Abstract
Atomic actions (or transactions) are useful for coping with concurrency and failures. One way of ensuring atomicity of actions is to implement applications in terms ofatomic data types: abstract data types whose objects ensure serializability and recoverability of actions using them. Many atomic types can be implemented to provide high levels of concurrency by taking advantage of algebraic properties of the type's operations, for example, that certain operations commute. In this paper we analyze the level of concurrency permitted by an atomic type. We introduce several local constraints on individual objects that suffice to ensure global atomicity of actions; we call these constraintslocal atomicity properties. We present three local atomicity properties, each of which isoptimal: no strictly weaker local constraint on objects suffices to ensure global atomicity for actions. Thus, the local atomicity properties define precise limits on the amount of concurrency that can be permitted by an atomic type.

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