Completeness of the Owicki-Gries System for Parameterized Parallel Programs

The Owicki-Gries system is extended to allow the veri cation of parameterized programs of the form ki=1S(i; n) where for each n we obtain a parallel program consisting of n sequential processes. By the completeness of the original Owicki-Gries system, we know that for any valid speci cation of a parallel program with a xed number of components there exists a proof in the system. However, we would like to know if there exists a single proof that works for any number of components. In this paper we prove completeness of the extended system, thus giving a positive answer to the question.