Establishing Qualitative Properties for Probabilistic Lossy Channel Systems: An Algorithmic Approach
ARTS '99 Proceedings of the 5th International AMAST Workshop on Formal Methods for Real-Time and Probabilistic Systems
Model checking for a probabilistic branching time logic with fairness
Distributed Computing
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Specifications for probabilistic programs often use the notion of {\em almost always} and {\em definitely sometime} to capture the probabilistic information. But there are a number of instances (eg. network protocols) where probabilistic information needs to be explicitly specified. In this paper we present PCTL$^*$, a probabilistic version of the branching time logic CTL$^*$, where the quantifiers for universality (almost always) and existence (definitely sometime) are replaced by a single probabilistic quantifier. We argue that this logic is more general than previous logics. We show how to model-check probabilistic programs (given as markov chains) against specifications in PCTL$^*$. We also prove our algorithm correct and provide an analysis of its computational complexity.