Specification and verification of synchronization with condition variables

This paper proposes a technique to specify and verify the correct synchronization of concurrent programs with condition variables. We define correctness of synchronization as the liveness property: “every thread synchronizing under a set of condition variables eventually exits the synchronization block”, under the assumption that every such thread eventually reaches its synchronization block. Our technique does not avoid the combinatorial explosion of interleavings of thread behaviours. Instead, we alleviate it by abstracting away all details that are irrelevant to the synchronization behaviour of the program, which is typically significantly smaller than its overall behaviour. First, we introduce SyncTask, a simple imperative language to specify parallel computations that synchronize via condition variables. 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 behaviour of the underlying program. We show that every Java program annotated according to the scheme (and satisfying the assumption mentioned above) has a correct synchronization iff its corresponding SyncTask program terminates. We then show how to transform the verification of termination of the SyncTask program into a standard reachability problem over Coloured 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.