Decidability and Complexity for Quiescent Consistency

Abstract

Quiescent consistency is a notion of correctness for a concurrent object that gives meaning to the object's behaviours in quiescent states, i.e., states in which none of the object's operations are being executed. The condition enables greater flexibility in object design by allowing more behaviours to be admitted, which in turn allows the algorithms implementing quiescent consistent objects to be more efficient (when executed in a multithreaded environment).Quiescent consistency of an implementation object is defined in terms of a corresponding abstract specification. This gives rise to two important verification questions: membership (checking whether a behaviour of the implementation is allowed by the specification) and correctness (checking whether all behaviours of the implementation are allowed by the specification). In this paper, we consider the membership and correctness conditions for quiescent consistency, as well as a restricted form that assumes an upper limit on the number of events between two quiescent states. We show that the membership problem for unrestricted quiescent consistency is NP-complete and that the correctness problem is decidable, coNEXPTIME-hard, and in EXPSPACE. For the restricted form, we show that membership is in PTIME, while correctness is PSPACE-complete.

Bounded Reordering in the Distributed Test Architecture

“…Interestingly, the notion of observational equivalence (σ 1 ∼ σ 2 ) is very similar to sequential consistency, a correctness condition for concurrent objects [33]. A number of other correctness conditions have been defined for concurrent objects and there is a small amount of work that looks at the complexity of decision problems related to those we consider in this paper [1], [11]. There has also been some work that describes quantitative notions of correctness for concurrent objects and this uses a notion of the distance between two traces.…”