Probably safe or live
In 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), CSL-LICS 2014
, pages 55, ACM
, 2014.Downloads: pdf, bibURL: http://doi.acm.org/10.1145/2603088.2603147
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 prop- erties. 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.