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Quiescent consistency is a notion of correctness for a concurrent object thatgives meaning to the object's behaviours in quiescent states, i.e., states inwhich none of the object's operations are being executed. Correctness of animplementation object is defined in terms of a corresponding abstractspecification. This gives rise to two important verification questions:membership (checking whether a behaviour of the implementation is allowed bythe specification) and correctness (checking whether all behaviours of theimplementation are allowed by the specification). In this paper, we show thatthe membership problem for quiescent consistency is NP-complete and that thecorrectness problem is decidable, but coNP-hard and in EXPSPACE. For bothproblems, we consider restricted versions of quiescent consistency by assumingan upper limit on the number of events between two quiescent points. Here, weshow that the membership problem is in PTIME, whereas correctness is in PSPACE.  Quiescent consistency does not guarantee sequential consistency, i.e., itallows operation calls by the same process to be reordered when mapping to anabstract specification. Therefore, we also consider quiescent sequentialconsistency, which strengthens quiescent consistency with an additionalsequential consistency condition. We show that the unrestricted versions ofmembership and correctness are NP-complete and undecidable, respectively. Whenby placing a limit on the number of events between two quiescent points,membership is in PTIME, while correctness is in PSPACE. Finally, we consider aversion of quiescent sequential consistency that places an upper limit on thenumber of processes for every run of the implementation, and show that themembership problem for quiescent sequential consistency with this restrictionis in PTIME.

Decidability and Complexity for Quiescent Consistency and its Variations