### Abstract

We reiterate the textbook automata-theoretic approach, which reduces the model checking problem to the graph problem of finding cycles. We discuss several parallel algorithms that attack this problem in various ways, each with different characteristics: Depth-first search (DFS) based algorithms rely on heuristics for good parallelization, but exhibit a low complexity and good on-the-fly behavior. Breadth-first search (BFS) based approaches, on the other hand, offer good parallel scalability and support distributed parallelism.

In addition, we present various simpler model checking tasks, which still solve a large and important subset of the LTL model checking problem, and how how these can be exploited to yield more efficient algorithms. In particular, we provide simplified DFS-based search algorithms and show that the BFS-based algorithms exhibit optimal runtimes in certain cases.

Original language | English |
---|---|

Title of host publication | Handbook of Parallel Constraint Reasoning |

Editors | Youssef Hamadi, Lakhdar Sais |

Place of Publication | Cham |

Publisher | Springer |

Chapter | 12 |

Pages | 457-507 |

Number of pages | 51 |

ISBN (Electronic) | 978-3-319-63516-3 |

ISBN (Print) | 978-3-319-63515-6 |

DOIs | |

Publication status | Published - 2018 |

### Fingerprint

### Keywords

- LTL model checking
- nested depth-first search
- strongly connected components
- NDFS
- SCC-detection
- Büchi emptiness
- TGBA

### Cite this

*Handbook of Parallel Constraint Reasoning*(pp. 457-507). Cham: Springer. https://doi.org/10.1007/978-3-319-63516-3_12

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*Handbook of Parallel Constraint Reasoning.*Springer, Cham, pp. 457-507. https://doi.org/10.1007/978-3-319-63516-3_12

**Parallel Model Checking Algorithms for Linear-Time Temporal Logic.** / Barnat, Jiri; Bloemen, Vincent; Duret-Lutz, Alexandre; Laarman, Alfons; Petrucci, Laure; van de Pol, Jaco; Renault, Etienne.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Parallel Model Checking Algorithms for Linear-Time Temporal Logic

AU - Barnat, Jiri

AU - Bloemen, Vincent

AU - Duret-Lutz, Alexandre

AU - Laarman, Alfons

AU - Petrucci, Laure

AU - van de Pol, Jaco

AU - Renault, Etienne

PY - 2018

Y1 - 2018

N2 - Model checking is a fully automated, formal method for demonstrating absence of bugs in reactive systems. Here, bugs are violations of properties in Linear-time Temporal Logic (LTL). A fundamental challenge to its application is the exponential explosion in the number of system states. The current chapter discusses the use of parallelism in order to overcome this challenge.We reiterate the textbook automata-theoretic approach, which reduces the model checking problem to the graph problem of finding cycles. We discuss several parallel algorithms that attack this problem in various ways, each with different characteristics: Depth-first search (DFS) based algorithms rely on heuristics for good parallelization, but exhibit a low complexity and good on-the-fly behavior. Breadth-first search (BFS) based approaches, on the other hand, offer good parallel scalability and support distributed parallelism.In addition, we present various simpler model checking tasks, which still solve a large and important subset of the LTL model checking problem, and how how these can be exploited to yield more efficient algorithms. In particular, we provide simplified DFS-based search algorithms and show that the BFS-based algorithms exhibit optimal runtimes in certain cases.

AB - Model checking is a fully automated, formal method for demonstrating absence of bugs in reactive systems. Here, bugs are violations of properties in Linear-time Temporal Logic (LTL). A fundamental challenge to its application is the exponential explosion in the number of system states. The current chapter discusses the use of parallelism in order to overcome this challenge.We reiterate the textbook automata-theoretic approach, which reduces the model checking problem to the graph problem of finding cycles. We discuss several parallel algorithms that attack this problem in various ways, each with different characteristics: Depth-first search (DFS) based algorithms rely on heuristics for good parallelization, but exhibit a low complexity and good on-the-fly behavior. Breadth-first search (BFS) based approaches, on the other hand, offer good parallel scalability and support distributed parallelism.In addition, we present various simpler model checking tasks, which still solve a large and important subset of the LTL model checking problem, and how how these can be exploited to yield more efficient algorithms. In particular, we provide simplified DFS-based search algorithms and show that the BFS-based algorithms exhibit optimal runtimes in certain cases.

KW - LTL model checking

KW - nested depth-first search

KW - strongly connected components

KW - NDFS

KW - SCC-detection

KW - Büchi emptiness

KW - TGBA

U2 - 10.1007/978-3-319-63516-3_12

DO - 10.1007/978-3-319-63516-3_12

M3 - Chapter

SN - 978-3-319-63515-6

SP - 457

EP - 507

BT - Handbook of Parallel Constraint Reasoning

A2 - Hamadi, Youssef

A2 - Sais, Lakhdar

PB - Springer

CY - Cham

ER -