On-the-fly probabilistic model checking. Extended version. QUANTICOL Technical Report nr. TR-QC-09-2014

Model checking approaches can be divided into two broad categories: global approaches that determine the set of all states in a model M that satisfy a temporal logic formula Φ, and local approaches in which, given a state s in M, the procedure determines whether s satisfies Φ. When s is a term of a process language, the model-checking procedure can be executed "on-the-fly", driven by the syntactical structure of s. For certain classes of systems, e.g. those composed of many parallel components, the local approach is preferable because, depending on the specific property, it may be sufficient to generate and inspect only a relatively small part of the state space. We propose an efficient, on-the-fly, PCTL model checking procedure that is parametric with respect to the semantic interpretation of the language. The procedure comprises both bounded and unbounded until modalities. The correctness of the procedure is shown and its efficiency is explored on a number of benchmark applications in comparison with the global PCTL model checker PRISM.