The concept of legality is a crucial one for the definition of many shared-memory consistency conditions. As originally defined, a sequence of operations on a given object is legal if it is in the set of valid sequences specified for that object. Being thus defined on totally ordered sets of operations, the notion of legality is not fully realistic, because parallel executions on sharedmemory multiprocessing systems are best represented by partially ordered sets of operations. It is conceivable, therefore, that the eventual derivation of practical systems based on consistency models that rely on some form of legality will tend to be excessively heavy on the required synchronization. In this paper, we introduce an alternative definition of legality that is based on partially ordered sets of operations. Our treatment starts with a system model that makes very few assumptions on machine architecture, and proceeds to employ a graph-theoretic formalism to handle the normally troublesome issue of write multiplicity and to characterize legality. Using this same formalism, we argue that the novel definition of legality is consonant with the one on totally ordered sets of operations, so it carries the same intuitive appeal intended by the original definition
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.