Synthesis of resource invariants for concurrent programs

Owicki and Gries have developed a proof system for conditional critical regions. In their system logically related variables accessed by more than one process are grouped together as resources, and processes are allowed access to a resource only in a critical region for that resource. Proofs of synchronization properties are constructed by devising predicates called resource invariants which describe relationships among the variables of a resource when no process is in a critical region for the resource. In constructing proofs using the system of Owicki and Gries, the programmer is required to supply the resource invariants.We show that convexity plays a key role in the derivation of strong resource invariants. We also develop methods for automatically synthesizing resource invariants. Specifically, we characterize the resource invariants of a concurrent program as least fixpoints of a functional which can be obtained from the text of the program. By using this fixpoint characterization and a widening operator which exploits our observation on the importance of convexity, good approximations may be obtained for the resource invariants of many concurrent programs.