  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 f, and local approaches in which, given a state s in M,
the procedure determines whether s satisfies f. 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 compared with a global PCTL model checker on
representative applications.
