## Visibly pushdown games (2004)

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Venue: | In FSTTCS 2004 |

Citations: | 18 - 6 self |

### BibTeX

@INPROCEEDINGS{Löding04visiblypushdown,

author = {Christof Löding and P. Madhusudan and Olivier Serre},

title = {Visibly pushdown games},

booktitle = {In FSTTCS 2004},

year = {2004},

pages = {408--420},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. The class of visibly pushdown languages has been recently defined as a subclass of context-free languages with desirable closure properties and tractable decision problems. We study visibly pushdown games, which are games played on visibly pushdown systems where the winning condition is given by a visibly pushdown language. We establish that, unlike pushdown games with pushdown winning conditions, visibly pushdown games are decidable and are 2Exptime-complete. We also show that pushdown games against Ltl specifications and Caret specifications are 3Exptime-complete. Finally, we establish the topological complexity of visibly pushdown languages by showing that they are a subclass of Boolean combinations of Σ3 sets. This leads to an alternative proof that visibly pushdown automata are not determinizable and also shows that visibly pushdown games are determined. 1

### Citations

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(Show Context)
Citation Context ...RI award DAAD19-01-1-0473, and NSF awards ITR/SY 0121431 and CCR 0306382.sprogram analysis questions, static code analysis, and compiler optimization can be reduced to reachability in pushdown models =-=[10]-=- and contemporary software model-checking tools such as Slam [3] implement these decision procedures. Although checking software models against regular specifications is useful, there are important co... |

337 |
On the synthesis of a reactive module
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(Show Context)
Citation Context ...ich is still open. Second, the theory of games form a natural abstraction of the synthesis and control-synthesis problems, where the aim is to synthesize a system that satisfies a given specification =-=[9]-=-. While most results in model checking involve problems on finite graphs, abstraction of data from software programs with procedures results in pushdown models, where the stack is required to maintain... |

220 | Bebop: A symbolic model checker for Boolean programs - Ball, Rajamani - 2000 |

135 | Pushdown processes: Games and model-checking
- Walukiewicz
(Show Context)
Citation Context ...ludes the class of languages defined by Caret and forms a robust subclass of context-free languages [2]. Turning back to games, pushdown games with parity winning conditions are known to be decidable =-=[15]-=-. This shows that pushdown games with any external ω-regular winning condition can also be solved. However, it is easy to see that solving pushdown games against pushdown winning conditions is undecid... |

134 | Visibly pushdown languages
- Alur, Madhusudan
(Show Context)
Citation Context ... inspection, etc. Recently, a temporal logic called Caret [1] has been defined which allows specification of such context-free properties and yet preserves decidability of pushdown model-checking. In =-=[2]-=-, the class of visibly pushdown languages (Vpl) is proposed as an automata theoretic generalization of Caret. These languages are accepted by visibly pushdown automata (Vpa), which are pushdown automa... |

119 | Borel determinacy - Martin - 1975 |

106 | Infinite games on finitely coloured graphs with applications to automata on infinite trees
- Zielonka
- 1998
(Show Context)
Citation Context ...isibly pushdown game is in 2Exptime and pushdown strategies can be effectively built for both players. It is a well known result that there always exists memoryless winning strategies in parity games =-=[6, 17]-=-. Nevertheless, it is not the case for the preceding winning conditions: Proposition 2. There exist a stair parity (resp. visibly) pushdown game and a configuration winning for Eve such that any winni... |

58 |
Classical descriptive set theory, volume 156 of Graduate Texts in Mathematics
- Kechris
- 1995
(Show Context)
Citation Context ...f visibly pushdown languages is contained in the Boolean closure of the third level of the Borel hierarchy. For more details on the definitions and results used in this section we refer the reader to =-=[7]-=- for set-theory in general and to [12] for results related to ω-languages. For a set X we consider X ω as a topological space with the Cantor topology. The open sets of X ω are those of the form U · X... |

54 | A temporal logic of nested calls and returns
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(Show Context)
Citation Context ...ful, there are important context-free requirements—specification of pre-post conditions for procedures, security properties that require stack inspection, etc. Recently, a temporal logic called Caret =-=[1]-=- has been defined which allows specification of such context-free properties and yet preserves decidability of pushdown model-checking. In [2], the class of visibly pushdown languages (Vpl) is propose... |

