### Abstract

Original language | English |
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Title of host publication | NASA Formal Methods - 11th International Symposium, NFM 2019, Proceedings |

Editors | Kristin Yvonne Rozier, Julia M. Badger |

Number of pages | 18 |

Publisher | Springer |

Publication date | 2019 |

Pages | 298-315 |

ISBN (Print) | 978-3-030-20651-2 |

ISBN (Electronic) | 978-3-030-20652-9 |

DOIs | |

Publication status | Published - 2019 |

Event | NFM19: 11th Annual NASA Formal Methods Symposium: Challenges for Future Exploration - Rice University, Houston, United States Duration: 7 May 2019 → 9 May 2019 Conference number: 11 https://robonaut.jsc.nasa.gov/R2/pages/nfm2019.html |

### Conference

Conference | NFM19: 11th Annual NASA Formal Methods Symposium |
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Number | 11 |

Location | Rice University |

Country | United States |

City | Houston |

Period | 07/05/2019 → 09/05/2019 |

Internet address |

Series | Lecture Notes in Computer Science |
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Volume | 11460 |

ISSN | 0302-9743 |

### Fingerprint

### Keywords

- Model Checking
- Dependency graph
- probabilistic CTL
- On-the-fly methods

### Cite this

*NASA Formal Methods - 11th International Symposium, NFM 2019, Proceedings*(pp. 298-315). Springer. Lecture Notes in Computer Science, Vol.. 11460 https://doi.org/10.1007/978-3-030-20652-9_20

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*NASA Formal Methods - 11th International Symposium, NFM 2019, Proceedings.*Springer, Lecture Notes in Computer Science, vol. 11460, pp. 298-315, NFM19: 11th Annual NASA Formal Methods Symposium, Houston, United States, 07/05/2019. https://doi.org/10.1007/978-3-030-20652-9_20

**Symbolic Model Checking of Weighted PCTL Using Dependency Graphs.** / Jensen, Mathias Claus; Mariegaard, Anders; Larsen, Kim Guldstrand.

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

TY - GEN

T1 - Symbolic Model Checking of Weighted PCTL Using Dependency Graphs

AU - Jensen, Mathias Claus

AU - Mariegaard, Anders

AU - Larsen, Kim Guldstrand

PY - 2019

Y1 - 2019

N2 - We present a global and local algorithm for model checking a weighted variant of PCTL with upper-bound weight constraints, on probabilistic weighted Kripke structures where the weights are vectors with non-zero magnitude. Both algorithms under- and over approximate a fixed-point over a symbolic dependency graph, until sufficient evidence to prove or disprove the given formula is found. Fixed-point computations are carried out in the domain of (multidimensional) probabilistic step functions, encoded as interval decision diagrams. The global algorithm works similarly to classic value iteration for PCTL in that it evaluates all nodes of the dependency graph iteratively, while the local algorithm performs a search-like evaluation of the given dependency graph in an attempt to find enough evidence locally to prove/disprove a given formula, without having to evaluate all nodes. Both algorithms are evaluated on several experiments and we show that the local algorithm generally outperforms the global algorithm.

AB - We present a global and local algorithm for model checking a weighted variant of PCTL with upper-bound weight constraints, on probabilistic weighted Kripke structures where the weights are vectors with non-zero magnitude. Both algorithms under- and over approximate a fixed-point over a symbolic dependency graph, until sufficient evidence to prove or disprove the given formula is found. Fixed-point computations are carried out in the domain of (multidimensional) probabilistic step functions, encoded as interval decision diagrams. The global algorithm works similarly to classic value iteration for PCTL in that it evaluates all nodes of the dependency graph iteratively, while the local algorithm performs a search-like evaluation of the given dependency graph in an attempt to find enough evidence locally to prove/disprove a given formula, without having to evaluate all nodes. Both algorithms are evaluated on several experiments and we show that the local algorithm generally outperforms the global algorithm.

KW - Model Checking

KW - Dependency graph

KW - probabilistic CTL

KW - On-the-fly methods

U2 - 10.1007/978-3-030-20652-9_20

DO - 10.1007/978-3-030-20652-9_20

M3 - Article in proceeding

SN - 978-3-030-20651-2

T3 - Lecture Notes in Computer Science

SP - 298

EP - 315

BT - NASA Formal Methods - 11th International Symposium, NFM 2019, Proceedings

A2 - Rozier, Kristin Yvonne

A2 - Badger, Julia M.

PB - Springer

ER -