Specification and Verification of Synchronization with Condition Variables.

In this paper we propose a technique to specify and verify the correct synchronization of concurrent programs with condition variables. We define correctness as the liveness property: “every thread synchronizing under a set of condition variables eventually exits the synchronization‿, under the assumption that every such thread eventually reaches its synchronization block. Our technique does not avoid the combinatorial explosion of interleavings of thread behaviors. In- stead, we alleviate it by abstracting away all details that are irrelevant to the synchronization behavior of the program, which is typically significantly smaller than its overall behavior. First, we introduce SyncTask, a simple imperative language to specify parallel computations that synchronize via condition vari- ables. We consider a SyncTask program to have a correct synchronization iff it terminates. Further, to relieve the programmer from the burden of providing specifications in SyncTask, we introduce an economic annotation scheme for Java programs to assist the automated extraction of SyncTask programs capturing the synchronization behavior of the underlying program. We prove that every Java program annotated according to the scheme (and satisfying the assumption) has a correct synchronization iff its corresponding SyncTask program terminates. We show how to transform the verification of termination into a standard reachabil- ity problem over Colored Petri Nets that is efficiently solvable by existing Petri Net analysis tools. Both the SyncTask program extraction and the generation of Petri Nets are implemented in our STaVe tool. We evaluate the proposed framework on a number of test cases as a proof-of-concept.