Reasoning about Threads with Bounded Lock Chains

The problem of model checking threads interacting purely via the standard synchronization primitives is key for many concurrent program analyses, particularly dataflow analysis. Unfortunately, it is undecidable even for the most commonly used synchronization primitive, i.e., mutex locks. Lock usage in concurrent programs can be characterized in terms of lock chains, where a sequence of mutex locks is said to be chained if the scopes of adjacent (non-nested) mutexes overlap. Although the model checking problem for fragments of Linear Temporal Logic (LTL) is known to be decidable for threads interacting via nested locks, i.e., chains of length one, these techniques don’t extend to programs with non-nested locks used in crucial applications like databases. We exploit the fact that lock usage patterns in real life programs do not produce unbounded lock chains. For such a framework, we show, by using the new concept of Lock Causality Automata (LCA), that

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-closures of regular sets of states can be computed efficiently. Leveraging this new technique then allows us to formulate decision procedures for model checking threads communicating via bounded lock chains for fragments of LTL. Our new results narrow the decidability gap for LTL model checking of threads communicating via locks by providing a more refined characterization for it in terms of boundedness of lock chains rather than the current state-of-the-art, i.e., nestedness of locks (chains of length one).