On the Strength of Owicki-Gries for Resources

In multithreaded programs data are often separated into lock- protected resources. Properties of those resources are typically verified by modular, Owicki-Gries-like methods. The modularity of the Owicki-Gries method has its price: proving some properties may require manual introduction of auxiliary variables. What properties can be proven without the burden of introducing auxiliary variables? We answer this question in the abstract interpretation framework. On one hand, we reveal a lattice structure of the method and supply a syntax-based abstract transformer that describes the method exactly. On the other hand, we bound the loss of precision from above and below by transition-relation-independent weakly relational closures. On infinitely many programs the closures coincide and describe the precision loss exactly; in general, the bounds are strict. We prove the absence of a general exact closure-based fixpoint characterization of the accuracy of the Owicki-Gries method, both in the collecting semantics and in certain trace semantics.