A Graph-Theoretic Model of Shared-Memory Legality

Legality is a key concept for the de nition of many shared-memory consistency conditions. As originally de ned, a sequence of operations on a given object is legal if it is in the set of valid sequences speci ed for that object. Because legality is de ned on totally ordered sets of operations, the actual derivation of algorithms and protocols to implement the consistency models that rely on some form of legality may tend to \exaggerate" the amount of synchronization that they eventually require. In this paper we introduce an alternative de nition for legality that is based on partially ordered sets of operations representing parallel executions on shared-memory multiprocessing systems. Using a graph-theoretic formalization, this novel de nition of legality is shown to be consonant with the one on totally ordered sets of operations.

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