52 | On model-checking for fragments of µ-calculus
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(Show Context)
Citation Context ...nd-order logic on trees [14, 16]. In formal verification, infinite games are useful in two contexts. First, the model-checking problem for the µ-calculus is intimately related to solving parity games =-=[6]-=-, the precise complexity of which is still open. Second, the theory of games form a natural abstraction of the synthesis and control-synthesis problems, where the aim is to synthesize a system that sa... |

23 |
A short introduction to infinite automata
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(Show Context)
Citation Context ...heory. In particular, the determinacy theorem for these games and the solvability of infinite games on finite graphs are closely related to the decidability of the monadic second-order logic on trees =-=[14, 16]-=-. In formal verification, infinite games are useful in two contexts. First, the model-checking problem for the µ-calculus is intimately related to solving parity games [6], the precise complexity of w... |

20 | Pushdown games with unboundedness and regular conditions
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- 2003
(Show Context)
Citation Context ... ∈ Q. Then (pin, ⊥) is winning for Eve in GH if and only if ((pin, qin), ⊥) is winning for Eve in GST . Now we explain how to adapt the classical techniques for pushdown parity games and its variants =-=[15, 4, 11]-=- in order to solve stair parity games. Let ST = (S, QE, QA, col) be a stair parity game, where S = (Q, Qin, Γ, ∆) and let G = (V, VE, VA, E) be the associated game graph. We construct a finite game gr... |

15 |
Solving pushdown games with a Σ3-winning condition
- Cachat, Duparc, et al.
- 2013
(Show Context)
Citation Context ...ows that pushdown games with any external ω-regular winning condition can also be solved. However, it is easy to see that solving pushdown games against pushdown winning conditions is undecidable. In =-=[5]-=- a new winning condition for pushdown games was proposed, which declares a play winning if and only if along the play, the stack is repeatedly bounded (i.e. there is some stack depth n such that the s... |

14 |
A Landscape with Games in the Background
- Walukiewicz
- 2004
(Show Context)
Citation Context ...heory. In particular, the determinacy theorem for these games and the solvability of infinite games on finite graphs are closely related to the decidability of the monadic second-order logic on trees =-=[14, 16]-=-. In formal verification, infinite games are useful in two contexts. First, the model-checking problem for the µ-calculus is intimately related to solving parity games [6], the precise complexity of w... |

7 | Games with winning conditions of high borel complexity, 2004
- Serre
(Show Context)
Citation Context ... ∈ Q. Then (pin, ⊥) is winning for Eve in GH if and only if ((pin, qin), ⊥) is winning for Eve in GST . Now we explain how to adapt the classical techniques for pushdown parity games and its variants =-=[15, 4, 11]-=- in order to solve stair parity games. Let ST = (S, QE, QA, col) be a stair parity game, where S = (Q, Qin, Γ, ∆) and let G = (V, VE, VA, E) be the associated game graph. We construct a finite game gr... |

2 |
Handbook of Formal Language Theory, volume
- Thomas
- 1997
(Show Context)
Citation Context ...ge over the alphabet TQ. Hence we can build a deterministic parity automaton ST = (S, sin, δ, Ω) which accepts the set of all good words. Moreover, ST can be constructed such that S = 2O(|Q|·log |Q|) =-=[13]-=-. We can also show that the summary information can be generated by a deterministic Vps. Formally, there is a deterministic Vps C with output such that on reading any finite word w, if the factorizati... |

1 |
Handbook of Formal Language Theory, volume III, chapter ωLanguages
- Staiger
- 1997
(Show Context)
Citation Context ...ined in the Boolean closure of the third level of the Borel hierarchy. For more details on the definitions and results used in this section we refer the reader to [7] for set-theory in general and to =-=[12]-=- for results related to ω-languages. For a set X we consider X ω as a topological space with the Cantor topology. The open sets of X ω are those of the form U · X ω for U ⊆ X ∗ . A set L ⊆ X ω is clos... |