We investigate the algorithmic feasibility of checking whether concurrent implementations of shared-memory objects adhere to their given sequential specifications; sequential consistency, linearizability, and conflict serializability are the canonical variations of this problem. While verifying sequential consistency of systems with unbounded concurrency is known to be undecidable, we demonstrate that conflict serializability, and linearizability with fixed linearization points are EXPSPACE-complete, while the general linearizability problem is undecidable.
Our (un)decidability proofs, besides bestowing novel theoretical results, also reveal novel program explorations strategies. For instance, we show that every violation to conflict serializability is captured by a conflict cycle whose length is bounded independently from the number of concurrent operations. This suggests an incomplete detection algorithm which only remembers a small subset of conflict edges, which can be made complete by increasing the number of remembered edges to the cycle-length bound. Similarly, our undecidability proof for linearizability suggests an incomplete detection algorithm which limits the number of “barriers” bisecting non-overlapping operations. Our decidability proof of bounded-barrier linearizability is interesting on its own, as it reduces the consideration of all possible operation serializations to numerical constraint solving. The literature seems to confirm that most violations are detectable by considering very few conflict edges or barriers.