig. 6). Unprocessed plates arrive on a feeding belt, are taken by a robot to a press, are processed, and are taken away to a departure belt. The robot has two arms (A and B) to take and ... |

4 |
Production Cell: A Comparative Study in Formal Specification and Verification
- Lewerentz, Lindner
- 1995
(Show Context)
Citation Context ...ted: with or without inclusion checking between zones, with or without back-propagation of the losing states, and with or without pruning. To benchmark the implementations we used the Production Cell =-=[14,17]-=- case study (Fig. 6). Unprocessed plates arrive on a feeding belt, are taken by a robot to a press, are processed, and are taken away to a departure belt. The robot has two arms (A and B) to take and ... |