From liveness to promptness

Orna Kupferman*, Nir Piterman, Moshe Y. Vardi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


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 languageAmerican English
Pages (from-to)83-103
Number of pages21
JournalFormal Methods in System Design
Issue number2
StatePublished - Apr 2009


  • Liveness
  • Temporal logic
  • Verification


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