Probably safe or live

Joost P. Katoen, Lei Song, Lijun Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

  • 7 Citations

Abstract

This paper presents a formal characterisation of safety and liveness properties for fully probabilistic systems. As for the classical setting, it is established that any (probabilistic tree) property is equivalent to a conjunction of a safety and liveness property. A simple algorithm is provided to obtain such a property decomposition for flat probabilistic CTL (PCTL). A safe fragment of PCTL is identified that provides a sound and complete characterisation of safety properties. For liveness properties, we provide two PCTL fragments, a sound and a complete one, and show that a sound and complete logical characterisation of liveness properties hinges on the (open) satisfiability problem for PCTL. We show that safety properties only have finite counterexamples, whereas liveness properties have none. We compare our characterisation for qualitative properties with the one for branching time properties by Manolios and Trefler, and present sound and complete PCTL fragments for characterising the notions of strong safety and absolute liveness coined by Sistla.
LanguageUndefined
Title of host publicationProceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
Place of PublicationNew York
PublisherAssociation for Computing Machinery
Pages55
Number of pages10
ISBN (Print)978-1-4503-2886-9
DOIs
StatePublished - Jul 2014
EventJoint Meeting of the 23rd EACSL Annual Conference on Computer Science Logic, CSL 2014 and the 29th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2014 - Vienna, Austria
Duration: 14 Jul 201418 Jul 2014

Publication series

Name
PublisherACM

Conference

ConferenceJoint Meeting of the 23rd EACSL Annual Conference on Computer Science Logic, CSL 2014 and the 29th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2014
Abbreviated titleCSL-LICS
CountryAustria
CityVienna
Period14/07/1418/07/14

Keywords

  • EWI-25693
  • IR-94428
  • METIS-309877

Cite this

Katoen, J. P., Song, L., & Zhang, L. (2014). Probably safe or live. In Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (pp. 55). New York: Association for Computing Machinery. DOI: 10.1145/2603088.2603147
Katoen, Joost P. ; Song, Lei ; Zhang, Lijun. / Probably safe or live. Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). New York : Association for Computing Machinery, 2014. pp. 55
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Katoen, JP, Song, L & Zhang, L 2014, Probably safe or live. in Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). Association for Computing Machinery, New York, pp. 55, Joint Meeting of the 23rd EACSL Annual Conference on Computer Science Logic, CSL 2014 and the 29th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2014, Vienna, Austria, 14/07/14. DOI: 10.1145/2603088.2603147

Probably safe or live. / Katoen, Joost P.; Song, Lei; Zhang, Lijun.

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). New York : Association for Computing Machinery, 2014. p. 55.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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T1 - Probably safe or live

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AU - Zhang,Lijun

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N2 - This paper presents a formal characterisation of safety and liveness properties for fully probabilistic systems. As for the classical setting, it is established that any (probabilistic tree) property is equivalent to a conjunction of a safety and liveness property. A simple algorithm is provided to obtain such a property decomposition for flat probabilistic CTL (PCTL). A safe fragment of PCTL is identified that provides a sound and complete characterisation of safety properties. For liveness properties, we provide two PCTL fragments, a sound and a complete one, and show that a sound and complete logical characterisation of liveness properties hinges on the (open) satisfiability problem for PCTL. We show that safety properties only have finite counterexamples, whereas liveness properties have none. We compare our characterisation for qualitative properties with the one for branching time properties by Manolios and Trefler, and present sound and complete PCTL fragments for characterising the notions of strong safety and absolute liveness coined by Sistla.

AB - This paper presents a formal characterisation of safety and liveness properties for fully probabilistic systems. As for the classical setting, it is established that any (probabilistic tree) property is equivalent to a conjunction of a safety and liveness property. A simple algorithm is provided to obtain such a property decomposition for flat probabilistic CTL (PCTL). A safe fragment of PCTL is identified that provides a sound and complete characterisation of safety properties. For liveness properties, we provide two PCTL fragments, a sound and a complete one, and show that a sound and complete logical characterisation of liveness properties hinges on the (open) satisfiability problem for PCTL. We show that safety properties only have finite counterexamples, whereas liveness properties have none. We compare our characterisation for qualitative properties with the one for branching time properties by Manolios and Trefler, and present sound and complete PCTL fragments for characterising the notions of strong safety and absolute liveness coined by Sistla.

KW - EWI-25693

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M3 - Conference contribution

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Katoen JP, Song L, Zhang L. Probably safe or live. In Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). New York: Association for Computing Machinery. 2014. p. 55. Available from, DOI: 10.1145/2603088.2603147