## Abstract

Liveness temporal properties state that something "good" eventually happens, e.g., every request is eventually granted. In Linear Temporal Logic (LTL), there is no a priori bound on the "wait time" for an eventuality to be fulfilled. That is, F θ asserts that θ holds eventually, but there is no bound on the time when θ will hold. This is troubling, as designers tend to interpret an eventuality F θ as an abstraction of a bounded eventuality F ^{≤k} θ, for an unknown k, and satisfaction of a liveness property is often not acceptable unless we can bound its wait time. We introduce here prompt-LTL, an extension of LTL with the prompt-eventually operator F _{p} . A system S satisfies a prompt-LTL formula φ if there is some bound k on the wait time for all prompt-eventually subformulas of φ in all computations of S. We study various problems related to prompt-LTL, including realizability, model checking, and assume-guarantee model checking, and show that they can be solved by techniques that are quite close to the standard techniques for LTL.

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

Pages (from-to) | 83-103 |

Number of pages | 21 |

Journal | Formal Methods in System Design |

Volume | 34 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2009 |

## Keywords

- Liveness
- Temporal logic
- Verification