Abstract
Two-thirds simulation provides a kind of abstract description of an implementation with respect to a specification. In order to characterize the approximate two-thirds simulation, we propose the definition of a two-thirds simulation index which expresses the degree to which a binary relation between processes is two-thirds simulation. ?-two-thirds simulation and its substitutivity laws are given in this paper. And, based on ?-two-thirds simulation, we present a measure model for describing the degree of approximation between processes. In particular, we give the modal logical characterization of ?-two-thirds simulation.
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